Christophe Geuzaine and Jean-François Remacle
Gmsh is an automatic 3D finite element mesh generator with build-in pre- and post-processing facilities. This is the Gmsh Reference Manual for Gmsh 2.6 (6 December 2012).
--- The Detailed Node Listing ---
Overview
How to read this reference manual?
Running Gmsh on your system
General tools
Expressions
Geometry module
Geometry commands
Mesh module
Mesh commands
Solver module
Post-processing module
File formats
Legacy formats
Tutorial
Options
Information for developers
Frequently asked questions
The source code and various pre-compiled versions of Gmsh (for Unix, Windows and Mac OS) can be downloaded from http://geuz.org/gmsh/. Gmsh is also directly available in pre-packaged form in various Linux and BSD distributions (Debian, Ubuntu, FreeBSD, ...).
If you use Gmsh, we would appreciate that you mention it in your work by citing the following paper: “C. Geuzaine and J.-F. Remacle, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, Volume 79, Issue 11, pages 1309-1331, 2009”. A preprint of that paper as well as other references and the latest news about Gmsh development are available on http://geuz.org/gmsh/.
Gmsh is “free software”; this means that everyone is free to use it and to redistribute it on a free basis. Gmsh is not in the public domain; it is copyrighted and there are restrictions on its distribution, but these restrictions are designed to permit everything that a good cooperating citizen would want to do. What is not allowed is to try to prevent others from further sharing any version of Gmsh that they might get from you.
Specifically, we want to make sure that you have the right to give away copies of Gmsh, that you receive source code or else can get it if you want it, that you can change Gmsh or use pieces of Gmsh in new free programs, and that you know you can do these things.
To make sure that everyone has such rights, we have to forbid you to deprive anyone else of these rights. For example, if you distribute copies of Gmsh, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must tell them their rights.
Also, for our own protection, we must make certain that everyone finds out that there is no warranty for Gmsh. If Gmsh is modified by someone else and passed on, we want their recipients to know that what they have is not what we distributed, so that any problems introduced by others will not reflect on our reputation.
The precise conditions of the license for Gmsh are found in the General Public License that accompanies the source code (see License). Further information about this license is available from the GNU Project webpage http://www.gnu.org/copyleft/gpl-faq.html. Detailed copyright information can be found in Copyright and credits.
If you want to integrate parts of Gmsh into a closed-source software, or want to sell a modified closed-source version of Gmsh, you will need to obtain a different license. Please contact us directly for more information.
Gmsh is a three-dimensional finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities.
Gmsh is built around four modules: geometry, mesh, solver and post-processing. All geometrical, mesh, solver and post-processing instructions are prescribed either interactively using the graphical user interface (GUI) or in text files using Gmsh's own scripting language. Interactive actions generate language bits in the input files, and vice versa. This makes it possible to automate all treatments, using loops, conditionals and external system calls. A brief description of the four modules is given hereafter.
Gmsh uses a boundary representation (“BRep”) to describe geometries. Models are created in a bottom-up flow by successively defining points, oriented lines (line segments, circles, ellipses, splines, ...), oriented surfaces (plane surfaces, ruled surfaces, triangulated surfaces, ...) and volumes. Groups of geometrical entities (called “physical groups”) can also be defined, based on these elementary geometric entities. Gmsh's scripting language allows all geometrical entities to be fully parametrized.
A finite element mesh is a tessellation of a given subset of the three-dimensional space by elementary geometrical elements of various shapes (in Gmsh's case: lines, triangles, quadrangles, tetrahedra, prisms, hexahedra and pyramids), arranged in such a way that if two of them intersect, they do so along a face, an edge or a node, and never otherwise. All the finite element meshes produced by Gmsh are considered as “unstructured”, even if they were generated in a “structured” way (e.g., by extrusion). This implies that the elementary geometrical elements are defined only by an ordered list of their nodes but that no predefined order relation is assumed between any two elements.
The mesh generation is performed in the same bottom-up flow as the geometry creation: lines are discretized first; the mesh of the lines is then used to mesh the surfaces; then the mesh of the surfaces is used to mesh the volumes. In this process, the mesh of an entity is only constrained by the mesh of its boundary. For example, in three dimensions, the triangles discretizing a surface will be forced to be faces of tetrahedra in the final 3D mesh only if the surface is part of the boundary of a volume; the line elements discretizing a curve will be forced to be edges of tetrahedra in the final 3D mesh only if the curve is part of the boundary of a surface, itself part of the boundary of a volume; a single node discretizing a point in the middle of a volume will be forced to be a vertex of one of the tetrahedra in the final 3D mesh only if this point is connected to a curve, itself part of the boundary of a surface, itself part of the boundary of a volume. This automatically assures the conformity of the mesh when, for example, two surfaces share a common line. But this also implies that the discretization of an “isolated” (n-1)-th dimensional entity inside an n-th dimensional entity does not constrain the n-th dimensional mesh—unless it is explicitly told to do so (see Miscellaneous mesh commands). Every meshing step is constrained by a “size field” (sometimes called “characteristic length field”), which prescribes the desired size of the elements in the mesh. This size field can be uniform, specified by values associated with points in the geometry, or defined by general “fields” (for example related to the distance to some boundary, to a arbitrary scalar field defined on another mesh, etc.).
For each meshing step, all structured mesh directives are executed first, and serve as additional constraints for the unstructured parts 1.
External solvers can be interfaced with Gmsh through Unix or TCP/IP sockets, which permits to modify solver parameters, launch external computations and process the results directly from within Gmsh's post-processing module. The default solver interfaced with Gmsh is GetDP (http://geuz.org/getdp/). Examples on how to interface other solvers are available in the source distribution (in the utils/solvers/ directory).
Gmsh can load and manipulate multiple post-processing scalar, vector or tensor maps along with the geometry and the mesh. Scalar fields are represented by iso-value lines/surfaces or color maps, while vector fields are represented by three-dimensional arrows or displacement maps. Post-processing functions include section computation, offset, elevation, boundary and component extraction, color map and range modification, animation, vector graphic output, etc. All the post-processing options can be accessed either interactively or through the input script files. Scripting permits to automate all post-processing operations, as for example to create animations. User-defined operations can also be performed on post-processing views through dynamically loadable plugins.
Here is a tentative list of what Gmsh does best:
As of version 2.6, here are some known weaknesses of Gmsh:
If you have the skills and some free time, feel free to join the project: we gladly accept any code contributions (see Information for developers) to remedy the aforementioned (and all other) shortcomings!
If you think you have found a bug in Gmsh, you can report it by email to the Gmsh mailing list at gmsh@geuz.org, or file it directly into our bug tracking database at https://geuz.org/trac/gmsh/report (login: gmsh, password: gmsh). Please send as precise a description of the problem as you can, including sample input files that produce the bug. Don't forget to mention both the version of Gmsh and the version of your operation system (see Command-line options to see how to get this information).
See Frequently asked questions, and the bug tracking system to see which problems we already know about.
Gmsh can be used at three levels:
You can skip most of this reference manual if you only want to use Gmsh at the first level (i.e., interactively with the GUI). Just read the next chapter (see Running Gmsh on your system) to learn how to launch Gmsh on your system, then go experiment with the GUI and the tutorial files (see Tutorial) provided in the distribution. Screencasts that show how to use the GUI are available here: http://geuz.org/gmsh/screencasts/.
The aim of the reference manual is to explain everything you need to use Gmsh at the second level, i.e., using the built-in scripting language. A Gmsh script file is an ASCII text file that contains instructions in Gmsh's built-in scripting language. Such a file is interpreted by Gmsh's parser, and can be given any extension (or no extension at all). By convention, Gmsh uses the .geo extension for geometry scripts, and the .pos extension for parsed post-processing datasets. Once you master the tutorial (read the source files: they are heavily commented!), start reading chapter General tools, then proceed with the next four chapters, which detail the syntax of the geometry, mesh, solver and post-processing scripting commands. You will see that most of the interactive actions in the GUI have a direct equivalent in the scripting language. If you want to use Gmsh as a pre- or post-processor for your own software, you will also want to learn about the non-scripting input/output files that Gmsh can read/write. In addition to Gmsh's native “MSH” file format (see File formats), Gmsh can read/write many standard mesh files, depending on how it was built: check the `File->Save As' menu for a list of available formats.
Finally, to use Gmsh at the third level (i.e., to link the Gmsh library with your own code), you will need to learn the internal Gmsh Application Programming Interface (API). No complete documentation of this API is available yet; a good starting point is Source code structure, which gives a short introduction to Gmsh's internal source code structure. Then have a look e.g. at the examples in the utils/api_demos/ directory in the source code. Due to the many possible configuration options (and associated external dependencies), we currently do not distibute precompiled versions of the Gmsh library. To build the library see the instructions in the top-level README.txt file in the source distribution.
Here are the rules we tried to follow when writing this reference manual. Note that metasyntactic variable definitions stay valid throughout the manual (and not only in the sections where the definitions appear).
this.
:) after a metasyntactic variable separates the variable
from its definition.
< > pairs.
|.
To launch Gmsh in interactive mode, just double-click on the Gmsh icon, or type
> gmsh
at your shell prompt in a terminal. This will open two windows: the graphic window (with a status bar at the bottom) and the menu window (with a menu bar and some context-dependent buttons).
To open the first tutorial file (see Tutorial), select the `File->Open' menu, and choose t1.geo in the input field. When using a terminal, you can specify the file name directly on the command line, i.e.:
> gmsh t1.geo
To perform the mesh generation, go to the mesh module (by selecting `Mesh' in the module menu) and choose the dimension in the context-dependent buttons (`1D' will mesh all the lines; `2D' will mesh all the surfaces—as well as all the lines if `1D' was not called before; `3D' will mesh all the volumes—and all the surfaces if `2D' was not called before). To save the resulting mesh in the current mesh format click on the `Save' button, or select the appropriate format and file name with the `File->Save As' menu. The default mesh file name is based on the name of the current active model, with an appended extension depending on the mesh format2.
To create a new geometry or to modify an existing geometry, select 'Geometry' in the module menu, and follow the context-dependent buttons. For example, to create a spline, select `Elementary', `Add', `New' and `Spline'. You will then be asked to select a list of points, and to type e to finish the selection (or q to abort it). Once the interactive command is completed, a text string is automatically added at the end of the current script file. You can edit the script file by hand at any time by pressing the `Edit' button in the `Geometry' menu and then reloading the model by pressing `Reload'. For example, it is often faster to define variables and points directly in the script file, and then use the GUI to define the lines, the surfaces and the volumes interactively.
Several files can be loaded simultaneously in Gmsh. The first one defines the active model and the others are `merged' into this model. You can merge such files with the `File->Merge' menu, or by directly specifying the names of the files on the command line. For example, to merge the post-processing views contained in the files view1.pos and view5.msh together with the geometry of the first tutorial t1.geo, you can type the following command:
> gmsh t1.geo view1.pos view5.msh
In the Post-Processing module (select `Post-Processing' in the module menu), three buttons will appear, respectively labeled `A scalar map', `Nodal scalar map' and `Element 1 vector'. In this example the views contain several time steps: you can loop through them with the small “remote-control” icons at the bottom of the graphic window. A mouse click on the view name will toggle the visibility of the selected view, while a click on the arrow button on the right will provide access to the view's options.
Note that all the options specified interactively can also be directly specified in the script files. You can save the current options of the current active model with the `File->Save Options' menu. This will create a new option file with the same filename as the active model, but with an extra .opt extension added. The next time you open this model, the associated options will be automatically loaded, too. To save the current options as your default preferences for all future Gmsh sessions, use the `File->Save Default Options' menu instead. Finally, you can also save the current options in an arbitrary file by choosing the `Gmsh options' format in `File->Save As'.
For more information about available options (and how to reset them to their default values), see Options.
Gmsh can be run non-interactively in `batch' mode, without GUI3. For example, to mesh the first tutorial in batch mode, just type:
> gmsh t1.geo -2
To mesh the same example, but with the background mesh available in the file bgmesh.pos, type:
> gmsh t1.geo -2 -bgm bgmesh.pos
For the list of all command-line options, see Command-line options.
-0-tol floatMesh options:
-1, -2, -3-refine-part int-saveall-o file-format string-bin-algo string-smooth int-optimize[_netgen]-order int-clscale float-clmin float-clmax float-clcurv-rand float-bgm file-check filePost-processing options:
-link int-combineDisplay options:
-n-nodb-fontsize int-theme string-display stringOther options:
--a, -g, -m, -s, -p-pid-listen-watch-v int-nopopup-string "string"-option file-convert files-version-info-helpIn the following, for a 2 button mouse, Middle button = Shift+Left button. For a 1 button mouse, Middle button = Shift+Left button and Right button = Alt+Left button.
Move the mouse:
Left button:
Ctrl+Left button: Start a lasso zoom or a lasso selection/unselection
Middle button:
Ctrl+Middle button: Orthogonalize display
Right button:
Ctrl+Right button: Reset to default viewpoint
(On Mac Ctrl is replaced by Cmd (the `Apple key') in the shortcuts below.)
This chapter describes the general commands and options that can be used in Gmsh's script files. By “general”, we mean “not specifically related to one of the geometry, mesh, solver or post-processing modules”. Commands peculiar to these modules will be introduced in Geometry module, Mesh module, Solver module, and Post-processing module, respectively.
Gmsh script files support both C and C++ style comments:
/* and */ pairs is ignored;
// is ignored.
These commands won't have the described effects inside double quotes or inside keywords. Also note that `white space' (spaces, tabs, new line characters) is ignored inside all expressions.
The two constant types used in Gmsh scripts are real and string (there is no integer type). These types have the same meaning and syntax as in the C or C++ programming languages.
Floating point expressions (or, more simply, “expressions”) are denoted by the metasyntactic variable expression (remember the definition of the syntactic rules in Syntactic rules), and are evaluated during the parsing of the script file:
expression:
real |
string |
string [ expression ] |
# string [ ] |
( expression ) |
operator-unary-left expression |
expression operator-unary-right |
expression operator-binary expression |
expression operator-ternary-left expression operator-ternary-right expression |
built-in-function |
real-option |
StrFind(char-expression, char-expression) |
GetValue("string", expression)
Such expressions are used in most of Gmsh's scripting
commands. The third and fourth cases in this definition permit to
extract one item from a list (see below) and get the size of a list,
respectively. The operators operator-unary-left,
operator-unary-right, operator-binary,
operator-ternary-left and operator-ternary-right are defined
in Operators. For the definition of built-in-functions,
see Built-in functions. The various real-options are
listed in Options. StrFind searches the first
char-expression for any occurrence of the second
char-expression.
The last case in the definition allows to ask the user for a value
interactively. For example, inserting GetValue("Value of parameter
alpha?", 5.76) in an input file will query the user for the value of a
certain parameter alpha, assuming the default value is 5.76. If the
option General.NoPopup is set (see General options list), no
question is asked and the default value is automatically used.
List of expressions are also widely used, and are defined as:
expression-list:
expression-list-item <, expression-list-item> ...
with
expression-list-item:
expression |
expression : expression |
expression : expression : expression |
string [ ] |
List [ string ] |
string [ { expression-list } ] |
Point { expression } |
transform |
extrude
Point { expression } |
Point|Line|Surface|Volume "*" |
Physical Point|Line|Surface|Volume { expression-list }
The second case in this last definition permits to create a list containing the range of numbers comprised between two expressions, with a unit incrementation step. The third case also permits to create a list containing the range of numbers comprised between two expressions, but with a positive or negative incrementation step equal to the third expression. The fourth and fifth cases permit to reference an expression list. The sixth case permits to reference an expression sublist (whose elements are those corresponding to the indices provided by the expression-list). The next two cases permit to retrieve the indices of entities created through geometrical transformations and extrusions (see Transformations, and Extrusions). The last three cases permit to retrieve the coordinates of a given geometry point (see Points), to retrieve the id numbers of all points, lines, surfaces or volumes in the model, or to retrieve the elementary entities making up physical groups.
To see the practical use of such expressions, have a look at the first
couple of examples in Tutorial. Note that, in order to lighten the
syntax, you can always omit the braces {} enclosing an
expression-list if this expression-list only contains a single
item. Also note that a braced expression-list can be preceded by a
minus sign in order to change the sign of all the
expression-list-items.
Character expressions are defined as:
char-expression:
"string" |
Today |
StrPrefix ( char-expression ) |
StrRelative ( char-expression ) |
StrCat ( char-expression , char-expression ) |
Sprintf ( char-expression , expression-list ) |
Sprintf ( char-expression ) |
Sprintf ( char-option ) |
GetEnv ( char-expression ) |
GetString ( char-expression , char-expression )
The third and fourth cases in this definition permit to take the
prefix (e.g. to remove the extension) or the relative path of a
string. The fifth case permits to concatenate two character expressions,
and the sixth and seventh are equivalent to the sprintf C
function (where char-expression is a format string that can
contain floating point formatting characters: %e, %g,
etc.). The eigth case permits to use the value of a char-option as
a char-expression. The ninth case gets the value of an environment
variable from the operating system. The last case in the definition
allows one to ask the user for a value interactively. The various
char-options are listed in Options.
Character expressions are mostly used to specify non-numeric options and input/output file names. See t8.geo, for an interesting usage of char-expressions in an animation script.
Colors expressions are hybrids between fixed-length braced expression-lists and strings:
color-expression:
string |
{ expression, expression, expression } |
{ expression, expression, expression, expression } |
color-option
The first case permits to use the X Windows names to refer to colors,
e.g., Red, SpringGreen, LavenderBlush3, ...
(see Common/Colors.h in the source code for a complete list). The
second case permits to define colors by using three expressions to
specify their red, green and blue components (with values comprised
between 0 and 255). The third case permits to define colors by using
their red, green and blue color components as well as their alpha
channel. The last case permits to use the value of a color-option
as a color-expression. The various color-options are
listed in Options.
See t3.geo, for an example of the use of color expressions.
Gmsh's operators are similar to the corresponding operators in C and C++. Here is the list of the unary, binary and ternary operators currently implemented.
operator-unary-left:
-!operator-unary-right:
++--operator-binary:
^*/%+-==!=>>=<<=&&|||| is evaluated even if the first one is true).
operator-ternary-left:
?:
The evaluation priorities are summarized below4 (from stronger to
weaker, i.e., * has a highest evaluation priority than +).
Parentheses () may be used anywhere to change the order of
evaluation:
(), [], ., #
^
!, ++, --, - (unary)
*, /, %
+, -
<, >, <=, >=
==, !=
&&
||
?:
=, +=, -=, *=, /=
A built-in function is composed of an identifier followed by a pair of parentheses containing an expression-list (the list of its arguments)5. Here is the list of the built-in functions currently implemented:
build-in-function:
Acos ( expression )Asin ( expression )Atan ( expression )Atan2 ( expression, expression )Ceil ( expression )Cos ( expression )Cosh ( expression )Exp ( expression )Fabs ( expression )Fmod ( expression, expression )Floor ( expression )Hypot ( expression, expression )Log ( expression )Log10 ( expression )Modulo ( expression, expression )Fmod( expression, expression ).
Rand ( expression )Sqrt ( expression )Sin ( expression )Sinh ( expression )Tan ( expression )Tanh ( expression )
User-defined functions take no arguments, and are evaluated as if a file
containing the function body was included at the location of the Call
statement.
Function stringFunction
string', and can contain any Gmsh command.
ReturnCall string;See t5.geo, for an example of a user-defined function. A shortcoming of Gmsh's scripting language is that all variables are “public”. Variables defined inside the body of a function will thus be available outside, too!
Loops and conditionals are defined as follows, and can be imbricated:
For ( expression : expression )For ( expression :
expression )' and the matching EndFor are executed.
For ( expression : expression : expression )For ( expression : expression :
expression )' and the matching EndFor are executed.
For string In { expression : expression }For string In {
expression : expression }' and the matching EndFor are
executed.
For string In { expression : expression : expression }For string In { expression :
expression : expression }' and the matching EndFor are
executed.
EndForFor command.
If ( expression )If ( expression )' and the matching
Endif is evaluated if expression is non-zero.
EndIfIf command.
See t5.geo, for an example of For and If commands. Gmsh
does not provide any Else (or similar) command at the time of this
writing.
The following commands can be used anywhere in a Gmsh script:
= expression;PiGMSH_MAJOR_VERSIONGMSH_MINOR_VERSIONGMSH_PATCH_VERSIONMPI_SizeMPI_Ranknewpnewp permits to know the highest number already attributed (plus
one). This is mostly useful when writing user-defined functions
(see User-defined functions) or general geometric primitives, when one
does not know a priori which numbers are already attributed, and
which ones are still available.
newlnewsnewvnewllnewslnewregnewreg returns
the maximum of newp, newl, news, newv,
newll, newsl and all physical entity numbers6.
= { }; = { expression-list };[] = { expression-list };
[ { expression-list } ] = { expression-list }; += expression; -= expression; *= expression; /= expression; += { expression-list }; -= { expression-list }; [ { expression-list } ] += { expression-list }; [ { expression-list } ] -= { expression-list }; [ { expression-list } ] *= { expression-list }; [ { expression-list } ] /= { expression-list }; = char-expression; = expression; = char-expression; = color-expression; += expression; -= expression; *= expression; /= expression;Abort;Exit;Printf ( char-expression <, expression-list> );Printf is equivalent to the printf C function:
char-expression is a format string that can contain formatting
characters (%f, %e, etc.). Note that all expressions
are evaluated as floating point values in Gmsh (see Expressions), so
that only valid floating point formatting characters make sense in
char-expression. See t5.geo, for an example of the use of
Printf.
Printf ( char-expression , expression-list ) > char-expression;Printf above, but output the expression in a file.
Printf ( char-expression , expression-list ) >> char-expression;Printf above, but appends the expression at the end of
the file.
Error ( char-expression <, expression-list> );Printf, but raises an error.
Merge char-expression;Draw;BoundingBox;BoundingBox { expression, expression, expression, expression, expression, expression };Delete Model;Delete Physicals;Delete Variables;Delete Options;Delete string;Mesh expression;RefineMesh;Mesh.SecondOrderLinear is set, the new vertices are inserted by
linear interpolatinon. Otherwise they are snapped on the actual
geometry.
Print char-expression;Print.Format (see General options list). If the
path in char-expression is not absolute, char-expression is
appended to the path of the current file.
Sleep expression;SystemCall char-expression;NonBlockingSystemCall char-expression;SetName char-expression;SyncModel;Include char-expression;The list of all the general char-options, real-options and color-options (in that order—check the default values to see the actual types) is given in General options list. Most of these options are accessible in the GUI, but not all of them. When running Gmsh interactively, changing an option in the script file will modify the option in the GUI in real time. This permits for example to resize the graphical window in a script, or to interact with animations in the script and in the GUI at the same time.
Gmsh's geometry module provides a simple CAD engine, using a boundary
representation (“BRep”) approach: you need to first define points
(using the Point command: see below), then lines (using
Line, Circle, Spline, ..., commands or by
extruding points), then surfaces (using for example the Plane
Surface or Ruled Surface commands, or by extruding lines), and
finally volumes (using the Volume command or by extruding
surfaces).
These geometrical entities are called “elementary” in Gmsh's jargon, and are assigned identification numbers when they are created:
Elementary geometrical entities can then be manipulated in various
ways, for example using the Translate, Rotate,
Scale or Symmetry commands. They can be deleted with the
Delete command, provided that no higher-dimension entity
references them.
Groups of elementary geometrical entities can also be defined and are called “physical” entities. These physical entities cannot be modified by geometry commands: their only purpose is to assemble elementary entities into larger groups, possibly modifying their orientation, so that they can be referred to by the mesh module as single entities. As is the case with elementary entities, each physical point, physical line, physical surface or physical volume must be assigned a unique identification number. See Mesh module, for more information about how physical entities affect the way meshes are saved.
The next subsections describe all the available geometry commands. These commands can be used anywhere in a Gmsh script file. Note that the following general syntax rule is followed for the definition of geometrical entities: “If an expression defines a new entity, it is enclosed between parentheses. If an expression refers to a previously defined entity, it is enclosed between braces.”
Point ( expression ) = { expression, expression, expression <, expression > };Physical Point ( expression | char-expression ) = { expression-list };BSpline ( expression ) = { expression-list };Circle ( expression ) = { expression, expression, expression };CatmullRom ( expression ) = { expression-list };CatmullRom is a synonym for Spline.
Ellipse ( expression ) = { expression, expression, expression, expression };Line ( expression ) = { expression, expression };Spline ( expression ) = { expression-list };Line Loop ( expression ) = { expression-list };Line Loop command. (Line loops are used to
create surfaces: see Surfaces.)
Compound Line ( expression ) = { expression-list };Compound Surface for additional information on compound
entities.
Physical Line ( expression | char-expression ) = { expression-list };Plane Surface ( expression ) = { expression-list };Ruled Surface ( expression ) = { expression-list } < In Sphere { expression } >;In Sphere argument forces the
surface to be a spherical patch (the extra parameter gives the
identification number of the center of the sphere).
Surface Loop ( expression ) = { expression-list };Compound Surface ( expression ) = { expression-list } < Boundary { { expression-list }, { expression-list }, { expression-list }, { expression-list } } > ;Physical Surface ( expression | char-expression ) = { expression-list };Volume ( expression ) = { expression-list };Compound Volume ( expression ) = { expression-list };Compound Surface for additional information on
compound entities.
Physical Volume ( expression | char-expression ) = { expression-list };Lines, surfaces and volumes can also be created through extrusion of points, lines and surfaces, respectively. Here is the syntax of the geometrical extrusion commands (go to Structured grids, to see how these commands can be extended in order to also extrude the mesh):
extrude:
Extrude { expression-list } { extrude-list }Extrude { { expression-list }, { expression-list }, expression } { extrude-list }Extrude { { expression-list }, { expression-list }, { expression-list }, expression } { extrude-list }with
extrude-list:
Point | Line | Surface { expression-list }; ...
As explained in Floating point expressions, extrude can be used in an expression, in which case it returns a list of identification numbers. By default, the list contains the “top” of the extruded entity at index 0 and the extruded entity at index 1, followed by the “sides” of the extruded entity at indices 2, 3, etc. For example:
Point(1) = {0,0,0};
Point(2) = {1,0,0};
Line(1) = {1, 2};
out[] = Extrude{0,1,0}{ Line{1}; };
Printf("top line = %g", out[0]);
Printf("surface = %g", out[1]);
Printf("side lines = %g and %g", out[2], out[3]);
This behaviour can be changed with the
Geometry.ExtrudeReturnLateralEntities option (see Geometry options list).
Geometrical transformations can be applied to elementary entities, or to
copies of elementary entities (using the Duplicata command: see
below). The syntax of the transformation commands is:
transform:
Dilate { { expression-list }, expression } { transform-list }Rotate { { expression-list }, { expression-list }, expression } { transform-list }Symmetry { expression-list } { transform-list }Translate { expression-list } { transform-list }Boundary { transform-list }CombinedBoundary { transform-list }with
transform-list:
Point | Line | Surface | Volume { expression-list }; ... |
Duplicata { Point | Line | Surface | Volume { expression-list }; ... } |
transform
Here is a list of all other geometry commands currently available:
Coherence;Coherence command automatically after each geometrical
transformation, unless Geometry.AutoCoherence is set to zero
(see Geometry options list).
Delete { Point | Line | Surface | Volume { expression-list }; ... }Delete has no effect (the line will have to be deleted before the
point can).
Hide { Point | Line | Surface | Volume { expression-list }; ... }General.VisibilityMode is set to 0 or 1.
Hide char-expression;General.VisibilityMode is
set to 0 or 1 (char-expression can for example be
"*").
Show { Point | Line | Surface | Volume { expression-list }; ... }General.VisibilityMode is set to 0 or 1.
Show char-expression;General.VisibilityMode is
set to 0 or 1 (char-expression can for example be
"*").
The list of all the options that control the behavior of geometry commands, as well as the way geometrical entities are handled in the GUI, is give in Geometry options list.
Gmsh's mesh module regroups several 1D, 2D and 3D meshing algorithms, all producing grids conforming in the sense of finite elements (see Mesh):
Recombine Surface is used: see
Miscellaneous mesh commands). The 3D unstructured
algorithms generate tetrahedra.
Recombine commands (see Structured grids, and
Miscellaneous mesh commands). The 3D structured algorithms
generate tetrahedra, hexahedra, prisms and pyramids, depending on the
type of the surface meshes they are based on.
All meshes can be subdivided to generate fully quadrangular or fully
hexahedral meshes with the Mesh.SubdivisionAlgorihm option
(see Mesh options list). However, beware that the quality of
subdivided elements initially generated with an unstructured
algorithm can be quite poor.
Gmsh currently provides a choice between three 2D unstructured algorithms and between two 3D unstructured algorithms. Each algorithm has its own advantages and disadvantages.
For all 2D unstructured algorithms a Delaunay mesh that contains all the points of the 1D mesh is initially constructed using a divide-and-conquer algorithm7. Missing edges are recovered using edge swaps8. After this initial step three different algorithms can be applied to generate the final mesh:
These algorithms can be ranked as follows:
Robustness Performance Element quality
MeshAdapt 1 3 2
Delaunay 2 1 2
Frontal 3 2 1
For very complex curved surfaces the “MeshAdapt” algorithm is the best choice. When high element quality is important, the “Frontal” algorithm should be tried. For very large meshes of plane surfaces the “Delaunay” algorithm is the fastest.
The “Automatic” algorithm tries to select the best algorithm automatically for each surface in the model. As of Gmsh 2.6, the “Automatic” algorithm selects “Delaunay” for plane surfaces and “MeshAdapt” for all other surfaces.
In 3D two unstructured algorithms are available:
The “Delaunay” algorithm is the most robust and the fastest, and is
the only one that supports the Field mechanism to specify element
sizes (see Specifying mesh element sizes). However, this algorithm
will sometimes modify the surface mesh, and is thus not suitable for
producing hybrid structured/unstructured grids. In that case the
“Frontal” algorithm should be preferred. The quality of the elements
produced by both algorithms is comparable. If element quality is
important the mesh optimizer(s) should be applied.
If only elementary geometrical entities are defined (or if the
Mesh.SaveAll option is set; see Mesh options list), the
grid produced by the mesh module will be saved “as is”. That is, all
the elements in the grid will be saved using the identification number
of the elementary entities they discretize as their elementary region
number (and 0 as their physical region number14; File formats). This can sometimes be
inconvenient:
To remedy these problems, the geometry module (see Geometry module) introduces the notion of “physical” entities (also called “physical groups”). The purpose of physical entities is to assemble elementary entities into larger, possibly overlapping groups, and to control the orientation of the elements in these groups. The introduction of physical entities in large models usually greatly facilitates the manipulation of the model (e.g., using `Tools->Visibility' in the GUI) and the interfacing with external solvers.
In the MSH file format (see File formats), if physical entities are defined, the output mesh only contains those elements that belong to physical entities. Other file formats each treat physical entities in slightly different ways, depending on their capability to define groups.
In all cases, Gmsh reindexes the mesh vertices and elements so that they are numbered in a continuous sequence in the output files. Note that the numbers displayed on screen after mesh generation thus usually differ from the ones saved in the mesh files. To check the actual numbers saved in the output file just load the file back using `File->Open'.
The mesh module commands mostly permit to modify the mesh element sizes and specify structured grid parameters. The actual mesh “actions” (i.e., “mesh the lines”, “mesh the surfaces” and “mesh the volumes”) cannot be specified in the script files. They have to be given either in the GUI or on the command line (see Running Gmsh on your system, and Command-line options).
There are three ways to specify the size of the mesh elements for a given geometry:
Mesh.CharacteristicLengthFromPoints is set (it is by
default), you can simply specify desired mesh element sizes at the
geometrical points of the model (with the Point command: see
Points). The size of the mesh elements will then be computed by
linearly interpolating these values on the initial mesh (see
Mesh). This might sometimes lead to over-refinement in some areas,
so that you may have to add “dummy” geometrical entities in the model
in order to get the desired element sizes.
This method works with all the algorithms implemented in the mesh module. The final element sizes are of course constrained by the structured algorithms for which the element sizes are explicitly specified (e.g., transfinite and extruded grids: see Structured grids).
Mesh.CharacteristicLengthFromCurvature is set (it is
not by default), the mesh will be adapted with respect to the curvature
of the geometrical entities. Warning: as of Gmsh 2.6 this feature is
still (very) experimental.
PostView field specifies an explicit background mesh in the
form of a scalar post-processing view (see Post-processing commands, and File formats) in which the nodal values are the
target element sizes. This method is very general but it requires a
first (usually rough) mesh and a way to compute the target sizes on this
mesh (usually through an error estimation procedure, in an iterative
process of mesh adaptation). Warning: only parsed (.pos) files
can currently be used as background meshes (.msh files cannot be
used, since the mesh used to define the field will be destroyed during
the meshing process).
(Note that you can also load a background mesh directly from the command
line using the -bgm option (see Command-line options), or in
the GUI by selecting `Apply as background mesh' in the post-processing
view option menu.)
Box field specifies the size of the elements inside and outside
of a parallelipipedic region.
Threshold field specifies the size of the mesh according to the
distance to some geometrical entities. These entities can for example be
geometry points and lines specified by an Attractor field.
MathEval field specifies the size of the mesh using an explicit
mathematical function.
Min field specifies the size as the minimum of the sizes
computed using other fields
Fields are supported by all the algorithms except those based on Netgen. The list of available fields with their options is given below.
The three aforementioned methods can be used simultaneously, in which case the smallest element size is selected at any given point.
All element sizes are further constrained by the
Mesh.CharacteristicLengthMin, Mesh.CharacteristicLengthMax
and Mesh.CharacteristicLengthFactor options (see Mesh options list)
Here are the mesh commands that are related to the specification of mesh element sizes:
Characteristic Length { expression-list } = expression;Field[expression] = string;Field[expression].string = char-expression | expression | expression-list;Background Field = expression;Min or Max field (see below).
Here is the list of all available fields with their associated options:
AttractorEdgesList{}
FacesList{}
FieldX-1
FieldY-1
FieldZ-1
NNodesByEdge20
NodesList{}
AttractorAnisoCurveEdgesList{}
NNodesByEdge20
dMax0.5
dMin0.1
lMaxNormal0.5
lMaxTangent0.5
lMinNormal0.05
lMinTangent0.5
BoundaryLayerAnisoMax10000000000
EdgesList{}
FacesList{}
IntersectMetrics0
NodesList{}
Quads0
fan_angle30
hfar1
hwall_n0.1
hwall_t0.5
ratio1.1
thickness0.01
BoxVIn0
VOut0
XMax0
XMin0
YMax0
YMin0
ZMax0
ZMin0
CenterlineFileName"centerlines.vtk"
closeVolume0
extrudeWall0
hLayer0.3
nbElemLayer3
nbPoints25
reMesh0
Actions:
runCurvatureDelta0
IField1
CylinderRadius0
VIn0
VOut0
XAxis0
XCenter0
YAxis0
YCenter0
ZAxis1
ZCenter0
FrustumR1_inner0
R1_outer1
R2_inner0
R2_outer1
V1_inner0.1
V1_outer1
V2_inner0.1
V2_outer1
X10
X20
Y10
Y20
Z11
Z25.98152627002258e-154
GradientDelta0
IField1
Kind0
LaplacianDelta0.1
IField1
LonLatFromStereo0
IField1
RadiusStereo6371000
MathEvalF"F2 + Sin(z)"
Actions:
testMathEvalAnisom11"F2 + Sin(z)"
m12"F2 + Sin(z)"
m13"F2 + Sin(z)"
m22"F2 + Sin(z)"
m23"F2 + Sin(z)"
m33"F2 + Sin(z)"
MaxFieldsList{}
MaxEigenHessianDelta0
IField1
MeanDelta0.0001
IField0
MinFieldsList{}
MinAnisoFieldsList{}
ParamFX""
FY""
FZ""
IField1
PostViewCropNegativeValues1
IView0
RestrictEdgesList{}
FacesList{}
IField1
RegionsList{}
StructuredFileName""
TextFormat0
ThresholdDistMax10
DistMin1
IField0
LcMax1
LcMin0.1
Sigmoid0
StopAtDistMax0
UTMIField1
Zone0
Extrude { expression-list } { extrude-list layers } layers:
Layers { expression } |
Layers { { expression-list }, { expression-list } } |
Recombine; ...
In the first Layers form, expression gives the number of
elements to be created in the (single) layer. In the second form, the
first expression-list defines how many elements should be created
in each extruded layer, and the second expression-list gives the
normalized height of each layer (the list should contain a sequence of
n numbers 0 < h1 < h2 < ... < hn <= 1). See
t3.geo, for an example.
For line extrusions, the Recombine option will recombine triangles
into quadrangles when possible. For surface extrusions, the
Recombine option will recombine tetrahedra into prisms, hexahedra or
pyramids.
Please note that, starting with Gmsh 2.0, region numbers cannot be
specified explicitly anymore in Layers commands. Instead, as with
all other geometry commands, you must use the automatically created
entity identifier created by the extrusion command. For example, the
following extrusion command will return the id of the new “top”
surface in num[0] and the id of the new volume in num[1]:
num[] = Extrude {0,0,1} { Surface{1}; Layers{10}; };
Extrude { { expression-list }, { expression-list }, expression } { extrude-list layers }Extrude { { expression-list }, { expression-list }, { expression-list }, expression } { extrude-list layers }Extrude { Surface { expression-list }; layers < Using Index[expr]; > < Using View[expr]; > }Transfinite Line { expression-list } | "*" = expression < Using Progression | Bump expression >;Using Progression
expression' instructs the transfinite algorithm to distribute the
nodes following a geometric progression (Progression 2 meaning
for example that each line element in the series will be twice as long
as the preceding one). The optional argument `Using Bump
expression' instructs the transfinite algorithm to distribute the
nodes with a refinement at both ends of the line.
Transfinite Surface { expression-list } | "*" < = { expression-list } > < Left | Right | Alternate > ;Transfinite Volume { expression-list } | "*" < = { expression-list } > ;Here is a list of all other mesh commands currently available:
Point | Line { expression-list } In Surface { expression };Periodic Line { expression-list } = { expression-list };Periodic Surface expression { expression-list } = expression { expression-list };Coherence Mesh;Color color-expression { Point | Line | Surface | Volume { expression-list }; ... }Hide { Point | Line | Surface | Volume { expression-list }; ... }General.VisibilityMode is set to 0 or 2.
Hide char-expression;General.VisibilityMode is set to 0 or 2
(char-expression can for example be "*").
Recombine Surface { expression-list } | "*" < = expression >;Save char-expression;Mesh.Format (see Mesh options list). If the path in
char-expression is not absolute, char-expression is appended
to the path of the current file.
Show { Point | Line | Surface | Volume { expression-list }; ... }General.VisibilityMode is set to 0 or 2.
Show char-expression;General.VisibilityMode is set to 0 or 2
(char-expression can for example be "*").
Smoother Surface { expression-list } = expression;Homology ( { expression-list } ) { { expression-list } , { expression-list } };Cohomology ( { expression-list } ) { { expression-list } , { expression-list } };Homology, but computes a basis representation
for cohomology spaces instead.
The list of all the options that control the behavior of mesh commands, as well as the way meshes are displayed in the GUI, is given in Mesh options list.
External solvers can be driven by Gmsh through the ONELAB
http://www.onelab.info interface. To add a new solver in the
solver module, you need to specify its name (Solver.Name0,
Solver.Name1, etc.) and the path to the executable
(Solver.Executable0, Solver.Executable1, etc.); see
Solver options list).
The client-server API for the solver interface is defined in the onelab.h header. See utils/solvers/c++/solver.cpp for a simple example on how to use the ONELAB programming interface. See the sources of GetDP (http://geuz.org/getdp for a more comprehensive example.
The list of all the solver options is given in Solver options list.
Gmsh's post-processing module can handle multiple scalar, vector or tensor datasets along with the geometry and the mesh. The datasets can be given in several formats: in human-readable “parsed” format (these are just part of a standard input script, but are usually put in separate files with a .pos extension), in native MSH files (ASCII or binary files with .msh extensions: see File formats), or in standard third-party formats (like MED: http://www.code-aster.org/outils/med/).
Once loaded into Gmsh, scalar fields can be displayed as iso-value lines
and surfaces or color maps, whereas vector fields can be represented
either by three-dimensional arrows or by displacement maps. (Tensor
fields are currently displayed as Von-Mises effective stresses, min/max
eigenvalues, eigenvectors, ellipsis or ellipsoid. To display other
(combinations of) components, you can use the Force scalar or
Force vector options, or use Plugin(MathEval): see
Post-processing plugins.)
In Gmsh's jargon, each dataset is called a “view”. Each view is given
a name, and can be manipulated either individually (each view has its
own button in the GUI and can be referred to by its index in a script)
or globally (see the PostProcessing.Link option in
Post-processing options list).
By default, Gmsh treats all post-processing views as three-dimensional plots, i.e., draws the scalar, vector and tensor primitives (points, lines, triangles, tetrahedra, etc.) in 3D space. But Gmsh can also represent each post-processing view containing scalar points as two-dimensional (“X-Y”) plots, either space- or time-oriented:
Although visualization is usually mostly an interactive task, Gmsh exposes all the post-processing commands and options to the user in its scripting language to permit a complete automation of the post-processing process (see e.g., t8.geo, and t9.geo).
The two following sections summarize all available post-processing commands and options. Most options apply to both 2D and 3D plots (colormaps, point/line sizes, interval types, time step selection, etc.), but some are peculiar to 3D (lightning, element selection, etc.) or 2D plots (abscissa labels, etc.). Note that 2D plots can be positioned explicitly inside the graphical window, or be automatically positioned in order to avoid overlaps.
Sample post-processing files in human-readable “parsed” format and in
the native MSH file format are available in the tutorial
directory of Gmsh's distribution (.pos and .msh
files). The “parsed” format is defined in the next section (cf. the
View command); the MSH format is defined in File formats.
Alias View[expression];Note that Alias creates a logical duplicate of the view without
actually duplicating the data in memory. This is very useful when you want
multiple simultaneous renderings of the same large dataset (usually with
different display options), but you cannot afford to store all copies in
memory. If what you really want is multiple physical copies of the data,
just merge the file containing the post-processing view multiple times.
AliasWithOptions View[expression];Combine ElementsByViewName;Combine ElementsFromAllViews | Combine Views;Combine ElementsFromVisibleViews;Combine TimeStepsByViewName | Combine TimeSteps;Combine TimeStepsFromAllViews;Combine TimeStepsFromVisibleViews;Delete View[expression];Delete Empty Views;Background Mesh View[expression];Plugin (string) . Run;Plugin (string) . string = expression | char-expression;Save View[expression] char-expression;View "string" { string < ( expression-list ) > { expression-list }; ... };"string". This
is an easy and quite powerful way to import post-processing data: all
the values are expressions, you can embed datasets directly into
your geometrical descriptions (see, e.g., t4.geo), the data can be
easily generated “on-the-fly” (there is no header containing a
priori information on the size of the dataset). The syntax is also very
permissive, which makes it ideal for testing purposes.
However this “parsed format” is read by Gmsh's script parser, which makes it inefficient if there are many elements in the dataset. Also, there is no connectivity information in parsed views and all the elements are independent (all fields can be discontinuous), so a lot of information can be duplicated. For large datasets, you should thus use the mesh-based post-processing file format described in File formats, or use one of the standard formats like MED.
More explicitly, the syntax for a parsed View is the following
View "string" {
type ( list-of-coords ) { list-of-values }; ...
< TIME { expression-list }; >
< INTERPOLATION_SCHEME { val-coef-matrix } { val-exp-matrix }
< { geo-coef-matrix } { geo-exp-matrix } > ; >
};
where the 47 object types that can be displayed are:
type #list-of-coords #list-of-values
--------------------------------------------------------------------
Scalar point SP 3 1 * nb-time-steps
Vector point VP 3 3 * nb-time-steps
Tensor point TP 3 9 * nb-time-steps
Scalar line SL 6 2 * nb-time-steps
Vector line VL 6 6 * nb-time-steps
Tensor line TL 6 18 * nb-time-steps
Scalar triangle ST 9 3 * nb-time-steps
Vector triangle VT 9 9 * nb-time-steps
Tensor triangle TT 9 27 * nb-time-steps
Scalar quadrangle SQ 12 4 * nb-time-steps
Vector quadrangle VQ 12 12 * nb-time-steps
Tensor quadrangle TQ 12 36 * nb-time-steps
Scalar tetrahedron SS 12 4 * nb-time-steps
Vector tetrahedron VS 12 12 * nb-time-steps
Tensor tetrahedron TS 12 36 * nb-time-steps
Scalar hexahedron SH 24 8 * nb-time-steps
Vector hexahedron VH 24 24 * nb-time-steps
Tensor hexahedron TH 24 72 * nb-time-steps
Scalar prism SI 18 6 * nb-time-steps
Vector prism VI 18 18 * nb-time-steps
Tensor prism TI 18 54 * nb-time-steps
Scalar pyramid SY 15 5 * nb-time-steps
Vector pyramid VY 15 15 * nb-time-steps
Tensor pyramid TY 15 45 * nb-time-steps
2D text T2 3 arbitrary
3D text T3 4 arbitrary
The coordinates are given `by node', i.e.,
(coord1, coord2, coord3) for a point,
(coord1-node1, coord2-node1, coord3-node1,, coord2-node2, coord3-node2) for a line,
(coord1-node1, coord2-node1, coord3-node1,, coord2-node2, coord3-node2,, coord2-node3, coord3-node3) for a triangle,
The ordering of the nodes is given in Node ordering.
The values are given by time step, by node and by component, i.e.:
comp1-node1-time1, comp2-node1-time1, comp3-node1-time1,
comp1-node2-time1, comp2-node2-time1, comp3-node2-time1,
comp1-node3-time1, comp2-node3-time1, comp3-node3-time1,
comp1-node1-time2, comp2-node1-time2, comp3-node1-time2,
comp1-node2-time2, comp2-node2-time2, comp3-node2-time2,
comp1-node3-time2, comp2-node3-time2, comp3-node3-time2,
...
For the 2D text objects, the two first expressions in list-of-coords give the X-Y position of the string in screen coordinates, measured from the top-left corner of the window. If the first (respectively second) expression is negative, the position is measured from the right (respectively bottom) edge of the window. If the value of the first (respectively second) expression is larger than 99999, the string is centered horizontally (respectively vertically). If the third expression is equal to zero, the text is aligned bottom-left and displayed using the default font and size. Otherwise, the third expression is converted into an integer whose eight lower bits give the font size, whose eight next bits select the font (the index corresponds to the position in the font menu in the GUI), and whose eight next bits define the text alignment (0=bottom-left, 1=bottom-center, 2=bottom-right, 3=top-left, 4=top-center, 5=top-right, 6=center-left, 7=center-center, 8=center-right).
For the 3D text objects, the three first expressions in list-of-coords give the XYZ position of the string in model (real world) coordinates. The fourth expression has the same meaning as the third expression in 2D text objects.
For both 2D and 3D text objects, the list-of-values can contain an arbitrary number of char-expressions.
The optional TIME list can contain a list of expressions giving the
value of the time (or any other variable) for which an evolution was saved.
The optional INTERPOLATION_SCHEME lists can contain the
interpolation matrices used for high-order adaptive visualization.
Let us assume that the approximation of the view's value over an element is written as a linear combination of d basis functions f[i], i=0, ..., d-1 (the coefficients being stored in list-of-values). Defining f[i] = Sum(j=0, ..., d-1) F[i][j] p[j], with p[j] = u^P[j][0] v^P[j][1] w^P[j][2] (u, v and w being the coordinates in the element's parameter space), then val-coef-matrix denotes the d x d matrix F and val-exp-matrix denotes the d x 3 matrix P.
In the same way, let us also assume that the coordinates x, y and z of the element are obtained through a geometrical mapping from parameter space as a linear combination of m basis functions g[i], i=0, ..., m-1 (the coefficients being stored in list-of-coords). Defining g[i] = Sum(j=0, ..., m-1) G[i][j] q[j], with q[j] = u^Q[j][0] v^Q[j][1] w^Q[j][2], then val-coef-matrix denotes the m x m matrix G and val-exp-matrix denotes the m x 3 matrix Q.
Here are for example the interpolation matrices for a first order quadrangle:
INTERPOLATION_SCHEME
{
{1/4,-1/4, 1/4,-1/4},
{1/4, 1/4,-1/4,-1/4},
{1/4, 1/4, 1/4, 1/4},
{1/4,-1/4,-1/4, 1/4}
}
{
{0, 0, 0},
{1, 0, 0},
{0, 1, 0},
{1, 1, 0}
};
Post-processing plugins permit to extend the functionality of Gmsh's post-processing module. The difference between regular post-processing options (see Post-processing options list) and post-processing plugins is that regular post-processing options only change the way the data is displayed, while post-processing plugins either create new post-processing views, or modify the data stored in a view (in a destructive, non-reversible way).
Plugins are available in the GUI by right-clicking on a view button (or by clicking on the black arrow next to the view button) and then selecting the `Plugin' submenu.
Here is the list of the plugins that are shipped by default with Gmsh:
Plugin(AnalyseCurvedMesh)Analysis : 0 do nothing +1 find invalid elements (*) +2 compute J_min and J_max of all elements and print some statistics
Effect (for *) : 0 do nothing +1 print a list of invalid elements +2 print some statistics +4 hide valid elements (for GUI)
MaxDepth = 0,1,... 0 : only sample the jacobian 1 : compute Bezier coefficients 2+ : execute a maximum of 1+ subdivision(s)
JacBreak = [0,1[ : if a value of the jacobian <= 'JacBreak' is found, the element is said to be invalid
BezBreak = [0,JacBreak[ : if all Bezier coefficients are > 'BezBreak', the element is said to be valid
Tolerance = R+ , << 1 : tolerance (relatively to J_min and J_max) used during the computation of J_min and J_max Numeric options:
Dim-1
Analysis2
Effect (1)6
JacBreak (1)0
BezBreak (1)0
MaxDepth (1,2)20
Tolerance (2)0.001
Plugin(Annotate)If `ThreeD' is equal to 1, the plugin inserts the string in model coordinates at the position (`X',`Y',`Z'). If `ThreeD' is equal to 0, the plugin inserts the string in screen coordinates at the position (`X',`Y').
If `View' < 0, the plugin is run on the current view.
Plugin(Annotate) is executed in-place for list-based datasets or creates a new view for other datasets. String options:
Text"My Text"
Font"Helvetica"
Align"Left"
X50
Y30
Z0
ThreeD0
FontSize14
View-1
Plugin(Bubbles)Plugin(Bubbles) creates one `.geo' file. String options:
OutputFile"bubbles.geo"
ShrinkFactor0
Plugin(Curl)If `View' < 0, the plugin is run on the current view.
Plugin(Curl) creates one new view. Numeric options:
View-1
Plugin(CutBox)The number of points along U, V, W is set with the options `NumPointsU', `NumPointsV' and `NumPointsW'.
If `ConnectPoints' is zero, the plugin creates points; otherwise, the plugin generates hexahedra, quadrangles, lines or points depending on the values of `NumPointsU', `NumPointsV' and `NumPointsW'.
If `Boundary' is zero, the plugin interpolates the view inside the box; otherwise the plugin interpolates the view at its boundary.
If `View' < 0, the plugin is run on the current view.
Plugin(CutBox) creates one new view. Numeric options:
X00
Y00
Z00
X11
Y10
Z10
X20
Y21
Z20
X30
Y30
Z31
NumPointsU20
NumPointsV20
NumPointsW20
ConnectPoints1
Boundary1
View-1
Plugin(CutGrid)The number of points along U and V is set with the options `NumPointsU' and `NumPointsV'.
If `ConnectPoints' is zero, the plugin creates points; otherwise, the plugin generates quadrangles, lines or points depending on the values of `NumPointsU' and `NumPointsV'.
If `View' < 0, the plugin is run on the current view.
Plugin(CutGrid) creates one new view. Numeric options:
X00
Y00
Z00
X11
Y10
Z10
X20
Y21
Z20
NumPointsU20
NumPointsV20
ConnectPoints1
View-1
Plugin(CutParametric)If `ConnectPoints' is set, the plugin creates surface or line elements; otherwise, the plugin generates points.
If `View' < 0, the plugin is run on the current view.
Plugin(CutParametric) creates one new view. String options:
X"2 * Cos(u) * Sin(v)"
Y"4 * Sin(u) * Sin(v)"
Z"0.1 + 0.5 * Cos(v)"
MinU0
MaxU6.2832
NumPointsU180
MinV0
MaxV6.2832
NumPointsV180
ConnectPoints0
View-1
Plugin(CutPlane)If `ExtractVolume' is nonzero, the plugin extracts the elements on one side of the plane (depending on the sign of `ExtractVolume').
If `View' < 0, the plugin is run on the current view.
Plugin(CutPlane) creates one new view. Numeric options:
A1
B0
C0
D-0.01
ExtractVolume0
RecurLevel4
TargetError0
View-1
Plugin(CutSphere)If `ExtractVolume' is nonzero, the plugin extracts the elements inside (if `ExtractVolume' < 0) or outside (if `ExtractVolume' > 0) the sphere.
If `View' < 0, the plugin is run on the current view.
Plugin(CutSphere) creates one new view. Numeric options:
Xc0
Yc0
Zc0
R0.25
ExtractVolume0
RecurLevel4
TargetError0
View-1
Plugin(DiscretizationError)SuperSamplingNodes10
Plugin(Distance)Define the physical entities to which the distance is computed. If Point=0, Line=0, and Surface=0, then the distance is computed to all the boundaries of the mesh (edges in 2D and faces in 3D).
Computation<0. computes the geometrical euclidian distance (warning: different than the geodesic distance), and Computation=a>0.0 solves a PDE on the mesh with the diffusion constant mu = a*bbox, with bbox being the max size of the bounding box of the mesh (see paper Legrand 2006).
Min Scale and max Scale, scale the distance function. If min Scale<0 and max Scale<0, then no scaling is applied to the distance function.
Plugin(Distance) creates a new distance view and also saves the view in the fileName.pos file. String options:
Filename"distance.pos"
PhysPoint0
PhysLine0
PhysSurface0
Computation-1
MinScale-1
MaxScale-1
Orthogonal-1
Plugin(Divergence)If `View' < 0, the plugin is run on the current view.
Plugin(Divergence) creates one new view. Numeric options:
View-1
Plugin(Eigenvalues)If `View' < 0, the plugin is run on the current view.
Plugin(Eigenvalues) creates three new scalar views. Numeric options:
View-1
Plugin(Eigenvectors)If `ScaleByEigenvalues' is set, each eigenvector is scaled by its associated eigenvalue. The plugin gives an error if the eigenvectors are complex.
If `View' < 0, the plugin is run on the current view.
Plugin(Eigenvectors) creates three new vector view. Numeric options:
ScaleByEigenvalues1
View-1
Plugin(ExtractEdges)Plugin(ExtractEdges) creates one new view. Numeric options:
Angle40
IncludeBoundary1
Plugin(ExtractElements)If `View' < 0, the plugin is run on the current view.
Plugin(ExtractElements) creates one new view. Numeric options:
MinVal0
MaxVal0
TimeStep0
Visible1
View-1
Plugin(FieldFromAmplitudePhase)The result is to be interpolated in a sufficiently fine mesh: 'MeshFile'.
Plugin(FieldFromAmplitudePhase) generates one new view. String options:
MeshFile"fine.msh"
Wavenumber5
AmplitudeView0
PhaseView1
Plugin(GSHHS)The principal application is to load GSHHS data (see http://www.soest.hawaii.edu/wessel/gshhs/gshhs.html).
Valid values for "Format" are:
- "gshhs": open GSHHS file
- "loops2": import 2D contour lines in simple text format:
NB_POINTS_IN_FIRST_LOOP FIRST_LOOP_IS_CLOSED COORD1 COORD2 COORD1 COORD2 ... ... NB_POINTS_IN_SECOND_LOOP SECOND_LOOP_IS_CLOSED ...
(LOOP_IS_CLOSED specifies if this coast line describes a closed curve (0=no, 1=yes)).
In the case of "loops2" format, you can specify the coordinate system used in the input file with the "Coordinate" option. Valid values are
- "lonlat" for longitude-latidute radian,
- "lonlat_degrees" for longitude-latitude degrees,
- "UTM" for universal transverse mercartor ("UTMZone" option should be specified)
- "cartesian" for full 3D coordinates
- "radius" specify the earth radius.
If the "iField" option is set, consecutive points closer than the value of the field iField (in meters) will not be added.
If "MinStraitsFactor" > 0 and if a field iField is provided, coastlines closer than MinStraitsFactor * field(IField) are merged and inner corners which form an angle < pi/3 are removed.
The output is always in stereographic coordinates, if the "WritePolarSphere" option is greater than 0, a sphere is added to the geo file.
WARNING: this plugin is still experimental and needs polishing and error-handling. In particular, it will probably crash if an inexistant field id is given or if the input/output cannot be open. String options:
InFileName"gshhs_c.b"
OutFileName"earth.geo"
Format"gshhs"
Coordinate"cartesian"
iField-1
UTMZone0
UTMEquatorialRadius6.37814e+06
UTMPolarRadius6.35675e+06
radius6.37101e+06
WritePolarSphere1
MinStraitsFactor1
Plugin(Gradient)If `View' < 0, the plugin is run on the current view.
Plugin(Gradient) creates one new view. Numeric options:
View-1
Plugin(HarmonicToTime)`View'[`RealPart'] * cos(p) - `View'[`ImaginaryPart'] * sin(p)
with p = 2*Pi*k/`NumSteps', k = 0, ..., `NumSteps'-1.
If `View' < 0, the plugin is run on the current view.
Plugin(HarmonicToTime) creates one new view. Numeric options:
RealPart0
ImaginaryPart1
NumSteps20
View-1
Plugin(HomologyComputation)Define physical groups in order to specify the computation domain and the relative subdomain. Otherwise the whole mesh is the domain and the relative subdomain is empty.
Plugin(HomologyComputation) creates new views, one for each basis element. The resulting basis chains of desired dimension together with the mesh are saved to the given file. String options:
DomainPhysicalGroups""
SubdomainPhysicalGroups""
ReductionImmunePhysicalGroups""
DimensionOfChainsToSave"0, 1, 2, 3"
Filename"homology.msh"
ComputeHomology1
ComputeCohomology0
HomologyPhysicalGroupsBegin-1
CohomologyPhysicalGroupsBegin-1
CreatePostProcessingViews1
ReductionOmit1
ReductionCombine2
PostProcessSimplify1
Plugin(HomologyPostProcessing)1. (co)homology basis transformation: 'TransformationMatrix': Integer matrix of the transformation. 'PhysicalGroupsOfOperatedChains': (Co)chains of a (co)homology space basis to be transformed. Results a new (co)chain basis that is an integer cobination of the given basis.
2. Make basis representations of a homology space and a cohomology space compatible: 'PhysicalGroupsOfOperatedChains': Chains of a homology space basis. 'PhysicalGroupsOfOperatedChains2': Cochains of a cohomology space basis. Results a new basis for the homology space such that the incidence matrix of the new basis and the basis of the cohomology space is the identity matrix.
Options: 'PhysicalGroupsToTraceResults': Trace the resulting cochains to the given physical groups. 'NameForResultChains': Post-processing view name prefix for the results. 'ApplyBoundaryOperatorToResults': Apply boundary operator to the resulting chains.
String options:
TransformationMatrix"1, 0; 0, 1"
PhysicalGroupsOfOperatedChains"1, 2"
PhysicalGroupsOfOperatedChains2""
PhysicalGroupsToTraceResults""
NameForResultChains"c"
ApplyBoundaryOperatorToResults0
Plugin(Integrate)If `View' < 0, the plugin is run on the current view.
Plugin(Integrate) creates one new view.If `OverTime' = 1 , the plugin integrates the scalar view over time instead of over space.
Plugin(Integrate) creates one new view. Numeric options:
View-1
OverTime-1
Plugin(Isosurface)If `ExtractVolume' is nonzero, the plugin extracts the isovolume with values greater (if `ExtractVolume' > 0) or smaller (if `ExtractVolume' < 0) than the isosurface `Value'.
If `OtherTimeStep' < 0, the plugin uses, for each time step in `View', the corresponding time step in `OtherView'. If `OtherView' < 0, the plugin uses `View' as the value source.
If `View' < 0, the plugin is run on the current view.
Plugin(Isosurface) creates as many views as there are time steps in `View'. Numeric options:
Value0
ExtractVolume0
RecurLevel4
TargetError0
View-1
OtherTimeStep-1
OtherView-1
Plugin(Lambda2)Vortices are well represented by regions where Lambda(2) is negative.
If `View' contains tensor elements, the plugin directly uses the tensors as the values of the velocity gradient tensor; if `View' contains vector elements, the plugin uses them as the velocities from which to derive the velocity gradient tensor.
If `View' < 0, the plugin is run on the current view.
Plugin(Lambda2) creates one new view. Numeric options:
Eigenvalue2
View-1
Plugin(LongitudeLatitude)If `View' < 0, the plugin is run on the current view.
Plugin(LongituteLatitude) is executed in place. Numeric options:
View-1
Plugin(MakeSimplex)If `View' < 0, the plugin is run on the current view.
Plugin(MakeSimplex) is executed in-place. Numeric options:
View-1
Plugin(MathEval)If only `Expression0' is given (and `Expression1', ..., `Expression8' are all empty), the plugin creates a scalar view. If `Expression0', `Expression1' and/or `Expression2' are given (and `Expression3', ..., `Expression8' are all empty) the plugin creates a vector view. Otherwise the plugin creates a tensor view.
In addition to the usual mathematical functions (Exp, Log, Sqrt, Sin, Cos, Fabs, etc.) and operators (+, -, *, /, ^), all expressions can contain:
- the symbols v0, v1, v2, ..., vn, which represent the n components in `View';
- the symbols w0, w1, w2, ..., wn, which represent the n components of `OtherView', at time step `OtherTimeStep';
- the symbols x, y and z, which represent the three spatial coordinates.
If `TimeStep' < 0, the plugin extracts data from all the time steps in the view.
If `View' < 0, the plugin is run on the current view.
Plugin(MathEval) creates one new view.If `PhysicalRegion' < 0, the plugin is runon all physical regions.
Plugin(MathEval) creates one new view. String options:
Expression0"Sqrt(v0^2+v1^2+v2^2)"
Expression1""
Expression2""
Expression3""
Expression4""
Expression5""
Expression6""
Expression7""
Expression8""
TimeStep-1
View-1
OtherTimeStep-1
OtherView-1
ForceInterpolation0
PhysicalRegion-1
Plugin(MinMax)If `View' < 0, the plugin is run on the current view.
If `OverTime' = 1, calculates the min/max over space AND time
If `Argument' = 1, calculates the min/max AND the argmin/argmax
Plugin(MinMax) creates two new views. Numeric options:
View-1
OverTime0
Argument0
Plugin(ModifyComponent)`Expression' can contain:
- the usual mathematical functions (Log, Sqrt, Sin, Cos, Fabs, ...) and operators (+, -, *, /, ^);
- the symbols x, y and z, to retrieve the coordinates of the current node;
- the symbols Time and TimeStep, to retrieve the current time and time step values;
- the symbol v, to retrieve the `Component'-th component of the field in `View' at the `TimeStep'-th time step;
- the symbols v0, v1, v2, ..., v8, to retrieve each component of the field in `View' at the `TimeStep'-th time step;
- the symbol w, to retrieve the `Component'-th component of the field in `OtherView' at the `OtherTimeStep'-th time step. If `OtherView' and `View' are based on different spatial grids, or if their data types are different, `OtherView' is interpolated onto `View';
- the symbols w0, w1, w2, ..., w8, to retrieve each component of the field in `OtherView' at the `OtherTimeStep'-th time step.
If `TimeStep' < 0, the plugin automatically loops over all the time steps in `View' and evaluates `Expression' for each one.
If `OtherTimeStep' < 0, the plugin uses `TimeStep' instead.
If `Component' < 0, the plugin automatically ops over all the components in the view and evaluates `Expression' for each one.
If `View' < 0, the plugin is run on the current view.
If `OtherView' < 0, the plugin uses `View' instead.
Plugin(ModifyComponent) is executed in-place. String options:
Expression"v0 * Sin(x)"
Component-1
TimeStep-1
View-1
OtherTimeStep-1
OtherView-1
ForceInterpolation0
Plugin(ModulusPhase)If `View' < 0, the plugin is run on the current view.
Plugin(ModulusPhase) is executed in-place. Numeric options:
RealPart0
ImaginaryPart1
View-1
Plugin(NearToFarField)Parameters: the wavenumber, the angular discretisation (phi in [0, 2*Pi] and theta in [0, Pi]) of the far field sphere and the indices of the views containing the complex-valued E and H fields. If `Normalize' is set, the far field is normalized to 1. If `dB' is set, the far field is computed in dB. If `NegativeTime' is set, E and H are assumed to have exp(-iwt) time dependency; otherwise they are assume to have exp(+iwt) time dependency. If `MatlabOutputFile' is given the raw far field data is also exported in Matlab format.
Plugin(NearToFarField) creates one new view. String options:
MatlabOutputFile"farfield.m"
Wavenumber1
PhiStart0
PhiEnd6.28319
NumPointsPhi60
ThetaStart0
ThetaEnd3.14159
NumPointsTheta30
EView0
HView1
Normalize1
dB1
NegativeTime0
Plugin(NearestNeighbor)If `View' < 0, the plugin is run on the current view.
Plugin(NearestNeighbor) is executed in-place. Numeric options:
View-1
Plugin(NewView)View-1
Plugin(Particles)The plugin takes as input a grid defined by the 3 points (`X0',`Y0',`Z0') (origin), (`X1',`Y1',`Z1') (axis of U) and (`X2',`Y2',`Z2') (axis of V).
The number of particles along U and V that are to be transported is set with the options `NumPointsU' and `NumPointsV'. The equation
A2 * d^2X(t)/dt^2 + A1 * dX(t)/dt + A0 * X(t) = F
is then solved with the initial conditions X(t=0) chosen as the grid, dX/dt(t=0)=0, and with F interpolated from the vector view.
Time stepping is done using a Newmark scheme with step size `DT' and `MaxIter' maximum number of iterations.
If `View' < 0, the plugin is run on the current view.
Plugin(Particles) creates one new view containing multi-step vector points. Numeric options:
X00
Y00
Z00
X11
Y10
Z10
X20
Y21
Z20
NumPointsU10
NumPointsV1
A21
A10
A00
DT0.1
MaxIter100
TimeStep0
View-1
Plugin(Probe)If `View' < 0, the plugin is run on the current view.
Plugin(Probe) creates one new view. Numeric options:
X0
Y0
Z0
View-1
Plugin(Remove)If `View' < 0, the plugin is run on the current view.
Plugin(Remove) is executed in-place. Numeric options:
Text2D1
Text3D1
Points0
Lines0
Triangles0
Quadrangles0
Tetrahedra0
Hexahedra0
Prisms0
Pyramids0
Scalar1
Vector1
Tensor1
View-1
Plugin(Scal2Vec)If the value of 'ViewX', 'ViewY' or 'ViewZ' is -1, the value of the vectorial field in the corresponding direction is 0. String options:
NameNewView"NewView"
ViewX-1
ViewY-1
ViewZ-1
Plugin(Skin)If `View' < 0, the plugin is run on the current view.
Plugin(Skin) creates one new view. Numeric options:
Visible1
View-1
Plugin(Smooth)If `View' < 0, the plugin is run on the current view.
Plugin(Smooth) is executed in-place. Numeric options:
View-1
Plugin(SphericalRaise)Instead of elevating the nodes along the X, Y and Z axes as with the View[`View'].RaiseX, View[`View'].RaiseY and View[`View'].RaiseZ options, the raise is applied along the radius of a sphere centered at (`Xc', `Yc', `Zc').
To produce a standard radiation pattern, set `Offset' to minus the radius of the sphere the original data lives on.
If `View' < 0, the plugin is run on the current view.
Plugin(SphericalRaise) is executed in-place. Numeric options:
Xc0
Yc0
Zc0
Raise1
Offset0
TimeStep0
View-1
Plugin(StreamLines)The plugin takes as input a grid defined by the 3 points (`X0',`Y0',`Z0') (origin), (`X1',`Y1',`Z1') (axis of U) and (`X2',`Y2',`Z2') (axis of V).
The number of points along U and V that are to be transported is set with the options `NumPointsU' and `NumPointsV'. The equation
dX(t)/dt = V(x,y,z)
is then solved with the initial condition X(t=0) chosen as the grid and with V(x,y,z) interpolated on the vector view.
The time stepping scheme is a RK44 with step size `DT' and `MaxIter' maximum number of iterations.
If `TimeStep' < 0, the plugin tries to compute streamlines of the unsteady flow.
If `View' < 0, the plugin is run on the current view.
Plugin(StreamLines) creates one new view. This view contains multi-step vector points if `OtherView' < 0, or single-step scalar lines if `OtherView' >= 0. Numeric options:
X00
Y00
Z00
X11
Y10
Z10
X20
Y21
Z20
NumPointsU10
NumPointsV1
DT0.1
MaxIter100
TimeStep0
View-1
OtherView-1
Plugin(Tetrahedralize)If `View' < 0, the plugin is run on the current view.
Plugin(Tetrahedralize) creates one new view. Numeric options:
View-1
Plugin(Transform)[`A11' `A12' `A13' `Tx'] [`A21' `A22' `A23' `Ty'] [`A31' `A32' `A33' `Tz'].
If `SwapOrientation' is set, the orientation of the elements is reversed.
If `View' < 0, the plugin is run on the current view.
Plugin(Transform) is executed in-place. Numeric options:
A111
A120
A130
A210
A221
A230
A310
A320
A331
Tx0
Ty0
Tz0
SwapOrientation0
View-1
Plugin(Triangulate)If `View' < 0, the plugin is run on the current view.
Plugin(Triangulate) creates one new view. Numeric options:
View-1
Plugin(Warp)If `View' < 0, the plugin is run on the current view.
If `OtherView' < 0, the vector field is taken as the field of surface normals multiplied by the `TimeStep' value in `View'. (The smoothing of the surface normals is controlled by the `SmoothingAngle' parameter.)
Plugin(Warp) is executed in-place. Numeric options:
Factor1
TimeStep0
SmoothingAngle180
View-1
OtherView-1
General post-processing option names have the form
`PostProcessing.string'. Options peculiar to post-processing
views take two forms.
View.string', before any view is loaded;
View[n].string' (n = 0, 1, 2,
...), after the n-th view is loaded.
The list of all post-processing and view options is given in Post-processing options list. See t8.geo, and t9.geo, for some examples.
This chapter describes Gmsh's native “MSH” file format, used to store meshes and associated post-processing datasets. The MSH format exists in two flavors: ASCII and binary. The format has a version number (currently: 2.2) that is independent of Gmsh's main version number.
(Remember that for small post-processing datasets you can also use human-readable “parsed” post-processing views, as described in Post-processing commands. Such “parsed” views do not require an underlying mesh, and can therefore be easier to use in some cases.)
The MSH ASCII file format contains one mandatory section giving
information about the file ($MeshFormat), followed by several
optional sections defining the nodes ($Nodes), elements
($Elements), region names ($PhysicalName) and
post-processing datasets ($NodeData, $ElementData,
$ElementNodeData).
Any section with an unrecognized header is simply ignored: you can thus
add comments in a .msh file by putting them e.g. inside a
$Comments/$EndComments section.
Sections can be repeated in the same file, and post-processing sections can be put into separate files (e.g. one file per time step). Nodes are assumed to be defined before elements.
The format is defined as follows:
$MeshFormat
version-number file-type data-size
$EndMeshFormat
$Nodes
number-of-nodes
node-number x-coord y-coord z-coord
...
$EndNodes
$Elements
number-of-elements
elm-number elm-type number-of-tags < tag > ... node-number-list
...
$EndElements
$PhysicalNames
number-of-names
physical-dimension physical-number "physical-name"
...
$EndPhysicalNames
$NodeData
number-of-string-tags
< "string-tag" >
...
number-of-real-tags
< real-tag >
...
number-of-integer-tags
< integer-tag >
...
node-number value ...
...
$EndNodeData
$ElementData
number-of-string-tags
< "string-tag" >
...
number-of-real-tags
< real-tag >
...
number-of-integer-tags
< integer-tag >
...
elm-number value ...
...
$EndElementData
$ElementNodeData
number-of-string-tags
< "string-tag" >
...
number-of-real-tags
< real-tag >
...
number-of-integer-tags
< integer-tag >
...
elm-number number-of-nodes-per-element value ...
...
$EndElementNodeData
$InterpolationScheme
"name"
number-of-element-topologies
elm-topology
number-of-interpolation-matrices
num-rows num-columns value ...
...
$EndInterpolationScheme
where
123456789101112131415161718192021222324252627282930319293$InterpolationScheme
section (see below).
NodeData (respectively ElementData) views,
there are ncomp values per node (resp. per element), where
ncomp is the number of field components. For
ElementNodeData views, there are ncomp times
number-of-nodes-per-elements values per element.
Below is a small example (a mesh consisting of two quadrangles with an associated nodal scalar dataset; the comments are not part of the actual file!):
$MeshFormat
2.2 0 8
$EndMeshFormat
$Nodes
6 six mesh nodes:
1 0.0 0.0 0.0 node #1: coordinates (0.0, 0.0, 0.0)
2 1.0 0.0 0.0 node #2: coordinates (1.0, 0.0, 0.0)
3 1.0 1.0 0.0 etc.
4 0.0 1.0 0.0
5 2.0 0.0 0.0
6 2.0 1.0 0.0
$EndNodes
$Elements
2 two elements:
1 3 2 99 2 1 2 3 4 quad #1: type 3, physical 99, elementary 2, nodes 1 2 3 4
2 3 2 99 2 2 5 6 3 quad #2: type 3, physical 99, elementary 2, nodes 2 5 6 3
$EndElements
$NodeData
1 one string tag:
"A scalar view" the name of the view ("A scalar view")
1 one real tag:
0.0 the time value (0.0)
3 three integer tags:
0 the time step (0; time steps always start at 0)
1 1-component (scalar) field
6 six associated nodal values
1 0.0 value associated with node #1 (0.0)
2 0.1 value associated with node #2 (0.1)
3 0.2 etc.
4 0.0
5 0.2
6 0.4
$EndNodeData
The binary file format is similar to the ASCII format described above:
$MeshFormat
version-number file-type data-size
one-binary
$EndMeshFormat
$Nodes
number-of-nodes
nodes-binary
$EndNodes
$Elements
number-of-elements
element-header-binary
elements-binary
element-header-binary
elements-binary
...
$EndElements
[ all other sections are identical to ASCII, except that node-number,
elm-number, number-of-nodes-per-element and values are written in
binary format ]
where
Here is a pseudo C code to write one-binary:
int one = 1;
fwrite(&one, sizeof(int), 1, file);
Here is a pseudo C code to write nodes-binary:
for(i = 0; i < number_of_nodes; i++){
fwrite(&num_i, sizeof(int), 1, file);
double xyz[3] = {node_i_x, node_i_y, node_i_z};
fwrite(&xyz, sizeof(double), 3, file);
}
Here is a pseudo C code to write element-header-binary:
int header[3] = {elm_type, num_elm_follow, num_tags};
fwrite(&header, sizeof(int), 2, file);
Here is a pseudo C code to write elements-binary for triangles with the 2 standard tags (the physical and elementary regions):
for(i = 0; i < number_of_triangles; i++){
int data[6] = {num_i, physical, elementary,
node_i_1, node_i_2, node_i_3};
fwrite(data, sizeof(int), 6, file);
}
Historically, Gmsh developpers have started by implementing linear elements (lines, triangles, quads, tets, prisms and hexes). Then, second and sometimes third order elements have been hardcoded. We here distinguish “low order elements” that have been hardcoded initially and “high order elements” that have been coded in a general fashion, theoretically valid for any order.
For all mesh and post-processing file formats, the reference elements are defined as follows.
Line: Line3: Line4:
0----------1 --> u 0-----2----1 0----2----3----1
Triangle: Triangle6: Triangle9/10: Triangle12/15:
v
^ 2
| | \
2 2 2 9 8
|`\ |`\ | \ | \
| `\ | `\ 7 6 10 (14) 7
| `\ 5 `4 | \ | \
| `\ | `\ 8 (9) 5 11 (12) (13) 6
| `\ | `\ | \ | \
0----------1 --> u 0-----3----1 0---3---4---1 0---3---4---5---1
Quadrangle: Quadrangle8: Quadrangle9:
v
^
|
3-----------2 3-----6-----2 3-----6-----2
| | | | | | |
| | | | | | |
| +---- | --> u 7 5 7 8 5
| | | | | |
| | | | | |
0-----------1 0-----4-----1 0-----4-----1
Tetrahedron: Tetrahedron10:
v
.
,/
/
2 2
,/|`\ ,/|`\
,/ | `\ ,/ | `\
,/ '. `\ ,6 '. `5
,/ | `\ ,/ 8 `\
,/ | `\ ,/ | `\
0-----------'.--------1 --> u 0--------4--'.--------1
`\. | ,/ `\. | ,/
`\. | ,/ `\. | ,9
`\. '. ,/ `7. '. ,/
`\. |/ `\. |/
`3 `3
`\.
` w
Hexahedron: Hexahedron20: Hexahedron27:
v
3----------2 3----13----2 3----13----2
|\ ^ |\ |\ |\ |\ |\
| \ | | \ | 15 | 14 |15 24 | 14
| \ | | \ 9 \ 11 \ 9 \ 20 11 \
| 7------+---6 | 7----19+---6 | 7----19+---6
| | +-- |-- | -> u | | | | |22 | 26 | 23|
0---+---\--1 | 0---+-8----1 | 0---+-8----1 |
\ | \ \ | \ 17 \ 18 \ 17 25 \ 18
\ | \ \ | 10 | 12| 10 | 21 12|
\| w \| \| \| \| \|
4----------5 4----16----5 4----16----5
Prism: Prism15: Prism18:
w
^
|
3 3 3
,/|`\ ,/|`\ ,/|`\
,/ | `\ 12 | 13 12 | 13
,/ | `\ ,/ | `\ ,/ | `\
4------+------5 4------14-----5 4------14-----5
| | | | 8 | | 8 |
| ,/|`\ | | | | | ,/|`\ |
| ,/ | `\ | | | | | 15 | 16 |
|,/ | `\| | | | |,/ | `\|
,| | |\ 10 | 11 10-----17-----11
,/ | 0 | `\ | 0 | | 0 |
u | ,/ `\ | v | ,/ `\ | | ,/ `\ |
| ,/ `\ | | ,6 `7 | | ,6 `7 |
|,/ `\| |,/ `\| |,/ `\|
1-------------2 1------9------2 1------9------2
Pyramid: Pyramid13: Pyramid14:
4 4 4
,/|\ ,/|\ ,/|\
,/ .'|\ ,/ .'|\ ,/ .'|\
,/ | | \ ,/ | | \ ,/ | | \
,/ .' | `. ,/ .' | `. ,/ .' | `.
,/ | '. \ ,7 | 12 \ ,7 | 12 \
,/ .' w | \ ,/ .' | \ ,/ .' | \
,/ | ^ | \ ,/ 9 | 11 ,/ 9 | 11
0----------.'--|-3 `. 0--------6-.'----3 `. 0--------6-.'----3 `.
`\ | | `\ \ `\ | `\ \ `\ | `\ \
`\ .' +----`\ - \ -> v `5 .' 10 \ `5 .' 13 10 \
`\ | `\ `\ \ `\ | `\ \ `\ | `\ \
`\.' `\ `\` `\.' `\` `\.' `\`
1----------------2 1--------8-------2 1--------8-------2
`\
u
The node ordering of a higher order (possibly curved) element is compatible with the numbering of low order element (it is a generalization). We number nodes in the following order:
The numbering for internal nodes is recursive, ie. the numbering follows that of the nodes of an embedded edge/face/volume of lower order. The higher order nodes are assumed to be equispaced. Edges and faces are numbered following the lowest order template that generates a single high-order on this edge/face. Furthermore, an edge is oriented from the vertex with the lowest to the highest index. The orientation of a face is such that the computed normal points outward; the starting point is the vertex with the lowest index.
This section describes Gmsh's older native file formats. Future versions of Gmsh will continue to support these formats, but we recommend that you do not use them in new applications.
The MSH file format version 1.0 is Gmsh's old native mesh file format, now superseded by the format described in MSH ASCII file format. It is defined as follows:
$NOD
number-of-nodes
node-number x-coord y-coord z-coord
...
$ENDNOD
$ELM
number-of-elements
elm-number elm-type reg-phys reg-elem number-of-nodes node-number-list
...
$ENDELM
where
12345678910111213141516171819The POS ASCII file is Gmsh's old native post-processing format, now superseded by the format described in MSH ASCII file format. It is defined as follows:
$PostFormat
1.4 file-type data-size
$EndPostFormat
$View
view-name nb-time-steps
nb-scalar-points nb-vector-points nb-tensor-points
nb-scalar-lines nb-vector-lines nb-tensor-lines
nb-scalar-triangles nb-vector-triangles nb-tensor-triangles
nb-scalar-quadrangles nb-vector-quadrangles nb-tensor-quadrangles
nb-scalar-tetrahedra nb-vector-tetrahedra nb-tensor-tetrahedra
nb-scalar-hexahedra nb-vector-hexahedra nb-tensor-hexahedra
nb-scalar-prisms nb-vector-prisms nb-tensor-prisms
nb-scalar-pyramids nb-vector-pyramids nb-tensor-pyramids
nb-scalar-lines2 nb-vector-lines2 nb-tensor-lines2
nb-scalar-triangles2 nb-vector-triangles2 nb-tensor-triangles2
nb-scalar-quadrangles2 nb-vector-quadrangles2 nb-tensor-quadrangles2
nb-scalar-tetrahedra2 nb-vector-tetrahedra2 nb-tensor-tetrahedra2
nb-scalar-hexahedra2 nb-vector-hexahedra2 nb-tensor-hexahedra2
nb-scalar-prisms2 nb-vector-prisms2 nb-tensor-prisms2
nb-scalar-pyramids2 nb-vector-pyramids2 nb-tensor-pyramids2
nb-text2d nb-text2d-chars nb-text3d nb-text3d-chars
time-step-values
< scalar-point-value > ... < vector-point-value > ...
< tensor-point-value > ...
< scalar-line-value > ... < vector-line-value > ...
< tensor-line-value > ...
< scalar-triangle-value > ... < vector-triangle-value > ...
< tensor-triangle-value > ...
< scalar-quadrangle-value > ... < vector-quadrangle-value > ...
< tensor-quadrangle-value > ...
< scalar-tetrahedron-value > ... < vector-tetrahedron-value > ...
< tensor-tetrahedron-value > ...
< scalar-hexahedron-value > ... < vector-hexahedron-value > ...
< tensor-hexahedron-value > ...
< scalar-prism-value > ... < vector-prism-value > ...
< tensor-prism-value > ...
< scalar-pyramid-value > ... < vector-pyramid-value > ...
< tensor-pyramid-value > ...
< scalar-line2-value > ... < vector-line2-value > ...
< tensor-line2-value > ...
< scalar-triangle2-value > ... < vector-triangle2-value > ...
< tensor-triangle2-value > ...
< scalar-quadrangle2-value > ... < vector-quadrangle2-value > ...
< tensor-quadrangle2-value > ...
< scalar-tetrahedron2-value > ... < vector-tetrahedron2-value > ...
< tensor-tetrahedron2-value > ...
< scalar-hexahedron2-value > ... < vector-hexahedron2-value > ...
< tensor-hexahedron2-value > ...
< scalar-prism2-value > ... < vector-prism2-value > ...
< tensor-prism2-value > ...
< scalar-pyramid2-value > ... < vector-pyramid2-value > ...
< tensor-pyramid2-value > ...
< text2d > ... < text2d-chars > ...
< text3d > ... < text3d-chars > ...
$EndView
where
......For example, vector-triangle-value is defined as:
coord1-node1 coord1-node2 coord1-node3
coord2-node1 coord2-node2 coord2-node3
coord3-node1 coord3-node2 coord3-node3
comp1-node1-time1 comp2-node1-time1 comp3-node1-time1
comp1-node2-time1 comp2-node2-time1 comp3-node2-time1
comp1-node3-time1 comp2-node3-time1 comp3-node3-time1
comp1-node1-time2 comp2-node1-time2 comp3-node1-time2
comp1-node2-time2 comp2-node2-time2 comp3-node2-time2
comp1-node3-time2 comp2-node3-time2 comp3-node3-time2
...
The ordering of the nodes is given in Node ordering.
coord1 coord2 style index
where coord1 and coord2 give the X-Y position of the 2D string
in screen coordinates (measured from the top-left corner of the window) and
where index gives the starting index of the string in
text2d-chars. If coord1 (respectively coord2) is negative,
the position is measured from the right (respectively bottom) edge of the
window. If coord1 (respectively coord2) is larger than 99999,
the string is centered horizontally (respectively vertically). If
style is equal to zero, the text is aligned bottom-left and displayed
using the default font and size. Otherwise, style is converted into an
integer whose eight lower bits give the font size, whose eight next bits
select the font (the index corresponds to the position in the font menu in
the GUI), and whose eight next bits define the text alignment
(0=bottom-left, 1=bottom-center, 2=bottom-right, 3=top-left, 4=top-center,
5=top-right, 6=center-left, 7=center-center, 8=center-right).
\0' character.
coord1 coord2 coord3 style index
where coord1, coord2 and coord3 give the XYZ coordinates
of the string in model (real world) coordinates, index gives the
starting index of the string in text3d-chars, and style has the
same meaning as in text2d.
\0' character.
The POS binary file format is the same as the POS ASCII file format described in POS ASCII file format, except that:
Here is a pseudo C code to write a post-processing file in binary format:
int one = 1;
fprintf(file, "$PostFormat\n");
fprintf(file, "%g %d %d\n", 1.4, 1, sizeof(double));
fprintf(file, "$EndPostFormat\n");
fprintf(file, "$View\n");
fprintf(file, "%s %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d\n",
view-name, nb-time-steps,
nb-scalar-points, nb-vector-points, nb-tensor-points,
nb-scalar-lines, nb-vector-lines, nb-tensor-lines,
nb-scalar-triangles, nb-vector-triangles, nb-tensor-triangles,
nb-scalar-quadrangles, nb-vector-quadrangles, nb-tensor-quadrangles,
nb-scalar-tetrahedra, nb-vector-tetrahedra, nb-tensor-tetrahedra,
nb-scalar-hexahedra, nb-vector-hexahedra, nb-tensor-hexahedra,
nb-scalar-prisms, nb-vector-prisms, nb-tensor-prisms,
nb-scalar-pyramids, nb-vector-pyramids, nb-tensor-pyramids,
nb-scalar-lines2, nb-vector-lines2, nb-tensor-lines2,
nb-scalar-triangles2, nb-vector-triangles2, nb-tensor-triangles2,
nb-scalar-quadrangles2, nb-vector-quadrangles2, nb-tensor-quadrangles2,
nb-scalar-tetrahedra2, nb-vector-tetrahedra2, nb-tensor-tetrahedra2,
nb-scalar-hexahedra2, nb-vector-hexahedra2, nb-tensor-hexahedra2,
nb-scalar-prisms2, nb-vector-prisms2, nb-tensor-prisms2,
nb-scalar-pyramids2, nb-vector-pyramids2, nb-tensor-pyramids2,
nb-text2d, nb-text2d-chars, nb-text3d, nb-text3d-chars);
fwrite(&one, sizeof(int), 1, file);
fwrite(time-step-values, sizeof(double), nb-time-steps, file);
fwrite(all-scalar-point-values, sizeof(double), ..., file);
...
fprintf(file, "\n$EndView\n");
In this pseudo-code, all-scalar-point-values is the array of double precision numbers containing all the scalar-point-value lists, put one after each other in order to form a long array of doubles. The principle is the same for all other kinds of values.
The following examples introduce new features gradually, starting with t1.geo. The files corresponding to these examples are available in the tutorial directory of the Gmsh distribution.
To learn how to run Gmsh on your computer, see Running Gmsh on your system. Screencasts that show how to use the GUI are available on http://geuz.org/gmsh/screencasts/.
/*********************************************************************
*
* Gmsh tutorial 1
*
* Variables, elementary entities (points, lines, surfaces), physical
* entities (points, lines, surfaces)
*
*********************************************************************/
// The simplest construction in Gmsh's scripting language is the
// `affectation'. The following command defines a new variable `lc':
lc = 1e-2;
// This variable can then be used in the definition of Gmsh's simplest
// `elementary entity', a `Point'. A Point is defined by a list of
// four numbers: three coordinates (X, Y and Z), and a characteristic
// length (lc) that sets the target element size at the point:
Point(1) = {0, 0, 0, lc};
// The distribution of the mesh element sizes is then obtained by
// interpolation of these characteristic lengths throughout the
// geometry. Another method to specify characteristic lengths is to
// use a background mesh (see `t7.geo' and `bgmesh.pos').
// We can then define some additional points as well as our first
// curve. Curves are Gmsh's second type of elementery entities, and,
// amongst curves, straight lines are the simplest. A straight line is
// defined by a list of point numbers. In the commands below, for
// example, the line 1 starts at point 1 and ends at point 2:
Point(2) = {.1, 0, 0, lc} ;
Point(3) = {.1, .3, 0, lc} ;
Point(4) = {0, .3, 0, lc} ;
Line(1) = {1,2} ;
Line(2) = {3,2} ;
Line(3) = {3,4} ;
Line(4) = {4,1} ;
// The third elementary entity is the surface. In order to define a
// simple rectangular surface from the four lines defined above, a
// line loop has first to be defined. A line loop is a list of
// connected lines, a sign being associated with each line (depending
// on the orientation of the line):
Line Loop(5) = {4,1,-2,3} ;
// We can then define the surface as a list of line loops (only one
// here, since there are no holes--see `t4.geo'):
Plane Surface(6) = {5} ;
// At this level, Gmsh knows everything to display the rectangular
// surface 6 and to mesh it. An optional step is needed if we want to
// associate specific region numbers to the various elements in the
// mesh (e.g. to the line segments discretizing lines 1 to 4 or to the
// triangles discretizing surface 6). This is achieved by the
// definition of `physical entities'. Physical entities will group
// elements belonging to several elementary entities by giving them a
// common number (a region number).
// We can for example group the points 1 and 2 into the physical
// entity 1:
Physical Point(1) = {1,2} ;
// Consequently, two punctual elements will be saved in the output
// mesh file, both with the region number 1. The mechanism is
// identical for line or surface elements:
MyLine = 99;
Physical Line(MyLine) = {1,2,4} ;
Physical Surface("My fancy surface label") = {6} ;
// All the line elements created during the meshing of lines 1, 2 and
// 4 will be saved in the output mesh file with the region number 99;
// and all the triangular elements resulting from the discretization
// of surface 6 will be given an automatic region number (100,
// associated with the label "My fancy surface label").
// Note that if no physical entities are defined, then all the
// elements in the mesh will be saved "as is", with their default
// orientation.
/*********************************************************************
*
* Gmsh tutorial 2
*
* Includes, geometrical transformations, extruded geometries,
* elementary entities (volumes), physical entities (volumes)
*
*********************************************************************/
// We first include the previous tutorial file, in order to use it as
// a basis for this one:
Include "t1.geo";
// We can then add new points and lines in the same way as we did in
// `t1.geo':
Point(5) = {0, .4, 0, lc};
Line(5) = {4, 5};
// But Gmsh also provides tools to tranform (translate, rotate, etc.)
// elementary entities or copies of elementary entities. For example,
// the point 3 can be moved by 0.05 units to the left with:
Translate {-0.05, 0, 0} { Point{3}; }
// The resulting point can also be duplicated and translated by 0.1
// along the y axis:
Translate {0, 0.1, 0} { Duplicata{ Point{3}; } }
// This command created a new point with an automatically assigned
// id. This id can be obtained using the graphical user interface by
// hovering the mouse over it and looking at the bottom of the graphic
// window: in this case, the new point has id "6". Point 6 can then be
// used to create new entities, e.g.:
Line(7) = {3, 6};
Line(8) = {6, 5};
Line Loop(10) = {5,-8,-7,3};
Plane Surface(11) = {10};
// Using the graphical user interface to obtain the ids of newly
// created entities can sometimes be cumbersome. It can then be
// advantageous to use the return value of the transformation commands
// directly. For example, the Translate command returns a list
// containing the ids of the translated entities. For example, we can
// translate copies of the two surfaces 6 and 11 to the right with the
// following command:
my_new_surfs[] = Translate {0.12, 0, 0} { Duplicata{ Surface{6, 11}; } };
// my_new_surfs[] (note the square brackets) denotes a list, which in
// this case contains the ids of the two new surfaces (check
// `Tools->Message console' to see the message):
Printf("New surfaces '%g' and '%g'", my_new_surfs[0], my_new_surfs[1]);
// In Gmsh lists use square brackets for their definition (mylist[] =
// {1,2,3};) as well as to access their elements (myotherlist[] =
// {mylist[0], mylist[2]};). Note that list indexing starts at 0.
// Volumes are the fourth type of elementary entities in Gmsh. In the
// same way one defines line loops to build surfaces, one has to
// define surface loops (i.e. `shells') to build volumes. The
// following volume does not have holes and thus consists of a single
// surface loop:
Point(100) = {0., 0.3, 0.13, lc}; Point(101) = {0.08, 0.3, 0.1, lc};
Point(102) = {0.08, 0.4, 0.1, lc}; Point(103) = {0., 0.4, 0.13, lc};
Line(110) = {4, 100}; Line(111) = {3, 101};
Line(112) = {6, 102}; Line(113) = {5, 103};
Line(114) = {103, 100}; Line(115) = {100, 101};
Line(116) = {101, 102}; Line(117) = {102, 103};
Line Loop(118) = {115, -111, 3, 110}; Plane Surface(119) = {118};
Line Loop(120) = {111, 116, -112, -7}; Plane Surface(121) = {120};
Line Loop(122) = {112, 117, -113, -8}; Plane Surface(123) = {122};
Line Loop(124) = {114, -110, 5, 113}; Plane Surface(125) = {124};
Line Loop(126) = {115, 116, 117, 114}; Plane Surface(127) = {126};
Surface Loop(128) = {127, 119, 121, 123, 125, 11};
Volume(129) = {128};
// When a volume can be extruded from a surface, it is usually easier
// to use the Extrude command directly instead of creating all the
// points, lines and surfaces by hand. For example, the following
// command extrudes the surface 11 along the z axis and automatically
// creates a new volume (as well as all the needed points, lines and
// surfaces):
Extrude {0, 0, 0.12} { Surface{my_new_surfs[1]}; }
// The following command permits to manually assign a characteristic
// length to some of the new points:
Characteristic Length {103, 105, 109, 102, 28, 24, 6, 5} = lc * 3;
// Note that, if the transformation tools are handy to create complex
// geometries, it is also sometimes useful to generate the `flat'
// geometry, with an explicit list of all elementary entities. This
// can be achieved by selecting the `File->Save as->Gmsh unrolled
// geometry' menu or by typing
//
// > gmsh t2.geo -0
//
// on the command line.
// To save all the tetrahedra discretizing the volumes 129 and 130
// with a common region number, we finally define a physical
// volume:
Physical Volume (1) = {129,130};
/*********************************************************************
*
* Gmsh tutorial 3
*
* Extruded meshes, parameters, options
*
*********************************************************************/
// Again, we start by including the first tutorial:
Include "t1.geo";
// As in `t2.geo', we plan to perform an extrusion along the z axis.
// But here, instead of only extruding the geometry, we also want to
// extrude the 2D mesh. This is done with the same `Extrude' command,
// but by specifying element 'Layers' (2 layers in this case, the
// first one with 8 subdivisions and the second one with 2
// subdivisions, both with a height of h/2):
h = 0.1;
Extrude {0,0,h} {
Surface{6}; Layers{ {8,2}, {0.5,1} };
}
// The extrusion can also be performed with a rotation instead of a
// translation, and the resulting mesh can be recombined into prisms
// (we use only one layer here, with 7 subdivisions). All rotations
// are specified by an axis direction ({0,1,0}), an axis point
// ({-0.1,0,0.1}) and a rotation angle (-Pi/2):
Extrude { {0,1,0} , {-0.1,0,0.1} , -Pi/2 } {
Surface{122}; Layers{7}; Recombine;
}
// Note that a translation ({-2*h,0,0}) and a rotation ({1,0,0},
// {0,0.15,0.25}, Pi/2) can also be combined. Here the angle is
// specified as a 'parameter', using the 'DefineConstant' syntax.
// This parameter can be modified insteractively in the GUI, and
// can be exchanged with other codes using the ONELAB framework:
DefineConstant[ angle = {90, Min 0, Max 120, Step 1,
Label "Extrusion angle", Path "Parameters"} ];
out[] = Extrude { {-2*h,0,0}, {1,0,0} , {0,0.15,0.25} , angle * Pi / 180 } {
Surface{144}; Layers{10}; Recombine;
};
// In this last extrusion command we retrieved the volume number
// programatically by using the return value (a list) of the Extrude
// command. This list contains the "top" of the extruded surface (in
// out[0]), the newly created volume (in out[1]) and the ids of the
// lateral surfaces (in out[2], out[3], ...)
// We can then define a new physical volume to save all the tetrahedra
// with a common region number (101):
Physical Volume(101) = {1, 2, out[1]};
// Let us now change some options... Since all interactive options are
// accessible in Gmsh's scripting language, we can for example define
// a global characteristic length factor or redefine some colors
// directly in the input file:
Mesh.CharacteristicLengthFactor = 4;
General.Color.Text = White;
Geometry.Color.Points = Orange;
Mesh.Color.Points = {255,0,0};
// Note that all colors can be defined literally or numerically, i.e.
// `Mesh.Color.Points = Red' is equivalent to `Mesh.Color.Points =
// {255,0,0}'; and also note that, as with user-defined variables, the
// options can be used either as right or left hand sides, so that the
// following command will set the surface color to the same color as
// the points:
Geometry.Color.Surfaces = Geometry.Color.Points;
// You can use the `Help->Current options' menu to see the current
// values of all options. To save all the options in a file, use
// `File->Save as->Gmsh options'. To associate the current options
// with the current file use `File->Save Options->For Current
// File'. To save the current options for all future Gmsh sessions use
// `File->Save Options->As default'.
/*********************************************************************
*
* Gmsh tutorial 4
*
* Built-in functions, holes, strings, mesh color
*
*********************************************************************/
// As usual, we start by defining some variables:
cm = 1e-02;
e1 = 4.5 * cm; e2 = 6 * cm / 2; e3 = 5 * cm / 2;
h1 = 5 * cm; h2 = 10 * cm; h3 = 5 * cm; h4 = 2 * cm; h5 = 4.5 * cm;
R1 = 1 * cm; R2 = 1.5 * cm; r = 1 * cm;
Lc1 = 0.01;
Lc2 = 0.003;
// We can use all the usual mathematical functions (note the
// capitalized first letters), plus some useful functions like
// Hypot(a, b) := Sqrt(a^2 + b^2):
ccos = (-h5*R1 + e2 * Hypot(h5, Hypot(e2, R1))) / (h5^2 + e2^2);
ssin = Sqrt(1 - ccos^2);
// Then we define some points and some lines using these variables:
Point(1) = {-e1-e2, 0 , 0, Lc1}; Point(2) = {-e1-e2, h1 , 0, Lc1};
Point(3) = {-e3-r , h1 , 0, Lc2}; Point(4) = {-e3-r , h1+r , 0, Lc2};
Point(5) = {-e3 , h1+r , 0, Lc2}; Point(6) = {-e3 , h1+h2, 0, Lc1};
Point(7) = { e3 , h1+h2, 0, Lc1}; Point(8) = { e3 , h1+r , 0, Lc2};
Point(9) = { e3+r , h1+r , 0, Lc2}; Point(10)= { e3+r , h1 , 0, Lc2};
Point(11)= { e1+e2, h1 , 0, Lc1}; Point(12)= { e1+e2, 0 , 0, Lc1};
Point(13)= { e2 , 0 , 0, Lc1};
Point(14)= { R1 / ssin, h5+R1*ccos, 0, Lc2};
Point(15)= { 0 , h5 , 0, Lc2};
Point(16)= {-R1 / ssin, h5+R1*ccos, 0, Lc2};
Point(17)= {-e2 , 0.0 , 0, Lc1};
Point(18)= {-R2 , h1+h3 , 0, Lc2}; Point(19)= {-R2 , h1+h3+h4, 0, Lc2};
Point(20)= { 0 , h1+h3+h4, 0, Lc2}; Point(21)= { R2 , h1+h3+h4, 0, Lc2};
Point(22)= { R2 , h1+h3 , 0, Lc2}; Point(23)= { 0 , h1+h3 , 0, Lc2};
Point(24)= { 0, h1+h3+h4+R2, 0, Lc2}; Point(25)= { 0, h1+h3-R2, 0, Lc2};
Line(1) = {1 , 17};
Line(2) = {17, 16};
// Gmsh provides other curve primitives than stright lines: splines,
// B-splines, circle arcs, ellipse arcs, etc. Here we define a new
// circle arc, starting at point 14 and ending at point 16, with the
// circle's center being the point 15:
Circle(3) = {14,15,16};
// Note that, in Gmsh, circle arcs should always be smaller than
// Pi. We can then define additional lines and circles, as well as a
// new surface:
Line(4) = {14,13}; Line(5) = {13,12}; Line(6) = {12,11};
Line(7) = {11,10}; Circle(8) = {8,9,10}; Line(9) = {8,7};
Line(10) = {7,6}; Line(11) = {6,5}; Circle(12) = {3,4,5};
Line(13) = {3,2}; Line(14) = {2,1}; Line(15) = {18,19};
Circle(16) = {21,20,24}; Circle(17) = {24,20,19};
Circle(18) = {18,23,25}; Circle(19) = {25,23,22};
Line(20) = {21,22};
Line Loop(21) = {17,-15,18,19,-20,16};
Plane Surface(22) = {21};
// But we still need to define the exterior surface. Since this
// surface has a hole, its definition now requires two lines loops:
Line Loop(23) = {11,-12,13,14,1,2,-3,4,5,6,7,-8,9,10};
Plane Surface(24) = {23,21};
// As a general rule, if a surface has N holes, it is defined by N+1
// line loops: the first loop defines the exterior boundary; the other
// loops define the boundaries of the holes.
// Finally, we can add some comments by embedding a post-processing
// view containing some strings, and change the color of some mesh
// entities:
View "comments" {
// Add a text string in window coordinates, 10 pixels from the left
// and 10 pixels from the bottom:
T2(10, -10, 0){ "Copyright (C) My Company" };
// Add another text string in window coordinates, 10 pixels from the
// left and 15 pixels from the top, using the StrCat() function to
// concatenate a string with the current date:
T2(10, 15, 0){ StrCat("File created on ", Today) };
// Add a text string in model coordinates at (X,Y,Z) = (0, 0.11, 0):
T3(0, 0.11, 0, 0){ "Hole" };
};
Color Grey50{ Surface{ 22 }; }
Color Purple{ Surface{ 24 }; }
Color Red{ Line{ 1:14 }; }
Color Yellow{ Line{ 15:20 }; }
/*********************************************************************
*
* Gmsh tutorial 5
*
* Characteristic lengths, arrays of variables, functions, loops
*
*********************************************************************/
// We start by defining some target mesh sizes:
lcar1 = .1;
lcar2 = .0005;
lcar3 = .055;
// If we wanted to change these mesh sizes globally (without changing
// the above definitions), we could give a global scaling factor for
// all characteristic lengths on the command line with the `-clscale'
// option (or with `Mesh.CharacteristicLengthFactor' in an option
// file). For example, with:
//
// > gmsh t5.geo -clscale 1
//
// this input file produces a mesh of approximately 1,300 nodes and
// 11,000 tetrahedra. With
//
// > gmsh t5.geo -clscale 0.2
//
// the mesh counts approximately 350,000 nodes and 2.1 million
// tetrahedra. You can check mesh statistics in the graphical user
// interface with the `Tools->Statistics' menu.
// We proceed by defining some elementary entities describing a
// truncated cube:
Point(1) = {0.5,0.5,0.5,lcar2}; Point(2) = {0.5,0.5,0,lcar1};
Point(3) = {0,0.5,0.5,lcar1}; Point(4) = {0,0,0.5,lcar1};
Point(5) = {0.5,0,0.5,lcar1}; Point(6) = {0.5,0,0,lcar1};
Point(7) = {0,0.5,0,lcar1}; Point(8) = {0,1,0,lcar1};
Point(9) = {1,1,0,lcar1}; Point(10) = {0,0,1,lcar1};
Point(11) = {0,1,1,lcar1}; Point(12) = {1,1,1,lcar1};
Point(13) = {1,0,1,lcar1}; Point(14) = {1,0,0,lcar1};
Line(1) = {8,9}; Line(2) = {9,12}; Line(3) = {12,11};
Line(4) = {11,8}; Line(5) = {9,14}; Line(6) = {14,13};
Line(7) = {13,12}; Line(8) = {11,10}; Line(9) = {10,13};
Line(10) = {10,4}; Line(11) = {4,5}; Line(12) = {5,6};
Line(13) = {6,2}; Line(14) = {2,1}; Line(15) = {1,3};
Line(16) = {3,7}; Line(17) = {7,2}; Line(18) = {3,4};
Line(19) = {5,1}; Line(20) = {7,8}; Line(21) = {6,14};
Line Loop(22) = {-11,-19,-15,-18}; Plane Surface(23) = {22};
Line Loop(24) = {16,17,14,15}; Plane Surface(25) = {24};
Line Loop(26) = {-17,20,1,5,-21,13}; Plane Surface(27) = {26};
Line Loop(28) = {-4,-1,-2,-3}; Plane Surface(29) = {28};
Line Loop(30) = {-7,2,-5,-6}; Plane Surface(31) = {30};
Line Loop(32) = {6,-9,10,11,12,21}; Plane Surface(33) = {32};
Line Loop(34) = {7,3,8,9}; Plane Surface(35) = {34};
Line Loop(36) = {-10,18,-16,-20,4,-8}; Plane Surface(37) = {36};
Line Loop(38) = {-14,-13,-12,19}; Plane Surface(39) = {38};
// Instead of using included files, we now use a user-defined function
// in order to carve some holes in the cube:
Function CheeseHole
// In the following commands we use the reserved variable name
// `newp', which automatically selects a new point number. This
// number is chosen as the highest current point number, plus
// one. (Note that, analogously to `newp', the variables `newc',
// `news', `newv' and `newreg' select the highest number amongst
// currently defined curves, surfaces, volumes and `any entities
// other than points', respectively.)
p1 = newp; Point(p1) = {x, y, z, lcar3} ;
p2 = newp; Point(p2) = {x+r,y, z, lcar3} ;
p3 = newp; Point(p3) = {x, y+r,z, lcar3} ;
p4 = newp; Point(p4) = {x, y, z+r,lcar3} ;
p5 = newp; Point(p5) = {x-r,y, z, lcar3} ;
p6 = newp; Point(p6) = {x, y-r,z, lcar3} ;
p7 = newp; Point(p7) = {x, y, z-r,lcar3} ;
c1 = newreg; Circle(c1) = {p2,p1,p7}; c2 = newreg; Circle(c2) = {p7,p1,p5};
c3 = newreg; Circle(c3) = {p5,p1,p4}; c4 = newreg; Circle(c4) = {p4,p1,p2};
c5 = newreg; Circle(c5) = {p2,p1,p3}; c6 = newreg; Circle(c6) = {p3,p1,p5};
c7 = newreg; Circle(c7) = {p5,p1,p6}; c8 = newreg; Circle(c8) = {p6,p1,p2};
c9 = newreg; Circle(c9) = {p7,p1,p3}; c10 = newreg; Circle(c10) = {p3,p1,p4};
c11 = newreg; Circle(c11) = {p4,p1,p6}; c12 = newreg; Circle(c12) = {p6,p1,p7};
// We need non-plane surfaces to define the spherical holes. Here we
// use ruled surfaces, which can have 3 or 4 sides:
l1 = newreg; Line Loop(l1) = {c5,c10,c4}; Ruled Surface(newreg) = {l1};
l2 = newreg; Line Loop(l2) = {c9,-c5,c1}; Ruled Surface(newreg) = {l2};
l3 = newreg; Line Loop(l3) = {c12,-c8,-c1}; Ruled Surface(newreg) = {l3};
l4 = newreg; Line Loop(l4) = {c8,-c4,c11}; Ruled Surface(newreg) = {l4};
l5 = newreg; Line Loop(l5) = {-c10,c6,c3}; Ruled Surface(newreg) = {l5};
l6 = newreg; Line Loop(l6) = {-c11,-c3,c7}; Ruled Surface(newreg) = {l6};
l7 = newreg; Line Loop(l7) = {-c2,-c7,-c12};Ruled Surface(newreg) = {l7};
l8 = newreg; Line Loop(l8) = {-c6,-c9,c2}; Ruled Surface(newreg) = {l8};
// We then store the surface loops identification numbers in a list
// for later reference (we will need these to define the final
// volume):
theloops[t] = newreg ;
Surface Loop(theloops[t]) = {l8+1,l5+1,l1+1,l2+1,l3+1,l7+1,l6+1,l4+1};
thehole = newreg ;
Volume(thehole) = theloops[t] ;
Return
// We can use a `For' loop to generate five holes in the cube:
x = 0 ; y = 0.75 ; z = 0 ; r = 0.09 ;
For t In {1:5}
x += 0.166 ;
z += 0.166 ;
// We call the `CheeseHole' function:
Call CheeseHole ;
// We define a physical volume for each hole:
Physical Volume (t) = thehole ;
// We also print some variables on the terminal (note that, since
// all variables are treated internally as floating point numbers,
// the format string should only contain valid floating point format
// specifiers like `%g', `%f', '%e', etc.):
Printf("Hole %g (center = {%g,%g,%g}, radius = %g) has number %g!",
t, x, y, z, r, thehole) ;
EndFor
// We can then define the surface loop for the exterior surface of the
// cube:
theloops[0] = newreg ;
Surface Loop(theloops[0]) = {35,31,29,37,33,23,39,25,27} ;
// The volume of the cube, without the 5 holes, is now defined by 6
// surface loops: the first surface loop defines the exterior surface;
// the surface loops other than the first one define holes. (Again,
// to reference an array of variables, its identifier is followed by
// square brackets):
Volume(186) = {theloops[]} ;
// We finally define a physical volume for the elements discretizing
// the cube, without the holes (whose elements were already tagged
// with numbers 1 to 5 in the `For' loop):
Physical Volume (10) = 186 ;
/*********************************************************************
*
* Gmsh tutorial 6
*
* Transfinite meshes
*
*********************************************************************/
// Let's use the geometry from the first tutorial as a basis for this
// one
Include "t1.geo";
// Delete the left line and create replace it with 3 new ones
Delete{ Surface{6}; Line{4}; }
p1 = newp; Point(p1) = {-0.05, 0.05, 0, lc};
p2 = newp; Point(p2) = {-0.05, 0.1, 0, lc};
l1 = newl; Line(l1) = {1, p1};
l2 = newl; Line(l2) = {p1, p2};
l3 = newl; Line(l3) = {p2, 4};
// Create surface
Line Loop(1) = {2, -1, l1, l2, l3, -3};
Plane Surface(1) = {1};
// Put 20 points with a refinement toward the extremities on curve 2
Transfinite Line{2} = 20 Using Bump 0.05;
// Put 20 points total on combination of curves l1, l2 and l3 (beware
// that the points p1 and p2 are shared by the curves, so we do not
// create 6 + 6 + 10 = 22 points, but 20!)
Transfinite Line{l1} = 6;
Transfinite Line{l2} = 6;
Transfinite Line{l3} = 10;
// Put 30 points following a geometric progression on curve 1
// (reversed) and on curve 3
Transfinite Line{-1,3} = 30 Using Progression 1.2;
// Define the Surface as transfinite, by specifying the four corners
// of the transfinite interpolation
Transfinite Surface{1} = {1,2,3,4};
// (Note that the list on the right hand side refers to points, not
// curves. When the surface has only 3 or 4 points on its boundary the
// list can be omitted. The way triangles are generated can be
// controlled by appending "Left", "Right" or "Alternate" after the
// list.)
// Recombine the triangles into quads
Recombine Surface{1};
// Apply an elliptic smoother to the grid
Mesh.Smoothing = 100;
Physical Surface(1) = 1;
/********************************************************************* * * Gmsh tutorial 7 * * Background mesh * *********************************************************************/ // Characteristic lengths can be specified very accuractely by // providing a background mesh, i.e., a post-processing view that // contains the target mesh sizes. // Merge the first tutorial Merge "t1.geo"; // Merge a post-processing view containing the target mesh sizes Merge "bgmesh.pos"; // Apply the view as the current background mesh Background Mesh View[0];
/*********************************************************************
*
* Gmsh tutorial 8
*
* Post-processing, scripting, animations, options
*
*********************************************************************/
// We first include `t1.geo' as well as some post-processing views:
Include "t1.geo";
Include "view1.pos";
Include "view1.pos";
Include "view4.pos";
// We then set some general options:
General.Trackball = 0;
General.RotationX = 0; General.RotationY = 0; General.RotationZ = 0;
General.Color.Background = White; General.Color.Foreground = Black;
General.Color.Text = Black;
General.Orthographic = 0;
General.Axes = 0; General.SmallAxes = 0;
// We also set some options for each post-processing view:
v0 = PostProcessing.NbViews-4;
v1 = v0+1; v2 = v0+2; v3 = v0+3;
View[v0].IntervalsType = 2;
View[v0].OffsetZ = 0.05;
View[v0].RaiseZ = 0;
View[v0].Light = 1;
View[v0].ShowScale = 0;
View[v0].SmoothNormals = 1;
View[v1].IntervalsType = 1;
View[v1].ColorTable = { Green, Blue };
View[v1].NbIso = 10;
View[v1].ShowScale = 0;
View[v2].Name = "Test...";
View[v2].Axes = 1;
View[v2].Color.Axes = Black;
View[v2].IntervalsType = 2;
View[v2].Type = 2;
View[v2].IntervalsType = 2;
View[v2].AutoPosition = 0;
View[v2].PositionX = 85;
View[v2].PositionY = 50;
View[v2].Width = 200;
View[v2].Height = 130;
View[v3].Visible = 0;
// We then loop from 1 to 255 with a step of 1. (To use a different
// step, just add a third argument in the list. For example, `For num
// In {0.5:1.5:0.1}' would increment num from 0.5 to 1.5 with a step
// of 0.1.)
t = 0;
//For num In {1:1}
For num In {1:255}
View[v0].TimeStep = t;
View[v1].TimeStep = t;
View[v2].TimeStep = t;
View[v3].TimeStep = t;
t = (View[v0].TimeStep < View[v0].NbTimeStep-1) ? t+1 : 0;
View[v0].RaiseZ += 0.01/View[v0].Max * t;
If (num == 3)
// We want to create 320x240 frames when num == 3:
General.GraphicsWidth = 320;
General.GraphicsHeight = 240;
EndIf
// It is possible to nest loops:
For num2 In {1:50}
General.RotationX += 10;
General.RotationY = General.RotationX / 3;
General.RotationZ += 0.1;
Sleep 0.01; // sleep for 0.01 second
Draw; // draw the scene
If (num == 3)
// The `Print' command saves the graphical window; the `Sprintf'
// function permits to create the file names on the fly:
Print Sprintf("t8-%02g.gif", num2);
Print Sprintf("t8-%02g.jpg", num2);
EndIf
EndFor
If(num == 3)
// Here we could make a system call to generate a movie. For example,
// with whirlgif:
//
// System "whirlgif -minimize -loop -o t8.gif t8-*.gif";
// with mpeg_encode:
//
// System "mpeg_encode t8.par";
// with mencoder:
//
// System "mencoder 'mf://*.jpg' -mf fps=5 -o t8.mpg -ovc lavc
// -lavcopts vcodec=mpeg1video:vhq";
// System "mencoder 'mf://*.jpg' -mf fps=5 -o t8.mpg -ovc lavc
// -lavcopts vcodec=mpeg4:vhq";
// with ffmpeg:
//
// System "ffmpeg -hq -r 5 -b 800 -vcodec mpeg1video
// -i t8-%02d.jpg t8.mpg"
// System "ffmpeg -hq -r 5 -b 800 -i t8-%02d.jpg t8.asf"
EndIf
EndFor
/********************************************************************* * * Gmsh tutorial 9 * * Post-processing plugins (levelsets, sections, annotations) * *********************************************************************/ // Plugins can be added to Gmsh in order to extend its // capabilities. For example, post-processing plugins can modify a // view, or create a new view based on previously loaded // views. Several default plugins are statically linked with Gmsh, // e.g. Isosurface, CutPlane, CutSphere, Skin, Transform or Smooth. // Plugins can be controlled in the same way as other options: either // from the graphical interface (right click on the view button, then // `Plugins'), or from the command file. // Let us for example include a three-dimensional scalar view: Include "view3.pos" ; // We then set some options for the `Isosurface' plugin (which // extracts an isosurface from a 3D scalar view), and run it: Plugin(Isosurface).Value = 0.67 ; // iso-value level Plugin(Isosurface).View = 0 ; // source view is View[0] Plugin(Isosurface).Run ; // run the plugin! // We also set some options for the `CutPlane' plugin (which computes // a section of a 3D view using the plane A*x+B*y+C*z+D=0), and then // run it: Plugin(CutPlane).A = 0 ; Plugin(CutPlane).B = 0.2 ; Plugin(CutPlane).C = 1 ; Plugin(CutPlane).D = 0 ; Plugin(CutPlane).View = 0 ; Plugin(CutPlane).Run ; // Add a title (By convention, for window coordinates a value greater // than 99999 represents the center. We could also use // `General.GraphicsWidth / 2', but that would only center the string // for the current window size.): Plugin(Annotate).Text = "A nice title" ; Plugin(Annotate).X = 1.e5; Plugin(Annotate).Y = 50 ; Plugin(Annotate).Font = "Times-BoldItalic" ; Plugin(Annotate).FontSize = 28 ; Plugin(Annotate).Align = "Center" ; Plugin(Annotate).View = 0 ; Plugin(Annotate).Run ; Plugin(Annotate).Text = "(and a small subtitle)" ; Plugin(Annotate).Y = 70 ; Plugin(Annotate).Font = "Times-Roman" ; Plugin(Annotate).FontSize = 12 ; Plugin(Annotate).Run ; // We finish by setting some options: View[0].Light = 1; View[0].IntervalsType = 1; View[0].NbIso = 6; View[0].SmoothNormals = 1; View[1].IntervalsType = 2; View[2].IntervalsType = 2;
/*********************************************************************
*
* Gmsh tutorial 10
*
* General mesh size fields
*
*********************************************************************/
// In addition to specifying target mesh sizes at the points of the
// geometry (see t1) or using a background mesh (see t7), you can use
// general mesh size "Fields".
// Let's create a simple rectangular geometry
lc = .15;
Point(1) = {0.0,0.0,0,lc}; Point(2) = {1,0.0,0,lc};
Point(3) = {1,1,0,lc}; Point(4) = {0,1,0,lc};
Point(5) = {0.2,.5,0,lc};
Line(1) = {3,2}; Line(2) = {2,1}; Line(3) = {1,4}; Line(4) = {4,3};
Line Loop(5) = {1,2,3,4}; Plane Surface(6) = {5};
// Say we would like to obtain mesh elements with size lc/30 near line
// 1 and point 5, and size lc elsewhere. To achieve this, we can use
// two fields: "Attractor", and "Threshold". We first define an
// Attractor field (Field[1]) on points 5 and on line 1. This field
// returns the distance to point 5 and to (100 equidistant points on)
// line 1.
Field[1] = Attractor;
Field[1].NodesList = {5};
Field[1].NNodesByEdge = 100;
Field[1].EdgesList = {1};
// We then define a Threshold field, which uses the return value of
// the Attractor Field[1] in order to define a simple change in
// element size around the attractors (i.e., around point 5 and line
// 1)
//
// LcMax - /------------------
// /
// /
// /
// LcMin -o----------------/
// | | |
// Attractor DistMin DistMax
Field[2] = Threshold;
Field[2].IField = 1;
Field[2].LcMin = lc / 30;
Field[2].LcMax = lc;
Field[2].DistMin = 0.15;
Field[2].DistMax = 0.5;
// Say we want to modulate the mesh element sizes using a mathematical
// function of the spatial coordinates. We can do this with the
// MathEval field:
Field[3] = MathEval;
Field[3].F = "Cos(4*3.14*x) * Sin(4*3.14*y) / 10 + 0.101";
// We could also combine MathEval with values coming from other
// fields. For example, let's define an Attractor around point 1
Field[4] = Attractor;
Field[4].NodesList = {1};
// We can then create a MathEval field with a function that depends on
// the return value of the Attractr Field[4], i.e., depending on the
// distance to point 1 (here using a cubic law, with minumum element
// size = lc / 100)
Field[5] = MathEval;
Field[5].F = Sprintf("F4^3 + %g", lc / 100);
// We could also use a Box field to impose a step change in element
// sizes inside a box
Field[6] = Box;
Field[6].VIn = lc / 15;
Field[6].VOut = lc;
Field[6].XMin = 0.3;
Field[6].XMax = 0.6;
Field[6].YMin = 0.3;
Field[6].YMax = 0.6;
// Many other types of fields are available: see the reference manual
// for a complete list. You can also create fields directly in the
// graphical user interface by selecting Define->Fields in the Mesh
// module.
// Finally, let's use the minimum of all the fields as the background
// mesh field
Field[7] = Min;
Field[7].FieldsList = {2, 3, 5, 6};
Background Field = 7;
// Don't extend the elements sizes from the boundary inside the domain
Mesh.CharacteristicLengthExtendFromBoundary = 0;
/*********************************************************************
*
* Gmsh tutorial 11
*
* Unstructured quadrangular meshes
*
*********************************************************************/
// We have seen in tutorials t3 and t6 that extruded and transfinite
// meshes can be "recombined" into quads/prisms/hexahedra by using the
// "Recombine" keyword. Unstructured meshes can be recombined in the
// same way. Let's define a simple geometry with an analytical mesh
// size field:
Point(1) = {-1.25, -.5, 0}; Point(2) = {-1.25, 1.25, 0};
Point(3) = {1.25, -.5, 0}; Point(4) = {1.25, 1.25, 0};
Line(1) = {1, 2}; Line(2) = {2, 4};
Line(3) = {4, 3}; Line(4) = {3, 1};
Line Loop(4) = {1,2, 3, 4}; Plane Surface(100) = {4};
Field[1] = MathEval;
Field[1].F = "0.01*(1.0+30.*(y-x*x)*(y-x*x) + (1-x)*(1-x))";
Background Field = 1;
// To generate quadrangles instead of triangles, we can simply add
Recombine Surface{100};
// If we'd had several surfaces, we could have used 'Recombine Surface
// "*";'. Yet another way would be to specify the global option
// "Mesh.RecombineAll = 1;".
// The default recombination algorithm is called "Blossom": it uses a
// minimum cost perfect matching algorithm to generate fully
// quadrilateral meshes from triangulations. More details about the
// algorithm can be found in the following paper: J.-F. Remacle,
// J. Lambrechts, B. Seny, E. Marchandise, A. Johnen and C. Geuzaine,
// "Blossom-Quad: a non-uniform quadrilateral mesh generator using a
// minimum cost perfect matching algorithm", International Journal for
// Numerical Methods in Engineering, 2011 (in press).
// For even better quadrilateral meshes, you can try the experimental
// "Delaunay for quads" (DelQuad) meshing algorithm: DelQuad is a
// triangulation algorithm that enables to create right triangles
// almost everywhere. Uncomment the following line to try DelQuad:
Mesh.Algorithm = 8; // DelQuad (experimental)
/*********************************************************************
*
* Gmsh tutorial 12
*
* Cross-patch meshing with compounds
*
*********************************************************************/
// Compound geometrical entities can be defined to compute a new
// parametrization of groups of elementary geometrical entities. This
// parametrization can then be used for remeshing the compound as if
// it were a single CAD entity.
lc = 0.2;
Point(1) = {0, 0, 0, lc}; Point(2) = {1, 0, 0, lc};
Point(3) = {1, 1, 0.5, lc}; Point(4) = {0, 1, 0.4, lc};
Point(5) = {0.3, 0.2, 0, lc}; Point(6) = {0, 0.01, 0.01, lc};
Point(7) = {0, 0.02, 0.02, lc}; Point(8) = {1, 0.05, 0.02, lc};
Point(9) = {1, 0.32, 0.02, lc};
Line(1) = {1, 2}; Line(2) = {2, 8}; Line(3) = {8, 9};
Line(4) = {9, 3}; Line(5) = {3, 4}; Line(6) = {4, 7};
Line(7) = {7, 6}; Line(8) = {6, 1}; Spline(9) = {7, 5, 9};
Line(10) = {6, 8};
Line Loop(11) = {5, 6, 9, 4}; Ruled Surface(12) = {11};
Line Loop(13) = {9, -3, -10, -7}; Ruled Surface(14) = {13};
Line Loop(15) = {10, -2, -1, -8}; Ruled Surface(16) = {15};
// Treat lines 2, 3 and 4 as a single line
Compound Line(100) = {2, 3, 4};
// Idem with lines 6, 7 and 8
Compound Line(101) = {6, 7, 8};
// Treat surfaces 12, 14 and 16 as a single surface
Compound Surface(200) = {12, 14, 16};
// Hide the original surfaces so we only see the compound
// (cross-patch) mesh
//Hide {Surface{12, 14, 16}; }
// More details about the reparametrization technique can be found in
// the following papers:
//
// * J.-F. Remacle, C. Geuzaine, G. Compère and E. Marchandise,
// "High-Quality Surface Remeshing Using Harmonic Maps",
// International Journal for Numerical Methods in Engineering,
// 83 (4), pp. 403-425, 2010.
//
// * E. Marchandise, G. Compère, M. Willemet, G. Bricteux, C. Geuzaine
// and J-F Remacle, "Quality meshing based on STL triangulations for
// biomedical simulations", International Journal for Numerical
// Methods in Biomedical Engineering", 26 (7), pp. 876-889, 2010.
//
// * E. Marchandise, C. Carton de Wiart, W. G. Vos, C. Geuzaine and
// J.-F. Remacle, "High Quality Surface Remeshing Using Harmonic
// Maps. Part II: Surfaces with High Genus and of Large Aspect
// Ratio", International Journal for Numerical Methods in
// Engineering, 86 (11), pp. 1303-1321, 2011.
/*********************************************************************
*
* Gmsh tutorial 13
*
* Remeshing STL with compounds
*
*********************************************************************/
// Since compound geometrical compute a new parametrization, one can
// also use them to remesh STL files, even if in this case there's
// usually only a single elementary geometrical entity per compound.
// Let's merge the mesh that we would like to remesh. This mesh was
// reclassified ("colored") from an initial STL triangulation using
// the "Reclassify 2D" tool in Gmsh, so that we could split it along
// sharp geometrical features.
Merge "t13_data.msh";
// Since the original mesh is a bit coarse, we refine it once
RefineMesh;
// Create the topology of the discrete model
CreateTopology;
// We can now define a compound line (resp. surface) for each discrete
// line (resp. surface) in the model
ll[] = Line "*";
For j In {0 : #ll[]-1}
Compound Line(newl) = ll[j];
EndFor
ss[] = Surface "*";
s = news;
For i In {0 : #ss[]-1}
Compound Surface(s+i) = ss[i];
EndFor
// And we can create the volume based on the new compound entities
Surface Loop(1) = {s : s + #ss[]-1};
Volume(1) = {1};
Physical Surface(1) = {s : s + #ss[]-1};
Physical Volume(1) = 1;
// Apply a funny mesh size field, just because we can :-)
Field[1] = MathEval;
Field[1].F = "2*Sin((x+y)/5) + 3";
Background Field = 1;
Mesh.RemeshAlgorithm = 1; // (0) no split (1) automatic (2) automatic only with metis
Mesh.RemeshParametrization = 1; // (0) harmonic (1) conformal
Geometry.HideCompounds = 0; // don't hide the compound entities
/*********************************************************************
*
* Gmsh tutorial 14
*
* Homology and cohomology computation
*
*********************************************************************/
// Homology computation in Gmsh finds representative chains of
// (relative) (co)homology space bases using a mesh of a model.
// The representative basis chains are stored in the mesh as
// physical groups of Gmsh, one for each chain.
// Create an example geometry
m = 0.5; // mesh characteristic length
h = 2; // height in the z-direction
Point(1) = {0, 0, 0, m}; Point(2) = {10, 0, 0, m};
Point(3) = {10, 10, 0, m}; Point(4) = {0, 10, 0, m};
Point(5) = {4, 4, 0, m}; Point(6) = {6, 4, 0, m};
Point(7) = {6, 6, 0, m}; Point(8) = {4, 6, 0, m};
Point(9) = {2, 0, 0, m}; Point(10) = {8, 0, 0, m};
Point(11) = {2, 10, 0, m}; Point(12) = {8, 10, 0, m};
Line(1) = {1, 9}; Line(2) = {9, 10}; Line(3) = {10, 2};
Line(4) = {2, 3}; Line(5) = {3, 12}; Line(6) = {12, 11};
Line(7) = {11, 4}; Line(8) = {4, 1}; Line(9) = {5, 6};
Line(10) = {6, 7}; Line(11) = {7, 8}; Line(12) = {8, 5};
Line Loop(13) = {6, 7, 8, 1, 2, 3, 4, 5};
Line Loop(14) = {11, 12, 9, 10};
Plane Surface(15) = {13, 14};
Extrude {0, 0, h}{ Surface{15}; }
// Create physical groups, which are used to define the domain of the
// (co)homology computation and the subdomain of the relative (co)homology
// computation.
// Whole domain
Physical Volume(1) = {1};
// Four "terminals" of the model
Physical Surface(70) = {36};
Physical Surface(71) = {44};
Physical Surface(72) = {52};
Physical Surface(73) = {60};
// Whole domain surface
bnd[] = Boundary{ Volume{1}; };
Physical Surface(80) = bnd[];
// Complement of the domain surface respect to the four terminals
bnd[] -= {36, 44, 52, 60};
Physical Surface(75) = bnd[];
// Find bases for relative homology spaces of
// the domain modulo the four terminals.
Homology {{1}, {70, 71, 72, 73}};
// Find homology space bases isomorphic to the previous bases:
// homology spaces modulo the non-terminal domain surface,
// a.k.a the thin cuts.
Homology {{1}, {75}};
// Find cohomology space bases isomorphic to the previous bases:
// cohomology spaces of the domain modulo the four terminals,
// a.k.a the thick cuts.
Cohomology {{1}, {70, 71, 72, 73}};
// More examples:
// Homology {1};
// Homology;
// Homology {{1}, {80}};
// Homology {{}, {80}};
This appendix lists all the available options. Gmsh's default behavior
is to save some of these options in a per-user “session resource” file
(cf. “Saved in: General.SessionFileName” in the lists below)
every time Gmsh is shut down. This permits for example to automatically
remember the size and location of the windows or which fonts to use. A
second set of options can be saved (automatically or manually with
the `File->Save Options->As Default' menu) in a per-user “option” file
(cf. “Saved in: General.OptionsFileName” in the lists below),
automatically loaded by Gmsh every time it starts up. Finally, other
options are only saved to disk manually, either by explicitely saving an
option file with `File->Save As', or when saving per-model options with
`File->Save Options->For Current File' (cf. “Saved in: -” in
the lists below).
To reset all options to their default values, use the `Restore default
options' button in `Tools->Options->General->Advanced', or erase the
General.SessionFileName and General.OptionsFileName files
by hand.
General.AxesFormatX"%.3g"General.OptionsFileName
General.AxesFormatY"%.3g"General.OptionsFileName
General.AxesFormatZ"%.3g"General.OptionsFileName
General.AxesLabelX""General.OptionsFileName
General.AxesLabelY""General.OptionsFileName
General.AxesLabelZ""General.OptionsFileName
General.BackgroundImageFileName""General.OptionsFileName
General.DefaultFileName"untitled.geo"General.OptionsFileName
General.Display""-
General.ErrorFileName".gmsh-errors"General.OptionsFileName
General.FileName""-
General.FltkTheme""General.OptionsFileName
General.GraphicsFont"Helvetica"General.OptionsFileName
General.GraphicsFontTitle"Helvetica"General.OptionsFileName
General.OptionsFileName".gmsh-options"General.SessionFileName
General.RecentFile0"untitled.geo"General.SessionFileName
General.RecentFile1"untitled.geo"General.SessionFileName
General.RecentFile2"untitled.geo"General.SessionFileName
General.RecentFile3"untitled.geo"General.SessionFileName
General.RecentFile4"untitled.geo"General.SessionFileName
General.SessionFileName".gmshrc"-
General.TextEditor"open -t %s"General.OptionsFileName
General.TmpFileName".gmsh-tmp"General.SessionFileName
General.WebBrowser"open %s"General.OptionsFileName
General.WatchFilePattern""-
General.AlphaBlending1General.OptionsFileName
General.Antialiasing0General.OptionsFileName
General.ArrowHeadRadius0.12General.OptionsFileName
General.ArrowStemLength0.56General.OptionsFileName
General.ArrowStemRadius0.02General.OptionsFileName
General.Axes0General.OptionsFileName
General.AxesMikado0General.OptionsFileName
General.AxesAutoPosition1General.OptionsFileName
General.AxesForceValue0General.OptionsFileName
General.AxesMaxX1General.OptionsFileName
General.AxesMaxY1General.OptionsFileName
General.AxesMaxZ1General.OptionsFileName
General.AxesMinX0General.OptionsFileName
General.AxesMinY0General.OptionsFileName
General.AxesMinZ0General.OptionsFileName
General.AxesTicsX5General.OptionsFileName
General.AxesTicsY5General.OptionsFileName
General.AxesTicsZ5General.OptionsFileName
General.AxesValueMaxX1General.OptionsFileName
General.AxesValueMaxY1General.OptionsFileName
General.AxesValueMaxZ1General.OptionsFileName
General.AxesValueMinX0General.OptionsFileName
General.AxesValueMinY0General.OptionsFileName
General.AxesValueMinZ0General.OptionsFileName
General.BackgroundGradient1General.OptionsFileName
General.BackgroundImagePositionX100000General.OptionsFileName
General.BackgroundImagePositionY100000General.OptionsFileName
General.Camera0General.OptionsFileName
General.CameraAperture40General.OptionsFileName
General.CameraEyeSeparationRatio1.5General.OptionsFileName
General.CameraFocalLengthRatio1General.OptionsFileName
General.Clip0A1-
General.Clip0B0-
General.Clip0C0-
General.Clip0D0-
General.Clip1A0-
General.Clip1B1-
General.Clip1C0-
General.Clip1D0-
General.Clip2A0-
General.Clip2B0-
General.Clip2C1-
General.Clip2D0-
General.Clip3A-1-
General.Clip3B0-
General.Clip3C0-
General.Clip3D1-
General.Clip4A0-
General.Clip4B-1-
General.Clip4C0-
General.Clip4D1-
General.Clip5A0-
General.Clip5B0-
General.Clip5C-1-
General.Clip5D1-
General.ClipFactor5-
General.ClipOnlyDrawIntersectingVolume0General.OptionsFileName
General.ClipOnlyVolume0General.OptionsFileName
General.ClipPositionX650General.SessionFileName
General.ClipPositionY150General.SessionFileName
General.ClipWholeElements0General.OptionsFileName
General.ColorScheme1General.OptionsFileName
General.ConfirmOverwrite1General.OptionsFileName
General.ContextPositionX650General.SessionFileName
General.ContextPositionY150General.SessionFileName
General.DetachedMenu0General.SessionFileName
General.DisplayBorderFactor0.2General.OptionsFileName
General.DoubleBuffer1General.OptionsFileName
General.DrawBoundingBoxes0General.OptionsFileName
General.ExpertMode0General.OptionsFileName
General.ExtraPositionX650General.SessionFileName
General.ExtraPositionY350General.SessionFileName
General.ExtraHeight100General.SessionFileName
General.ExtraWidth100General.SessionFileName
General.FastRedraw0General.OptionsFileName
General.FieldPositionX650General.SessionFileName
General.FieldPositionY550General.SessionFileName
General.FieldHeight300General.SessionFileName
General.FieldWidth300General.SessionFileName
General.FileChooserPositionX200General.SessionFileName
General.FileChooserPositionY200General.SessionFileName
General.FontSize-1General.OptionsFileName
General.GraphicsFontSize17General.OptionsFileName
General.GraphicsFontSizeTitle19General.OptionsFileName
General.GraphicsHeight600General.SessionFileName
General.GraphicsPositionX50General.SessionFileName
General.GraphicsPositionY50General.SessionFileName
General.GraphicsWidth800General.SessionFileName
General.InitialModule0General.OptionsFileName
General.Light01General.OptionsFileName
General.Light0X0.65General.OptionsFileName
General.Light0Y0.65General.OptionsFileName
General.Light0Z1General.OptionsFileName
General.Light0W0General.OptionsFileName
General.Light10General.OptionsFileName
General.Light1X0.5General.OptionsFileName
General.Light1Y0.3General.OptionsFileName
General.Light1Z1General.OptionsFileName
General.Light1W0General.OptionsFileName
General.Light20General.OptionsFileName
General.Light2X0.5General.OptionsFileName
General.Light2Y0.3General.OptionsFileName
General.Light2Z1General.OptionsFileName
General.Light2W0General.OptionsFileName
General.Light30General.OptionsFileName
General.Light3X0.5General.OptionsFileName
General.Light3Y0.3General.OptionsFileName
General.Light3Z1General.OptionsFileName
General.Light3W0General.OptionsFileName
General.Light40General.OptionsFileName
General.Light4X0.5General.OptionsFileName
General.Light4Y0.3General.OptionsFileName
General.Light4Z1General.OptionsFileName
General.Light4W0General.OptionsFileName
General.Light50General.OptionsFileName
General.Light5X0.5General.OptionsFileName
General.Light5Y0.3General.OptionsFileName
General.Light5Z1General.OptionsFileName
General.Light5W0General.OptionsFileName
General.LineWidth1General.OptionsFileName
General.ManipulatorPositionX650General.SessionFileName
General.ManipulatorPositionY150General.SessionFileName
General.MaxX0-
General.MaxY0-
General.MaxZ0-
General.MenuWidth200General.SessionFileName
General.MenuHeight200General.SessionFileName
General.MenuPositionX400General.SessionFileName
General.MenuPositionY400General.SessionFileName
General.MessageHeight300General.SessionFileName
General.MinX0-
General.MinY0-
General.MinZ0-
General.MouseHoverMeshes0General.OptionsFileName
General.MouseSelection1General.OptionsFileName
General.NonModalWindows1General.SessionFileName
General.NoPopup0General.OptionsFileName
General.OptionsPositionX650General.SessionFileName
General.OptionsPositionY150General.SessionFileName
General.Orthographic1General.OptionsFileName
General.PluginPositionX650General.SessionFileName
General.PluginPositionY550General.SessionFileName
General.PluginHeight300General.SessionFileName
General.PluginWidth300General.SessionFileName
General.PointSize3General.OptionsFileName
General.PolygonOffsetAlwaysOn0General.OptionsFileName
General.PolygonOffsetFactor0.5General.OptionsFileName
General.PolygonOffsetUnits1General.OptionsFileName
General.ProgressMeterStep20General.OptionsFileName
General.QuadricSubdivisions6General.OptionsFileName
General.RotationX0-
General.RotationY0-
General.RotationZ0-
General.RotationCenterGravity1General.OptionsFileName
General.RotationCenterX0-
General.RotationCenterY0-
General.RotationCenterZ0-
General.SaveOptions0General.SessionFileName
General.SaveSession1General.SessionFileName
General.ScaleX1-
General.ScaleY1-
General.ScaleZ1-
General.Shininess0.4General.OptionsFileName
General.ShininessExponent40General.OptionsFileName
General.SmallAxes1General.OptionsFileName
General.SmallAxesPositionX-60General.OptionsFileName
General.SmallAxesPositionY-40General.OptionsFileName
General.SmallAxesSize30General.OptionsFileName
General.StatisticsPositionX650General.SessionFileName
General.StatisticsPositionY150General.SessionFileName
General.Stereo0General.OptionsFileName
General.SystemMenuBar1General.SessionFileName
General.Terminal0General.OptionsFileName
General.Tooltips1General.OptionsFileName
General.Trackball1General.OptionsFileName
General.TrackballHyperbolicSheet1General.OptionsFileName
General.TrackballQuaternion00-
General.TrackballQuaternion10-
General.TrackballQuaternion20-
General.TrackballQuaternion31-
General.TranslationX0-
General.TranslationY0-
General.TranslationZ0-
General.VectorType4General.OptionsFileName
General.Verbosity5General.OptionsFileName
General.VisibilityPositionX650General.SessionFileName
General.VisibilityPositionY150General.SessionFileName
General.ZoomFactor4General.OptionsFileName
General.Color.Background{255,255,255}General.OptionsFileName
General.Color.BackgroundGradient{128,147,255}General.OptionsFileName
General.Color.Foreground{85,85,85}General.OptionsFileName
General.Color.Text{0,0,0}General.OptionsFileName
General.Color.Axes{0,0,0}General.OptionsFileName
General.Color.SmallAxes{0,0,0}General.OptionsFileName
General.Color.AmbientLight{25,25,25}General.OptionsFileName
General.Color.DiffuseLight{255,255,255}General.OptionsFileName
General.Color.SpecularLight{255,255,255}General.OptionsFileName
Print.Background0General.OptionsFileName
Print.CompositeWindows0General.OptionsFileName
Print.DeleteTemporaryFiles1General.OptionsFileName
Print.EpsBestRoot1General.OptionsFileName
Print.EpsCompress0General.OptionsFileName
Print.EpsLineWidthFactor1General.OptionsFileName
Print.EpsOcclusionCulling1General.OptionsFileName
Print.EpsPointSizeFactor1General.OptionsFileName
Print.EpsPS3Shading0General.OptionsFileName
Print.EpsQuality1General.OptionsFileName
Print.Format10General.OptionsFileName
Print.GeoLabels1General.OptionsFileName
Print.GeoOnlyPhysicals1General.OptionsFileName
Print.GifDither0General.OptionsFileName
Print.GifInterlace0General.OptionsFileName
Print.GifSort1General.OptionsFileName
Print.GifTransparent0General.OptionsFileName
Print.Height-1General.OptionsFileName
Print.JpegQuality100General.OptionsFileName
Print.JpegSmoothing0General.OptionsFileName
Print.PostElementary1General.OptionsFileName
Print.PostElement0General.OptionsFileName
Print.PostGamma0General.OptionsFileName
Print.PostEta0General.OptionsFileName
Print.PostRho0General.OptionsFileName
Print.PostDisto0General.OptionsFileName
Print.TexAsEquation0General.OptionsFileName
Print.Text1General.OptionsFileName
Print.Width-1General.OptionsFileName
Geometry.AutoCoherence1General.OptionsFileName
Geometry.Clip0-
Geometry.CopyMeshingMethod0General.OptionsFileName
Geometry.ExactExtrusion1General.OptionsFileName
Geometry.ExtrudeReturnLateralEntities1General.OptionsFileName
Geometry.ExtrudeSplinePoints5General.OptionsFileName
Geometry.HideCompounds1General.OptionsFileName
Geometry.HighlightOrphans0General.OptionsFileName
Geometry.LabelType1General.OptionsFileName
Geometry.Light1General.OptionsFileName
Geometry.LightTwoSide1General.OptionsFileName
Geometry.Lines1General.OptionsFileName
Geometry.LineNumbers0General.OptionsFileName
Geometry.LineSelectWidth2General.OptionsFileName
Geometry.LineType0General.OptionsFileName
Geometry.LineWidth2General.OptionsFileName
Geometry.MatchGeomAndMesh0General.OptionsFileName
Geometry.Normals0General.OptionsFileName
Geometry.NumSubEdges20General.OptionsFileName
Geometry.OCCFixDegenerated0General.OptionsFileName
Geometry.OCCFixSmallEdges0General.OptionsFileName
Geometry.OCCFixSmallFaces0General.OptionsFileName
Geometry.OCCSewFaces0General.OptionsFileName
Geometry.OCCConnectFaces0General.OptionsFileName
Geometry.OffsetX0-
Geometry.OffsetY0-
Geometry.OffsetZ0-
Geometry.OldCircle0General.OptionsFileName
Geometry.OldNewReg1General.OptionsFileName
Geometry.Points1General.OptionsFileName
Geometry.PointNumbers0General.OptionsFileName
Geometry.PointSelectSize5General.OptionsFileName
Geometry.PointSize4General.OptionsFileName
Geometry.PointType0General.OptionsFileName
Geometry.ScalingFactor1General.OptionsFileName
Geometry.SnapX0.1General.OptionsFileName
Geometry.SnapY0.1General.OptionsFileName
Geometry.SnapZ0.1General.OptionsFileName
Geometry.Surfaces0General.OptionsFileName
Geometry.SurfaceNumbers0General.OptionsFileName
Geometry.SurfaceType2General.OptionsFileName
Geometry.Tangents0General.OptionsFileName
Geometry.Tolerance1e-06General.OptionsFileName
Geometry.Transform0-
Geometry.TransformXX1-
Geometry.TransformXY0-
Geometry.TransformXZ0-
Geometry.TransformYX0-
Geometry.TransformYY1-
Geometry.TransformYZ0-
Geometry.TransformZX0-
Geometry.TransformZY0-
Geometry.TransformZZ1-
Geometry.Volumes0General.OptionsFileName
Geometry.VolumeNumbers0General.OptionsFileName
Geometry.Color.Points{90,90,90}General.OptionsFileName
Geometry.Color.Lines{0,0,255}General.OptionsFileName
Geometry.Color.Surfaces{128,128,128}General.OptionsFileName
Geometry.Color.Volumes{255,255,0}General.OptionsFileName
Geometry.Color.Selection{255,0,0}General.OptionsFileName
Geometry.Color.HighlightZero{255,0,0}General.OptionsFileName
Geometry.Color.HighlightOne{255,150,0}General.OptionsFileName
Geometry.Color.HighlightTwo{255,255,0}General.OptionsFileName
Geometry.Color.Tangents{255,255,0}General.OptionsFileName
Geometry.Color.Normals{255,0,0}General.OptionsFileName
Geometry.Color.Projection{0,255,0}General.OptionsFileName
Mesh.Algorithm2General.OptionsFileName
Mesh.Algorithm3D1General.OptionsFileName
Mesh.AngleSmoothNormals30General.OptionsFileName
Mesh.AnisoMax1e+33General.OptionsFileName
Mesh.AllowSwapAngle10General.OptionsFileName
Mesh.BdfFieldFormat1General.OptionsFileName
Mesh.Binary0General.OptionsFileName
Mesh.Bunin0General.OptionsFileName
Mesh.CgnsImportOrder1General.OptionsFileName
Mesh.ChacoArchitecture1General.OptionsFileName
Mesh.ChacoEigensolver1General.OptionsFileName
Mesh.ChacoEigTol0.001General.OptionsFileName
Mesh.ChacoGlobalMethod1General.OptionsFileName
Mesh.ChacoHypercubeDim0General.OptionsFileName
Mesh.ChacoLocalMethod1General.OptionsFileName
Mesh.ChacoMeshDim11General.OptionsFileName
Mesh.ChacoMeshDim21General.OptionsFileName
Mesh.ChacoMeshDim31General.OptionsFileName
Mesh.ChacoPartitionSection1General.OptionsFileName
Mesh.ChacoSeed7.65432e+06General.OptionsFileName
Mesh.ChacoVMax250General.OptionsFileName
Mesh.ChacoParamINTERNAL_VERTICES0General.OptionsFileName
Mesh.ChacoParamREFINE_MAP1General.OptionsFileName
Mesh.ChacoParamREFINE_PARTITION0General.OptionsFileName
Mesh.ChacoParamTERMINAL_PROPOGATION0General.OptionsFileName
Mesh.CharacteristicLengthExtendFromBoundary1General.OptionsFileName
Mesh.CharacteristicLengthFactor1General.OptionsFileName
Mesh.CharacteristicLengthMin0General.OptionsFileName
Mesh.CharacteristicLengthMax1e+22General.OptionsFileName
Mesh.CharacteristicLengthFromCurvature0General.OptionsFileName
Mesh.CharacteristicLengthFromPoints1General.OptionsFileName
Mesh.Clip0-
Mesh.ColorCarousel1General.OptionsFileName
Mesh.CpuTime0-
Mesh.DrawSkinOnly0General.OptionsFileName
Mesh.Dual0General.OptionsFileName
Mesh.ElementOrder1General.OptionsFileName
Mesh.Explode1General.OptionsFileName
Mesh.Format10General.OptionsFileName
Mesh.Hexahedra1General.OptionsFileName
Mesh.HighOrderNumLayers3-
Mesh.HighOrderOptimize0General.OptionsFileName
Mesh.HighOrderPoissonRatio0.33-
Mesh.HighOrderSmoothingThreshold0.5General.OptionsFileName
Mesh.LabelSampling1General.OptionsFileName
Mesh.LabelType0General.OptionsFileName
Mesh.LcIntegrationPrecision1e-09General.OptionsFileName
Mesh.Light1General.OptionsFileName
Mesh.LightLines1General.OptionsFileName
Mesh.LightTwoSide1General.OptionsFileName
Mesh.Lines0General.OptionsFileName
Mesh.LineNumbers0General.OptionsFileName
Mesh.LineWidth1General.OptionsFileName
Mesh.MeshOnlyVisible0General.OptionsFileName
Mesh.MetisAlgorithm1General.OptionsFileName
Mesh.MetisEdgeMatching3General.OptionsFileName
Mesh.MetisRefinementAlgorithm3General.OptionsFileName
Mesh.MinimumCirclePoints7General.OptionsFileName
Mesh.MinimumCurvePoints3General.OptionsFileName
Mesh.MshFileVersion2.2General.OptionsFileName
Mesh.MshFilePartitioned0General.OptionsFileName
Mesh.MultiplePassesMeshes0General.OptionsFileName
Mesh.PartitionHexWeight1General.OptionsFileName
Mesh.PartitionPrismWeight1General.OptionsFileName
Mesh.PartitionPyramidWeight1General.OptionsFileName
Mesh.PartitionQuadWeight1General.OptionsFileName
Mesh.PartitionTetWeight1General.OptionsFileName
Mesh.PartitionTriWeight1General.OptionsFileName
Mesh.NbHexahedra0-
Mesh.NbNodes0-
Mesh.NbPartitions1General.OptionsFileName
Mesh.NbPrisms0-
Mesh.NbPyramids0-
Mesh.NbQuadrangles0-
Mesh.NbTetrahedra0-
Mesh.NbTriangles0-
Mesh.Normals0General.OptionsFileName
Mesh.NumSubEdges2General.OptionsFileName
Mesh.Optimize0General.OptionsFileName
Mesh.OptimizeNetgen0General.OptionsFileName
Mesh.Partitioner2General.OptionsFileName
Mesh.Points0General.OptionsFileName
Mesh.PointNumbers0General.OptionsFileName
Mesh.PointSize4General.OptionsFileName
Mesh.PointType0General.OptionsFileName
Mesh.Prisms1General.OptionsFileName
Mesh.Pyramids1General.OptionsFileName
Mesh.Quadrangles1General.OptionsFileName
Mesh.QualityInf0General.OptionsFileName
Mesh.QualitySup0General.OptionsFileName
Mesh.QualityType2General.OptionsFileName
Mesh.RadiusInf0General.OptionsFileName
Mesh.RadiusSup0General.OptionsFileName
Mesh.RandomFactor1e-09General.OptionsFileName
Mesh.IgnorePartitionBoundary0General.OptionsFileName
Mesh.RecombinationAlgorithm1General.OptionsFileName
Mesh.RecombineAll0General.OptionsFileName
Mesh.RemeshAlgorithm0General.OptionsFileName
Mesh.RemeshParametrization4General.OptionsFileName
Mesh.RefineSteps10General.OptionsFileName
Mesh.Remove4Triangles0General.OptionsFileName
Mesh.ReverseAllNormals0General.OptionsFileName
Mesh.SaveAll0-
Mesh.SaveElementTagType1General.OptionsFileName
Mesh.SaveParametric0General.OptionsFileName
Mesh.SaveGroupsOfNodes0General.OptionsFileName
Mesh.ScalingFactor1General.OptionsFileName
Mesh.SecondOrderExperimental0General.OptionsFileName
Mesh.SecondOrderIncomplete0General.OptionsFileName
Mesh.SecondOrderLinear0General.OptionsFileName
Mesh.Smoothing1General.OptionsFileName
Mesh.SmoothNormals0General.OptionsFileName
Mesh.SmoothRatio1.8General.OptionsFileName
Mesh.SubdivisionAlgorithm0General.OptionsFileName
Mesh.SurfaceEdges1General.OptionsFileName
Mesh.SurfaceFaces0General.OptionsFileName
Mesh.SurfaceNumbers0General.OptionsFileName
Mesh.SwitchElementTags0General.OptionsFileName
Mesh.Tangents0General.OptionsFileName
Mesh.Tetrahedra1General.OptionsFileName
Mesh.ToleranceEdgeLength0General.OptionsFileName
Mesh.Triangles1General.OptionsFileName
Mesh.VolumeEdges1General.OptionsFileName
Mesh.VolumeFaces0General.OptionsFileName
Mesh.VolumeNumbers0General.OptionsFileName
Mesh.Voronoi0General.OptionsFileName
Mesh.ZoneDefinition0General.OptionsFileName
Mesh.Color.Points{0,0,255}General.OptionsFileName
Mesh.Color.PointsSup{255,0,255}General.OptionsFileName
Mesh.Color.Lines{0,0,0}General.OptionsFileName
Mesh.Color.Triangles{160,150,255}General.OptionsFileName
Mesh.Color.Quadrangles{130,120,225}General.OptionsFileName
Mesh.Color.Tetrahedra{160,150,255}General.OptionsFileName
Mesh.Color.Hexahedra{130,120,225}General.OptionsFileName
Mesh.Color.Prisms{232,210,23}General.OptionsFileName
Mesh.Color.Pyramids{217,113,38}General.OptionsFileName
Mesh.Color.Tangents{255,255,0}General.OptionsFileName
Mesh.Color.Normals{255,0,0}General.OptionsFileName
Mesh.Color.Zero{255,120,0}General.OptionsFileName
Mesh.Color.One{0,255,132}General.OptionsFileName
Mesh.Color.Two{255,160,0}General.OptionsFileName
Mesh.Color.Three{0,255,192}General.OptionsFileName
Mesh.Color.Four{255,200,0}General.OptionsFileName
Mesh.Color.Five{0,216,255}General.OptionsFileName
Mesh.Color.Six{255,240,0}General.OptionsFileName
Mesh.Color.Seven{0,176,255}General.OptionsFileName
Mesh.Color.Eight{228,255,0}General.OptionsFileName
Mesh.Color.Nine{0,116,255}General.OptionsFileName
Mesh.Color.Ten{188,255,0}General.OptionsFileName
Mesh.Color.Eleven{0,76,255}General.OptionsFileName
Mesh.Color.Twelve{148,255,0}General.OptionsFileName
Mesh.Color.Thirteen{24,0,255}General.OptionsFileName
Mesh.Color.Fourteen{108,255,0}General.OptionsFileName
Mesh.Color.Fifteen{84,0,255}General.OptionsFileName
Mesh.Color.Sixteen{68,255,0}General.OptionsFileName
Mesh.Color.Seventeen{104,0,255}General.OptionsFileName
Mesh.Color.Eighteen{0,255,52}General.OptionsFileName
Mesh.Color.Nineteen{184,0,255}General.OptionsFileName
Solver.Executable0""General.SessionFileName
Solver.Executable1""General.SessionFileName
Solver.Executable2""General.SessionFileName
Solver.Executable3""General.SessionFileName
Solver.Executable4""General.SessionFileName
Solver.Name0"GetDP"General.SessionFileName
Solver.Name1""General.SessionFileName
Solver.Name2""General.SessionFileName
Solver.Name3""General.SessionFileName
Solver.Name4""General.SessionFileName
Solver.RemoteLogin0""General.SessionFileName
Solver.RemoteLogin1""General.SessionFileName
Solver.RemoteLogin2""General.SessionFileName
Solver.RemoteLogin3""General.SessionFileName
Solver.RemoteLogin4""General.SessionFileName
Solver.SocketName".gmshsock"General.OptionsFileName
Solver.AlwaysListen0General.OptionsFileName
Solver.AutoArchiveOutputFiles0General.OptionsFileName
Solver.AutoCheck1General.OptionsFileName
Solver.AutoSaveDatabase1General.OptionsFileName
Solver.AutoMesh1General.OptionsFileName
Solver.AutoMergeFile1General.OptionsFileName
Solver.AutoHideNewViews0General.OptionsFileName
Solver.AutoShowLastStep1General.OptionsFileName
Solver.Plugins0General.OptionsFileName
Solver.Timeout5General.OptionsFileName
PostProcessing.AnimationDelay0.1General.OptionsFileName
PostProcessing.AnimationCycle0General.OptionsFileName
PostProcessing.AnimationStep1General.OptionsFileName
PostProcessing.CombineRemoveOriginal1General.OptionsFileName
PostProcessing.Format10General.OptionsFileName
PostProcessing.HorizontalScales1General.OptionsFileName
PostProcessing.Link0General.OptionsFileName
PostProcessing.NbViews0-
PostProcessing.Plugins1General.OptionsFileName
PostProcessing.Smoothing0General.OptionsFileName
View.Attributes""General.OptionsFileName
View.AxesFormatX"%.3g"General.OptionsFileName
View.AxesFormatY"%.3g"General.OptionsFileName
View.AxesFormatZ"%.3g"General.OptionsFileName
View.AxesLabelX""General.OptionsFileName
View.AxesLabelY""General.OptionsFileName
View.AxesLabelZ""General.OptionsFileName
View.FileName""-
View.Format"%.3g"General.OptionsFileName
View.GeneralizedRaiseX"v0"General.OptionsFileName
View.GeneralizedRaiseY"v1"General.OptionsFileName
View.GeneralizedRaiseZ"v2"General.OptionsFileName
View.Name""-
View.Stipple0"1*0x1F1F"General.OptionsFileName
View.Stipple1"1*0x3333"General.OptionsFileName
View.Stipple2"1*0x087F"General.OptionsFileName
View.Stipple3"1*0xCCCF"General.OptionsFileName
View.Stipple4"2*0x1111"General.OptionsFileName
View.Stipple5"2*0x0F0F"General.OptionsFileName
View.Stipple6"1*0xCFFF"General.OptionsFileName
View.Stipple7"2*0x0202"General.OptionsFileName
View.Stipple8"2*0x087F"General.OptionsFileName
View.Stipple9"1*0xFFFF"General.OptionsFileName
View.AbscissaRangeType1General.OptionsFileName
View.AdaptVisualizationGrid0General.OptionsFileName
View.AngleSmoothNormals30General.OptionsFileName
View.ArrowSizeMax60General.OptionsFileName
View.ArrowSizeMin0General.OptionsFileName
View.AutoPosition1General.OptionsFileName
View.Axes0General.OptionsFileName
View.AxesMikado0General.OptionsFileName
View.AxesAutoPosition1General.OptionsFileName
View.AxesMaxX1General.OptionsFileName
View.AxesMaxY1General.OptionsFileName
View.AxesMaxZ1General.OptionsFileName
View.AxesMinX0General.OptionsFileName
View.AxesMinY0General.OptionsFileName
View.AxesMinZ0General.OptionsFileName
View.AxesTicsX5General.OptionsFileName
View.AxesTicsY5General.OptionsFileName
View.AxesTicsZ5General.OptionsFileName
View.Boundary0General.OptionsFileName
View.CenterGlyphs0General.OptionsFileName
View.Clip0-
View.ColormapAlpha1General.OptionsFileName
View.ColormapAlphaPower0General.OptionsFileName
View.ColormapBeta0General.OptionsFileName
View.ColormapBias0General.OptionsFileName
View.ColormapCurvature0General.OptionsFileName
View.ColormapInvert0General.OptionsFileName
View.ColormapNumber2General.OptionsFileName
View.ColormapRotation0General.OptionsFileName
View.ColormapSwap0General.OptionsFileName
View.ComponentMap00General.OptionsFileName
View.ComponentMap11General.OptionsFileName
View.ComponentMap22General.OptionsFileName
View.ComponentMap33General.OptionsFileName
View.ComponentMap44General.OptionsFileName
View.ComponentMap55General.OptionsFileName
View.ComponentMap66General.OptionsFileName
View.ComponentMap77General.OptionsFileName
View.ComponentMap88General.OptionsFileName
View.CustomAbscissaMax0-
View.CustomAbscissaMin0-
View.CustomMax0-
View.CustomMin0-
View.DisplacementFactor1General.OptionsFileName
View.DrawHexahedra1General.OptionsFileName
View.DrawLines1General.OptionsFileName
View.DrawPoints1General.OptionsFileName
View.DrawPrisms1General.OptionsFileName
View.DrawPyramids1General.OptionsFileName
View.DrawQuadrangles1General.OptionsFileName
View.DrawScalars1General.OptionsFileName
View.DrawSkinOnly0General.OptionsFileName
View.DrawStrings1General.OptionsFileName
View.DrawTensors1General.OptionsFileName
View.DrawTetrahedra1General.OptionsFileName
View.DrawTriangles1General.OptionsFileName
View.DrawVectors1General.OptionsFileName
View.Explode1General.OptionsFileName
View.ExternalView-1General.OptionsFileName
View.FakeTransparency0General.OptionsFileName
View.ForceNumComponents0General.OptionsFileName
View.GeneralizedRaiseFactor1General.OptionsFileName
View.GeneralizedRaiseView-1General.OptionsFileName
View.GlyphLocation1General.OptionsFileName
View.Height200General.OptionsFileName
View.IntervalsType2General.OptionsFileName
View.Light1General.OptionsFileName
View.LightLines1General.OptionsFileName
View.LightTwoSide1General.OptionsFileName
View.LineType0General.OptionsFileName
View.LineWidth1General.OptionsFileName
View.MaxRecursionLevel0General.OptionsFileName
View.Max0-
View.MaxX0-
View.MaxY0-
View.MaxZ0-
View.Min0-
View.MinX0-
View.MinY0-
View.MinZ0-
View.NbIso10General.OptionsFileName
View.NbTimeStep1-
View.NormalRaise0-
View.Normals0General.OptionsFileName
View.OffsetX0-
View.OffsetY0-
View.OffsetZ0-
View.PointSize3General.OptionsFileName
View.PointType0General.OptionsFileName
View.PositionX100General.OptionsFileName
View.PositionY50General.OptionsFileName
View.RaiseX0-
View.RaiseY0-
View.RaiseZ0-
View.RangeType1General.OptionsFileName
View.Sampling1General.OptionsFileName
View.SaturateValues0General.OptionsFileName
View.ScaleType1General.OptionsFileName
View.ShowElement0General.OptionsFileName
View.ShowScale1General.OptionsFileName
View.ShowTime3General.OptionsFileName
View.SmoothNormals0General.OptionsFileName
View.Stipple0General.OptionsFileName
View.Tangents0General.OptionsFileName
View.TargetError0.01General.OptionsFileName
View.TensorType1General.OptionsFileName
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View.VectorType4General.OptionsFileName
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View.Color.Lines{0,0,0}General.OptionsFileName
View.Color.Triangles{0,0,0}General.OptionsFileName
View.Color.Quadrangles{0,0,0}General.OptionsFileName
View.Color.Tetrahedra{0,0,0}General.OptionsFileName
View.Color.Hexahedra{0,0,0}General.OptionsFileName
View.Color.Prisms{0,0,0}General.OptionsFileName
View.Color.Pyramids{0,0,0}General.OptionsFileName
View.Color.Tangents{255,255,0}General.OptionsFileName
View.Color.Normals{255,0,0}General.OptionsFileName
View.Color.Text2D{0,0,0}General.OptionsFileName
View.Color.Text3D{0,0,0}General.OptionsFileName
View.Color.Axes{0,0,0}General.OptionsFileName
View.Color.Background2D{255,255,255}General.OptionsFileName
View.ColorTableGeneral.OptionsFileName
Gmsh is written in C++, the scripting language is parsed using Lex and Yacc (actually, Flex and Bison), and the GUI relies on OpenGL for the 3D graphics and FLTK (http://www.fltk.org) for the widget set. Gmsh's build system is based on CMake (http://www.cmake.org). Practical notes on how to compile Gmsh's source code are included in the distribution. See Frequently asked questions, for more information.
Stable releases and nightly source snapshots are available from http://geuz.org/gmsh/src/.
You can also access the subversion repository directly:
svn co https://geuz.org/svn/gmsh/trunk gmsh
You will be asked to accept the security certificate and to provide your username and password. (Use gmsh/gmsh for read-only access.)
svn update
svn commit
Gmsh's code is structured in several subdirectories, roughly separated between the four core modules (Geo, Mesh, Solver, Post) and associated utilities (Common, Numeric) on one hand, and the graphics (Graphics) and interface (Fltk, Parser) code on the other.
The geometry and mesh modules are based on an object-oriented model class (Geo/GModel.h), built upon abstract geometrical entity classes (Geo/GVertex.h, Geo/GEdge.h, Geo/GFace.h and Geo/GRegion.h). Concrete implementations of the geometrical entity classes are provided for each supported CAD kernel (e.g. Geo/gmshVertex.h for geometry points in Gmsh's native CAD format, or Geo/OCCVertex.h for geometry points from OpenCASCADE). The post-processing module is based on the concept of views (Post/PView.h) and abstract data containers (derived from Post/PViewData.h).
If you plan to contribute code to the Gmsh project, here are some easy rules to make the code easy to read/debug/maintain:
-Wall with
g++) and don't commit until there is no warning left.
valgrind --leak-check=yes --show-reachable=yes gmsh file.geo -3
(gdb) set env DYLD_INSERT_LIBRARIES /usr/lib/libgmalloc.dylib
export LD_PRELOAD=libnjamd.so
kill -USR1
Msg:: class to print information or errors
To add a new option in Gmsh:
CTX class (Common/Context.h) if
it's a classical option, or in the PViewOptions class
(Post/PViewOptions.h) if it's a post-processing view-dependent
option;
opt_XXX) and a
default value for this option;
opt_XXX in Common/Options.cpp (and
add the prototype in Common/Options.h);
Gmsh is an automatic three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. With Gmsh you can create or import 1D, 2D and 3D geometrical models, mesh them, launch external finite element solvers and visualize solutions. Gmsh can be used either as a stand-alone program (graphical or not) or as a C++ library.
Gmsh is distributed under the terms of the GNU General Public License, with an exception to allow for easier linking with external libraries. See License for more information.
Nothing... The name was derived from a previous version called “msh” (a shortcut for “mesh”), with the “g” prefix added to differentiate it. The default mesh file format used by Gmsh still uses the .msh extension.
In English people tend to pronounce `Gmsh' as “gee-mesh”.
http://geuz.org/gmsh is the primary location to obtain information about Gmsh. There you will for example find the complete reference manual, a bug tracking database and a searchable archive of the Gmsh mailing list (gmsh@geuz.org).
Gmsh runs on Windows XP/Vista, Mac OS X, Linux and most Unix variants.
You should have the OpenGL libraries installed on your system, and in the path of the library loader. A free replacement for OpenGL can be found at http://www.mesa3d.org.
You need cmake (http://www.cmake.org) and a C++ compiler. See the README.txt file in the top-level source directory for more information.
Gmsh will attempt to save temporary files and persistent configuration
options first in the $GMSH_HOME directory, then in the
$HOME, $TMP or $TEMP directories (in that order) if
the $GMSH_HOME environment variable is not defined. If none of
these variables are defined, Gmsh will try to save/load its
configuration files from the current working directory.
On Windows, if your system complains about missing OPENGL32.DLL or GLU32.DLL libraries, then OpenGL is not properly installed on your machine. You can download OpenGL from Microsoft's web site, or directly from http://www.opengl.org.
On Unix try `ldd gmsh' (or `otool -L gmsh' on Mac OS X) to check if all the required shared libraries are installed on your system. If not, install them. If it still doesn't work, recompile Gmsh from the source code.
Disable opaque move in your window manager.
Are you are executing Gmsh from a remote host (via the network) without GLX? You should turn double buffering off (with the `-nodb' command line option).
No, there isn't. This “ghost triangulation” is due to the fact that most PostScript previewers nowadays antialias the graphic primitives when they display the page on screen. (For example, in gv, you can disable antialising with the `State->Antialias' menu.) You should not see this ghost triangulation in the printed output (on paper).
Just choose the appropriate format in `File->Save As'. By default Gmsh guesses the format from the file extension, so you can just type myfile.jpg in the dialog and Gmsh will automatically create a JPEG image file.
Using a script. Have a look at tutorial/t8.geo or demos/anim.script for some examples.
Yes: dragging the mouse in a numeric input field slides the value! The left button moves one step per pixel, the middle by `10*step', and the right button by `100*step'.
Yes: selecting the content of an input field, or lines in the message console (`Tools->Message Console'), copies the selected text to the clipboard.
Yes, but only via STEP, IGES or BREP model import (not in .geo files). Gmsh has to be compiled with OpenCASCADE support for this to work.
The default behavior of Gmsh is to check and suppress all duplicate entities (points, lines and surfaces) each time a transformation command is issued. This can slow down things a lot if many transformations are performed. There are two solutions to this problem:
Geometry.AutoCoherence option to 0. This will
prevent any automatic duplicate check/replacement. If you still need to
remove the duplicates entities, simply add Coherence; at strategic
locations in your geo files (e.g. before the creation of line loops,
etc.).
Use `Tools->Visibility'. This allows you to select elementary entities and physical groups, as well as mesh elements, in a variety of ways (in a list or tree browser, by identification number, interactively, or per window).
Not yet. At the moment you can only change mesh element sizes, define
volumes and physical groups, or delete entities. The easiest way to do
this is to merge the model in a .geo file using Merge
"file.step"; and add the relevant scripting command after that. We plan
to add more advanced editing features in the future (to delete entities,
to create “mixed” surfaces and volumes, to export in .geo
format, etc.).
Define common geometrical objects and options in separate files, reusable in all your problem definition structures. Then Include the files in your main project file.
Verify that the curves in the model do not self-intersect. If `Mesh.RandomFactor*size(triangle)/size(model)' approaches machine accuracy, increase Mesh.RandomFactor.
If everything fails file a bug report with the version of your operating system and the full geometry.
Verify that the surfaces in your model do not self-intersect or partially overlap. If they don't, try the other 3D algorithms (`Tool->Options->Mesh->General->3D algorithm') or try to adapt the mesh element sizes in your input file so that the surface mesh better matches the geometrical details of the model.
If nothing works, file a bug report with the version of your operating system and and the full geometry.
IGES files do not contain the topology of the model, and tolerance problems can thus appear when the OpenCASCADE importer cannot identify two (close) curves as actually being identical.
The best solution is to not use IGES and use STEP instead. If you really have to use IGES, check that you don't have duplicate curves (e.g. by displaying their numbers in the GUI with `Tools->Options->Geometry->Visibility->Line numbers'). If there are duplicates, try to change the geometrical tolerance and sew the faces (see options in `Tools->Options->Geometry->General').
Use `Optimize quality' in the mesh menu.
The swapping algorithm is not very clever at the moment. Try to change the surface mesh a bit, or recombine your mesh to generate prisms or hexahedra instead of tetrahedra.
No. We need your help to implement this.
No, this feature has been removed in Gmsh 2.0. You must use the standard entity number instead.
Yes. You can achieve the same result by using the transfinite
algorithm with smoothing (e.g., with Mesh.Smoothing = 10).
Yes, Gmsh can generate both 1st order and 2nd order elements. To
generate second order elements, click on `High order' in the mesh
menu after the mesh is completed. To always generate 2nd order
elements, select `Generate second order elements' in the mesh option
panel. From the command line, you can also use -order 2.
Yes, you can import a surface mesh in any one of the supported mesh file formats, define a volume, and mesh it. For an example see demos/sphere-discrete.geo.
By design, Gmsh does not try to incorporate every possible definition of boundary conditions or material properties—this is a job best left to the solver. Instead, Gmsh provides a simple mechanism to tag groups of elements, and it is up to the solver to interpret these tags as boundary conditions, materials, etc. Associating tags with elements in Gmsh is done by defining Physical entities (Physical Points, Physical Lines, Physical Surfaces and Physical Volumes). See the reference manual as well as the tutorials (in particular tutorial/t1.geo) for a detailed description and some examples.
See “How can I display only selected parts of my model?”.
You can use `Tools->Clipping Planes' to clip the region of interest. You can define up to 6 clipping planes in Gmsh (i.e., enough to define a “cube” inside your model) and each plane can clip either the geometry, the mesh, the post-processing views, or any combination of the above. The clipping planes are defined using the four coefficients A,B,C,D of the equation A*x+B*y+C*y+D=0, which can be adjusted interactively by dragging the mouse in the input fields.
They measure the quality of the tetrahedra in a mesh:
Gamma ~ inscribed_radius / circumscribed_radius Eta ~ volume^(2/3) / sum_edge_length^2 Rho ~ min_edge_length / max_edge_length
For the exact definitions, see Geo/MElement.cpp. The graphs plot the the number of elements vs. the quality measure.
Gmsh reindexes the mesh vertices and elements so that they are numbered in a continuous sequence in the output files. The numbers displayed on screen after mesh generation thus usually differ from the ones saved in the mesh files. To check the actual numbers saved in the output file just load the mesh file back using `File->Open'.
Gmsh uses the ONELAB interface (http://www.onelab.info) to interact with external solvers. Have a look at the GetDP finite element solver (http://geuz.org/getdp) to see how this is done.
Sure. The simplest (but rather crude) approach if to re-launch Gmsh
everytime you want to visualize something (a simple C program showing
how to do this is given in utils/misc/callgmsh.c). A better approach
is to modify your program so that it can communicate with Gmsh over a
socket (see “How do I integrate my own solver with Gmsh?” above; you
can skip the option file creation). Then select `Always listen to
incoming connection requests' in the solver option panel (or run gmsh
with the -listen command line option) and Gmsh will always listen for
your program on the Solver.SocketName socket.
Use `Tools->Plugins->Cut Plane'.
Yes: first run `Tools->Plugins->Cut Map' to extract the isosurface, then use `View->Save As' to save the new view.
Yes, with the CutMap plugin (set the ExtractVolume option to -1 or 1 to extract the negative or positive levelset).
If the views contain multiple time steps, you can press the `play' button at the bottom of the graphic window, or change the time step by hand in the view option panel. You can also use the left and right arrow keys on your keyboard to change the time step in all visible views in real time.
If you want to loop through different views instead of time steps, you can use the `Loop through views instead of time steps' option in the view option panel, or use the up and down arrow keys on your keyboard.
Load a vector view containing the displacement field, and set `Vector display' to `Displacement' in `View->Options->Aspect'. If the displacement is too small (or too large), you can scale it with the `Displacement factor' option. (Remember that you can drag the mouse in all numeric input fields to slide the value!)
Another option is to use the `General transformation expressions' (in View->Options->Offset) on a scalar view, with the displacement map selected as the data source.
Yes, there are several ways to do that.
The easiest is to load two views: the first one containing a displacement field (a vector view that will be used to deform the mesh), and the second one containing the field you want to display (this view has to contain the same number of elements as the displacement view). You should then set `Vector display' to `Displacement' in the first view, as well as set `Data source' to point to the second view. (You might want to make the second view invisible, too. If you want to amplify or decrease the amount of deformation, just modify the `Displacement factor' option.)
Another solution is to use the `General transformation expressions' (in `View->Options->Offset') on the field you want to display, with the displacement map selected as the data source.
And yet another solution is to use the Warp plugin.
Yes: load both the vector and the scalar fields (the two views must have the same number of elements) and, in the vector field options, select the scalar view in `Data source'.
Yes, using either the CutMap plugin (with the `dView' option) or the Evaluate plugin.
Yes, using scripts. Have a look at tutorial/t8.geo or demos/anim.script for some examples.
Yes, by using either the “Force field” options in `Tools->Options->View->Visibility', or by using `Tools->Plugins->MathEval'.
Yes, with the Evaluate plugin.
There can be several reasons:
Plugin(DecomposeinSimplex) to transform all quads, hexas, prisms
and pyramids into triangles and tetrahedra).
Plugin(Triangulate) to transform a
point cloud into a triangulated surface. In 3D you can use
Plugin(Tetrahedralize).
In any case, you can automatically remove all empty views with
`View->Remove->Empty Views' in the GUI, or with Delete Empty
Views; in a script.
Use `Tools->Clipping Planes'.
When viewing 3D scalar fields, you can also modify the colormap (`Tools->Options->View->Map') to make the iso-surfaces “transparent”: either by holding `Ctrl' while dragging the mouse to draw the alpha channel by hand, or by using the `a', `Ctrl+a', `p' and `Ctrl+p' keyboard shortcuts.
Yet another (destructive) option is to use the ExtractVolume option in the CutSphere or CutPlane plugins.
If your dataset is constant per element make sure you don't use the `Iso-values' interval type in `Tools->Options->View->Range'.
?: new single-window GUI, with dynamically customizable widget tree; faster
STEP/BRep import; minor bug fixes.
2.6.1 (July 15, 2012): minor improvements and bug fixes.
2.6.0 (Jun 19, 2012): new quadrilateral meshing algorithms (Blossom and
DelQuad); new solver module based on ONELAB project (requires FLTK 1.3); new
tensor field visualization modes (eigenvectors, ellipsoid, etc.); added support
for interpolation schemes in .msh file; added support for MED3 format; rescale
viewport around visible entities (shift+1:1 in GUI); unified post-processing
field export; new experimental stereo+camera visualization mode; added
experimental BAMG & MMG3D support for anisotropic mesh generation; new OCC cut &
merge algorithm imported from Salome; new ability to connect extruded meshes to
tetrahedral grids using pyramids; new homology solver; Abaqus (INP) mesh export;
new Python and Java wrappers; bug fixes and small improvements all over the
place.
2.5.0 (Oct 15, 2010): new compound geometrical entities (for remeshing and/or
trans-patch meshing); improved mesh reclassification tool; new client/server
visualization mode; new ability to watch a pattern of files to merge; new
integrated MPEG export; new option to force the type of views dynamically;
bumped mesh version format to 2.2 (small change in the meaning of the partition
tags; this only affects partitioned (i.e. parallel) meshes); renamed several
post-processing plugins (as well as plugin options) to make them easier to
understand; many bug fixes and usability improvements all over the place.
2.4.2 (Sep 21, 2009): solver code refactoring + better IDE integration.
2.4.1 (Sep 1, 2009): fixed surface mesh orientation bug introduced in 2.4.0;
mesh and graphics code refactoring, small usability enhancements and bug fixes.
2.4.0 (Aug 22, 2009): switched build system to CMake; optionally copy
transfinite mesh contraints during geometry transformations; bumped mesh version
format to 2.1 (small change in the $PhysicalNames section, where the group
dimension is now required); ported most plugins to the new post-processing API;
switched from MathEval to MathEx and Flu_Tree_Browser to Fl_Tree; small bug
fixes and improvements all over the place.
2.3.1 (Mar 18, 2009): removed GSL dependency (Gmsh now simply uses Blas and
Lapack); new per-window visibility; added support for composite window printing
and background images; fixed string option affectation in parser; fixed surface
mesh orientation for Open CASCADE models; fixed random triangle orientations in
Delaunay and Frontal algorithms.
2.3.0 (Jan 23, 2009): major graphics and GUI code refactoring; new
full-quad/hexa subdivision algorithm; improved automatic transfinite corner
selection (now also for volumes); improved visibility browser; new automatic
adaptive visualization for high-order simplices; modified arrow size, clipping
planes and transform options; many improvements and bug fixes all over the
place.
2.2.6 (Nov 21, 2008): better transfinite smoothing and automatic corner
selection; fixed high order meshing crashes on Windows and Linux; new uniform
mesh refinement (thanks Brian!); fixed various other small bugs.
2.2.5 (Oct 25, 2008): Gmsh now requires FLTK 1.1.7 or above; various small
improvements (STL and VTK mesh IO, Netgen upgrade, Visual C++ support, Fields,
Mesh.{Msh,Stl,...}Binary changed to Mesh.Bindary) and bug fixes (pyramid
interpolation, Chaco crashes).
2.2.4 (Aug 14, 2008): integrated Metis and Chaco mesh partitioners; variables
can now be deleted in geo files; added support for point datasets in model-based
postprocessing views; small bug fixes.
2.2.3 (Jul 14, 2008): enhanced clipping interface; API cleanup; fixed various
bugs (Plugin(Integrate), high order meshes, surface info crash).
2.2.2 (Jun 20, 2008): added geometrical transformations on volumes; fixed bug in
high order mesh generation.
2.2.1 (Jun 15, 2008): various small improvements (adaptive views, GUI, code
cleanup) and bug fixes (high order meshes, Netgen interface).
2.2.0 (Apr 19, 2008): new model-based post-processing backend; added MED I/O for
mesh and post-processing; fixed BDF vertex ordering for 2nd order elements;
replaced Mesh.ConstrainedBackgroundMesh with
Mesh.CharacteristicLength{FromPoints,ExtendFromBoundary}; new Fields interface;
control windows are now non-modal by default; new experimental 2D frontal
algorithm; fixed various bugs.
2.1.1 (Mar 1, 2008): small bug fixes (second order meshes, combine views, divide
and conquer crash, ...).
2.1.0 (Feb 23, 2008): new post-processing database; complete rewrite of
post-processing drawing code; improved surface mesh algorithms; improved
STEP/IGES/BREP support; new 3D mesh optimization algorithm; new default native
file choosers; fixed 'could not find extruded vertex' in extrusions; many
improvements and bug fixes all over the place.
2.0.8 (Jul 13, 2007): unused vertices are not saved in mesh files anymore; new
plugin GUI; automatic GUI font size selection; renamed
Plugin(DecomposeInSimplex) into Plugin(MakeSimplex); reintroduced enhanced
Plugin(SphericalRaise); clarified meshing algo names; new option to save groups
of nodes in UNV meshes; new background mesh infrastructure; many small
improvements and small bug fixes.
2.0.7 (Apr 3, 2007): volumes can now be defined from external CAD surfaces;
Delaunay/Tetgen algorithm is now used by default when available; re-added
support for Plot3D structured mesh format; added ability to export external CAD
models as GEO files (this only works for the limited set of geometrical
primitives available in the GEO language, of course--so trying to convert e.g. a
trimmed NURBS from a STEP file into a GEO file will fail); "lateral" entities
are now added at the end of the list returned by extrusion commands; fixed
various bugs.
2.0 (Feb 5, 2007): new geometry and mesh databases, with support for STEP and
IGES import via Open CASCADE; complete rewrite of geometry and mesh drawing
code; complete rewrite of mesh I/O layer (with new native binary MSH format and
support for import/export of I-deas UNV, Nastran BDF, STL, Medit MESH and VRML
1.0 files); added support for incomplete second order elements; new 2D and 3D
meshing algorithms; improved integration of Netgen and TetGen algorithms;
removed anisotropic meshing algorithm (as well as attractors); removed explicit
region number specification in extrusions; option changes in the graphical
interface are now applied instantaneously; added support for offscreen rendering
using OSMesa; added support for SVG output; added string labels for Physical
entities; lots of other improvements all over the place.
1.65 (May 15, 2006): new Plugin(ExtractEdges); fixed compilation errors with
gcc4.1; replaced Plugin(DisplacementRaise) and Plugin(SphericalRaise) with the
more flexible Plugin(Warp); better handling of discrete curves; new Status
command in parser; added option to renumber nodes in .msh files (to avoid holes
in the numbering sequence); fixed 2 special cases in quad->prism extrusion;
fixed saving of 2nd order hexas with negative volume; small bug fixes and
cleanups.
1.64 (Mar 18, 2006): Windows versions do no depend on Cygwin anymore; various
bug fixes and cleanups.
1.63 (Feb 01, 2006): post-processing views can now be exported as meshes;
improved background mesh handling (a lot faster, and more accurate); improved
support for input images; new Plugin(ExtractElements); small bug fixes and
enhancements.
1.62 (Jan 15, 2006): new option to draw color gradients in the background;
enhanced perspective projection mode; new "lasso" selection mode (same as
"lasso" zoom, but in selection mode); new "invert selection" button in the
visibility browser; new snapping grid when adding points in the GUI; nicer
normal smoothing; new extrude syntax (old syntax still available, but
deprecated); various small bug fixes and enhancements.
1.61 (Nov 29, 2005): added support for second order (curved) elements in
post-processor; new version (1.4) of post-processing file formats; new stippling
options for 2D plots; removed limit on allowed number of files on command line;
all "Combine" operations are now available in the parser; changed
View.ArrowLocation into View.GlyphLocation; optimized memory usage when loading
many (>1000) views; optimized loading and drawing of line meshes and 2D iso
views; optimized handling of meshes with large number of physical entities;
optimized vertex array creation for large post-processing views on
Windows/Cygwin; removed Discrete Line and Discrete Surface commands (the same
functionality can now be obtained by simply loading a mesh in .msh format);
fixed coloring by mesh partition; added option to light wireframe meshes and
views; new "mesh statistics" export format; new full-quad recombine option; new
Plugin(ModulusPhase); hexas and prisms are now always saved with positive
volume; improved interactive entity selection; new experimental Tetgen
integration; new experimental STL remeshing algorithm; various small bug fixes
and improvements.
1.60 (Mar 15, 2005): added support for discrete curves; new Window menu on Mac
OS X; generalized all octree-based plugins (CutGrid, StreamLines, Probe, etc.)
to handle all element types (and not only scalar and vector
triangles+tetrahedra); generalized Plugin(Evaluate), Plugin(Extract) and
Plugin(Annotate); enhanced clipping plane interface; new grid/axes/rulers for 3D
post-processing views (renamed the AbscissaName, NbAbscissa and AbscissaFormat
options to more general names in the process); better automatic positioning of
2D graphs; new manipulator dialog to specify rotations, translations and
scalings "by hand"; various small enhancements and bug fixes.
1.59 (Feb 06, 2005): added support for discrete (triangulated) surfaces, either
in STL format or with the new "Discrete Surface" command; added STL and Text
output format for post-processing views and STL output format for surface
meshes; all levelset-based plugins can now also compute isovolumes; generalized
Plugin(Evaluate) to handle external view data (based on the same or on a
different mesh); generalized Plugin(CutGrid); new plugins (Eigenvalues,
Gradient, Curl, Divergence); changed default colormap to match Matlab's "Jet"
colormap; new transformation matrix option for views (for non-destructive
rotations, symmetries, etc.); improved solver interface to keep the GUI
responsive during solver calls; new C++ and Python solver examples; simplified
Tools->Visibility GUI; transfinite lines with "Progression" now allow negative
line numbers to reverse the progression; added ability to retrieve Gmsh's
version number in the parser (to help write backward compatible scripts); fixed
white space in unv mesh output; fixed various small bugs.
1.58 (Jan 01, 2005): fixed UNIX socket interface on Windows (broken by the TCP
solver patch in 1.57); bumped version number of default post-processing file
formats to 1.3 (the only small modification is the handling of the end-of-string
character for text2d and text3d objects in the ASCII format); new File->Rename
menu; new colormaps+improved colormap handling; new color+min/max options in
views; new GetValue() function to ask for values interactively in scripts;
generalized For/EndFor loops in parser; new plugins (Annotate, Remove, Probe);
new text attributes in views; renamed some shortcuts; fixed TeX output for large
scenes; new option dialogs for various output formats; fixed many small memory
leaks in parser; many small enhancements to polish the graphics and the user
interface.
1.57 (Dec 23, 2004): generalized displacement maps to display arbitrary view
types; the arrows representing a vector field can now also be colored by the
values from other scalar, vector or tensor fields; new adaptive high order
visualization mode; new options (Solver.SocketCommand, Solver.NameCommand,
View.ArrowSizeProportional, View.Normals, View.Tangents and General.ClipFactor);
fixed display of undesired solver plugin popups; enhanced interactive plugin
behavior; new plugins (HarmonicToTime, Integrate, Eigenvectors); tetrahedral
mesh file reading speedup (50% faster on large meshes); large memory footprint
reduction (up to 50%) for the visualization of triangular/tetrahedral meshes;
the solver interface now supports TCP/IP connections; new generalized raise mode
(allows to use complex expressions to offset post-processing maps); upgraded
Netgen kernel to version 4.4; new optional TIME list in parsed views to specify
the values of the time steps; several bug fixes in the Elliptic mesh algorithm;
various other small bug fixes and enhancements.
1.56 (Oct 17, 2004): new post-processing option to draw a scalar view raised by
a displacement view without using Plugin(DisplacementRaise) (makes drawing
arbitrary scalar fields on deformed meshes much easier); better post-processing
menu (arbitrary number of views+scrollable+show view number); improved
view->combine; new horizontal post-processing scales; new option to draw the
mesh nodes per element; views can now also be saved in "parsed" format; fixed
various path problems on Windows; small bug fixes.
1.55 (Aug 21, 2004): added background mesh support for Triangle; meshes can now
be displayed using "smoothed" normals (like post-processing views); added GUI
for clipping planes; new interactive clipping/cutting plane definition;
reorganized the Options GUI; enhanced 3D iso computation; enhanced lighting;
many small bug fixes.
1.54 (Jul 03, 2004): integrated Netgen (3D mesh quality optimization +
alternative 3D algorithm); Extrude Surface now always automatically creates a
new volume (in the same way Extrude Point or Extrude Line create new lines and
surfaces, respectively); fixed UNV output; made the "Layers" region numbering
consistent between lines, surfaces and volumes; fixed home directory problem on
Win98; new Plugin(CutParametric); the default project file is now created in the
home directory if no current directory is defined (e.g., when double-clicking on
the icon on Windows/Mac); fixed the discrepancy between the orientation of
geometrical surfaces and the associated surface meshes; added automatic
orientation of surfaces in surface loops; generalized Plugin(Triangulate) to
handle vector and tensor views; much nicer display of discrete iso-surfaces and
custom ranges using smooth normals; small bug fixes and cleanups.
1.53 (Jun 04, 2004): completed support for second order elements in the mesh
module (line, triangles, quadrangles, tetrahedra, hexahedra, prisms and
pyramids); various background mesh fixes and enhancements; major performance
improvements in mesh and post-processing drawing routines (OpenGL vertex arrays
for tri/quads); new Plugin(Evaluate) to evaluate arbitrary expressions on
post-processing views; generalized Plugin(Extract) to handle any combination of
components; generalized "Coherence" to handle transfinite surface/volume
attributes; plugin options can now be set in the option file (like all other
options); added "undo" capability during geometry creation; rewrote the contour
guessing routines so that entities can be selected in an arbitrary order; Mac
users can now double click on geo/msh/pos files in the Finder to launch Gmsh;
removed support for FLTK 1.0; rewrote most of the code related to quadrangles;
fixed 2d elliptic algorithm; removed all OpenGL display list code and options;
fixed light positioning; new BoundingBox command to set the bounding box
explicitly; added support for inexpensive "fake" transparency mode; many code
cleanups.
1.52 (May 06, 2004): new raster ("bitmap") PostScript/EPS/PDF output formats;
new Plugin(Extract) to extract a given component from a post-processing view;
new Plugin(CutGrid) and Plugin(StreamLines); improved mesh projection on
non-planar surfaces; added support for second order tetrahedral elements; added
interactive control of element order; refined mesh entity drawing selection (and
renamed most of the corresponding options); enhanced log scale in
post-processing; better font selection; simplified View.Raise{X,Y,Z} by removing
the scaling; various bug fixes (default postscript printing mode, drawing of 3D
arrows/cylinders on Linux, default home directory on Windows, default initial
file browser directory, extrusion of points with non-normalized axes of
rotation, computation of the scene bounding box in scripts, + the usual
documentation updates).
1.51 (Feb 29, 2004): initial support for visualizing mesh partitions; integrated
version 2.0 of the MSH mesh file format; new option to compute post-processing
ranges (min/max) per time step; Multiple views can now be combined into multi
time step ones (e.g. for programs that generate data one time step at a time);
new syntax: #var[] returns the size of the list var[]; enhanced "gmsh -convert";
temporary and error files are now created in the home directory to avoid file
permission issues; new 3D arrows; better lighting support; STL facets can now be
converted into individual geometrical surfaces; many other small improvements
and bug fixes (multi timestep tensors, color by physical entity, parser cleanup,
etc.).
1.50 (Dec 06, 2003): small changes to the visibility browser + made visibility
scriptable (new Show/Hide commands); fixed (rare) crash when deleting views;
split File->Open into File->Open and File->New to behave like most other
programs; Mac versions now use the system menu bar by default (if possible);
fixed bug leading to degenerate and/or duplicate tetrahedra in extruded meshes;
fixed crash when reloading sms meshes.
1.49 (Nov 30, 2003): made Merge, Save and Print behave like Include (i.e., open
files in the same directory as the main project file if the path is relative);
new Plugin(DecomposeInSimplex); new option View.AlphaChannel to set the
transparency factor globally for a post-processing view; new "Combine Views"
command; various bug fixes and cleanups.
1.48 (Nov 23, 2003): new DisplacementRaise plugin to plot arbitrary fields on
deformed meshes; generalized CutMap, CutPlane, CutSphere and Skin plugins to
handle all kinds of elements and fields; new "Save View[n]" command to save
views from a script; many small bug fixes (configure tests for libpng, handling
of erroneous options, multi time step scalar prism drawings, copy of surface
mesh attributes, etc.).
1.47 (Nov 12, 2003): fixed extrusion of surfaces defined by only two curves; new
syntax to retrieve point coordinates and indices of entities created through
geometrical transformations; new PDF and compressed PostScript output formats;
fixed numbering of elements created with "Extrude Point/Line"; use $GMSH_HOME as
home directory if defined.
1.46 (Aug 23, 2003): fixed crash for very long command lines; new options for
setting the displacement factor and Triangle's parameters + renamed a couple of
options to more sensible names (View.VectorType, View.ArrowSize); various small
bug fixes; documentation update.
1.45 (Jun 14, 2003): small bug fixes (min/max computation for tensor views,
missing physical points in read mesh, "jumping" geometry during interactive
manipulation of large models, etc.); variable definition speedup; restored
support for second order elements in one- and two-dimensional meshes;
documentation updates.
1.44 (Apr 21, 2003): new reference manual; added support for PNG output; fixed
small configure script bugs.
1.43 (Mar 28, 2003): fixed solver interface problem on Mac OS X; new option to
specify the interactive rotation center (default is now the pseudo "center of
gravity" of the object, instead of (0,0,0)).
1.42 (Mar 19, 2003): suppressed the automatic addition of a ".geo" extension if
the file given on the command line is not recognized; added missing Layer option
for Extrude Point; fixed various small bugs.
1.41 (Mar 04, 2003): Gmsh is now licensed under the GNU General Public License;
general code cleanup (indent).
1.40 (Feb 26, 2003): various small bug fixes (mainly GSL-related).
1.39 (Feb 23, 2003): removed all non-free routines; more build system work;
implemented Von-Mises tensor display for all element types; fixed small GUI
bugs.
1.38 (Feb 17, 2003): fixed custom range selection for 3D iso graphs; new build
system based on autoconf; new image reading code to import bitmaps as
post-processing views.
1.37 (Jan 25, 2003): generalized smoothing and cuts of post-processing views;
better Windows integration (solvers, external editors, etc.); small bug fixes.
1.36 (Nov 20, 2002): enhanced view duplication (one can now use "Duplicata
View[num]" in the input file); merged all option dialogs in a new general option
window; enhanced discoverability of the view option menus; new 3D point and line
display; many small bug fixes and enhancements ("Print" format in parser,
post-processing statistics, smooth normals, save window positions, restore
default options, etc.).
1.35 (Sep 11, 2002): graphical user interface upgraded to FLTK 1.1 (tooltips,
new file chooser with multiple selection, full keyboard navigation, cut/paste of
messages, etc.); colors can be now be directly assigned to mesh entities;
initial tensor visualization; new keyboard animation (right/left arrow for time
steps; up/down arrow for view cycling); new VRML output format for surface
meshes; new plugin for spherical elevation plots; new post-processing file
format (version 1.2) supporting quadrangles, hexahedra, prisms and pyramids;
transparency is now enabled by default for post-processing plots; many small bug
fixes (read mesh, ...).
1.34 (Feb 18, 2002): improved surface mesh of non-plane surfaces; fixed
orientation of elements in 2D anisotropic algorithm; minor user interface polish
and additions (mostly in post-processing options); various small bug fixes.
1.33 (Jan 24, 2002): new parameterizable solver interface (allowing up to 5
user-defined solvers); enhanced 2D aniso algorithm; 3D initial mesh speedup.
1.32 (Oct 04, 2001): new visibility browser; better floating point exception
checks; fixed infinite looping when merging meshes in project files; various
small clean ups (degenerate 2D extrusion, view->reload, ...).
1.31 (Nov 30, 2001): corrected ellipses; PostScript output update (better
shading, new combined PS/LaTeX output format); more interface polish; fixed
extra memory allocation in 2D meshes; Physical Volume handling in unv format;
various small fixes.
1.30 (Nov 16, 2001): interface polish; fix crash when extruding quadrangles.
1.29 (Nov 12, 2001): translations and rotations can now be combined in
extrusions; fixed coherence bug in Extrude Line; various small bug fixes and
additions.
1.28 (Oct 30, 2001): corrected the 'Using Progression' attribute for tranfinite
meshes to actually match a real geometric progression; new Triangulate plugin;
new 2D graphs (space+time charts); better performance of geometrical
transformations (warning: the numbering of some automatically created entities
has changed); new text primitives in post-processing views (file format updated
to version 1.1); more robust mean plane computation and error checks; various
other small additions and clean-ups.
1.27 (Oct 05, 2001): added ability to extrude curves with Layers/Recombine
attributes; new PointSize/LineWidth options; fixed For/EndFor loops in included
files; fixed error messages (line numbers+file names) in loops and functions;
made the automatic removal of duplicate geometrical entities optional
(Geometry.AutoCoherence=0); various other small bug fixes and clean-ups.
1.26 (Sep 06, 2001): enhanced 2D anisotropic mesh generator (metric
intersections); fixed small bug in 3D initial mesh; added alternative syntax for
built-in functions (for GetDP compatibility); added line element display; Gmsh
now saves all the elements in the mesh if no physical groups are defined (or if
Mesh.SaveAll=1).
1.25 (Sep 01, 2001): fixed bug with mixed recombined/non-recombined extruded
meshes; Linux versions are now build with no optimization, due to bugs in gcc
2.95.X.
1.24 (Aug 30, 2001): fixed characteristic length interpolation for Splines;
fixed edge swapping bug in 3D initial mesh; fixed degenerated case in
geometrical extrusion (ruled surface with 3 borders); fixed generation of
degenerated hexahedra and prisms for recombined+extruded meshes; added BSplines
creation in the GUI; integrated Jonathan Shewchuk's Triangle as an alternative
isotropic 2D mesh generator; added AngleSmoothNormals to control sharp edge
display with smoothed normals; fixed random crash for lighted 3D iso surfaces.
1.23 (Aug, 2001): fixed duplicate elements generation + non-matching tetrahedra
faces in 3D extruded meshes; better display of displacement maps; fixed
interactive ellipsis construction; generalized boundary operator; added new
explode option for post-processing views; enhanced link view behavior (to update
only the changed items); added new default plugins: Skin, Transform, Smooth;
fixed various other small bugs (mostly in the post-processing module and for
extruded meshes).
1.22 (Aug 03, 2001): fixed (yet another) bug for 2D mesh in the mean plane;
fixed surface coherence bug in extruded meshes; new double logarithmic scale,
saturate value and smoothed normals option for post-processing views; plugins
are now enabled by default; three new experimental statically linked plugins:
CutMap (extracts a given iso surface from a 3D scalar map), CutPlane (cuts a 3D
scalar map with a plane section), CutSphere (cuts a 3D scalar map with a
sphere); various other bug fixes, additions and clean-ups.
1.21 (Jul 25, 2001): fixed more memory leaks; added -opt command line option to
parse definitions directly from the command line; fixed missing screen refreshes
during contour/surface/volume selection; enhanced string manipulation functions
(Sprintf, StrCat, StrPrefix); many other small fixes and clean-ups.
1.20 (Jun 14, 2001): fixed various bugs (memory leaks, functions in included
files, solver command selection, ColorTable option, duplicate nodes in extruded
meshes (not finished yet), infinite loop on empty views, orientation of
recombined quadrangles, ...); reorganized the interface menus; added constrained
background mesh and mesh visibility options; added mesh quality histograms;
changed default mesh colors; reintegrated the old command-line extrusion mesh
generator.
1.19 (May 07, 2001): fixed seg. fault for scalar simplex post-processing; new
Solver menu; interface for GetDP solver through sockets; fixed multiple scale
alignment; added some options + full option descriptions.
1.18 (Apr 26, 2001): fixed many small bugs and incoherences in post-processing;
fixed broken background mesh in 1D mesh generation.
1.17 (Apr 17, 2001): corrected physical points saving; fixed parsing of DOS
files (carriage return problems); easier geometrical selections (cursor change);
plugin manager; enhanced variable arrays (sublist selection and affectation);
line loop check; New arrow display; reduced number of 'fatal' errors + better
handling in interactive mode; fixed bug when opening meshes; enhanced File->Open
behavior for meshes and post-processing views.
1.16 (Feb 26, 2001): added single/double buffer selection (only useful for Unix
versions of Gmsh run from remote hosts without GLX); fixed a bug for recent
versions of the opengl32.dll on Windows, which caused OpenGL fonts not to show
up.
1.15 (Feb 23, 2001): added automatic visibility setting during entity selection;
corrected geometrical extrusion bug.
1.14 (Feb 17, 2001): corrected a few bugs in the GUI (most of them were
introduced in 1.13); added interactive color selection; made the option database
bidirectional (i.e. scripts now correctly update the GUI); default options can
now be saved and automatically reloaded at startup; made some changes to the
scripting syntax (PostProcessing.View[n] becomes View[n]; Offset0 becomes
OffsetX, etc.); corrected the handling of simple triangular surfaces with large
characteristic lengths in the 2D isotropic algorithm; added an ASCII to binary
post-processing view converter.
1.13 (Feb 09, 2001): added support for JPEG output on Windows.
1.12: corrected vector lines in the post-processing parsed format; corrected
animation on Windows; corrected file creation in scripts on Windows; direct
affectation of variable arrays.
1.11 (Feb 07, 2001): corrected included file loading problem.
1.10 (Feb 04, 2001): switched from Motif to FLTK for the GUI. Many small tweaks.
1.00 (Jan 15, 2001): added PPM and YUV output; corrected nested If/Endif;
Corrected several bugs for pixel output and enhanced GIF output (dithering,
transparency); slightly changed the post-processing file format to allow both
single and double precision numbers.
0.999 (Dec 20, 2000): added JPEG output and easy MPEG generation (see t8.geo in
the tutorial); clean up of export functions; small fixes; Linux versions are now
compiled with gcc 2.95.2, which should fix the problems encountered with
Mandrake 7.2.
0.998 (Dec 19, 2000): corrected bug introduced in 0.997 in the generation of the
initial 3D mesh.
0.997 (Dec 14, 2000): corrected bug in interactive surface/volume selection;
Added interactive symmetry; corrected geometrical extrusion with rotation in
degenerated or partially degenerated cases; corrected bug in 2D mesh when
meshing in the mean plane.
0.996: arrays of variables; enhanced Printf and Sprintf; Simplified options
(suppression of option arrays).
0.995 (Dec 11, 2000): totally rewritten geometrical database (performance has
been drastically improved for all geometrical transformations, and most notably
for extrusion). As a consequence, the internal numbering of geometrical entities
has changed: this will cause incompatibilities with old .geo files, and will
require a partial rewrite of your old .geo files if these files made use of
geometrical transformations. The syntax of the .geo file has also been
clarified. Many additions for scripting purposes. New extrusion mesh
generator. Preliminary version of the coupling between extruded and Delaunay
meshes. New option and procedural database. All interactive operations can be
scripted in the input files. See the last example in the tutorial for an
example. Many stability enhancements in the 2D and 3D mesh
algorithms. Performance boost of the 3D algorithm. Gmsh is still slow, but the
performance becomes acceptable. An average 1000 tetrahedra/second is obtained on
a 600Mhz computer for a mesh of one million tetrahedra. New anisotropic 2D mesh
algorithm. New (ASCII and binary) post-processing file format and clarified mesh
file format. New handling for interactive rotations (trackball mode). New
didactic interactive mesh construction (watch the Delaunay algorithm in real
time on complex geometries: that's exciting ;-). And many, many bug fixes and
cleanups.
0.992 (Nov 13, 2000): corrected recombined extrusion; corrected ellipses; added
simple automatic animation of post-processing maps; fixed various bugs.
0.991 (Oct 24, 2000): fixed a serious allocation bug in 2D algorithm, which
caused random crashes. All users should upgrade to 0.991.
0.990: bug fix in non-recombined 3D transfinite meshes.
0.989 (Sep 01, 2000): added ability to reload previously saved meshes; some new
command line options; reorganization of the scale menu; GIF output.
0.987: fixed bug with smoothing (leading to the possible generation of erroneous
3d meshes); corrected bug for mixed 3D meshes; moved the 'toggle view link'
option to Opt->Postprocessing_Options.
0.986: fixed overlay problems; SGI version should now also run on 32 bits
machines; fixed small 3d mesh bug.
0.985: corrected colormap bug on HP, SUN, SGI and IBM versions; corrected small
initialization bug in postscript output.
0.984: corrected bug in display lists; added some options in Opt->General.
0.983: corrected some seg. faults in interactive mode; corrected bug in
rotations; changed default window sizes for better match with 1024x768 screens
(default X resources can be changed: see ex03.geo).
0.982: lighting for mesh and post-processing; corrected 2nd order mesh on non
plane surfaces; added example 13.
Gmsh is copyright (C) 1997-2012
Christophe Geuzaine
<cgeuzaine at ulg.ac.be>
and
Jean-Francois Remacle
<jean-francois.remacle at uclouvain.be>
Code contributions to Gmsh have been provided by David Colignon (colormaps),
Emilie Marchandise (compound geometrical entities), Gaetan Bricteux (Gauss
integration and levelsets), Jacques Lechelle (DIFFPACK mesh format), Jonathan
Lambrechts (fields, solver), Jozef Vesely (help with Tetgen integration), Koen
Hillewaert (high order elements), Laurent Stainier (eigenvalue solvers, tensor
display and MacOS bits), Marc Ume (original list code), Mark van Doesburg (Open
CASCADE face connection), Matt Gundry (Plot3d mesh format), Matti Pellikka (Cell
complex and Homology solver), Nicolas Tardieu (help with Netgen integration),
Pascale Noyret (MED mesh format), Pierre Badel (root finding and minimization),
Ruth Sabariego (pyramids), Stephen Guzik (CGNS and partitioners), Bastien
Gorissen (parallel remote post-processing), Eric Bechet (solver), Gilles
Marckmann (camera and stero mode), Ashish Negi (Salome/Netgen CAD healing),
Trevor Strickler (structured/unstructured coupling with pyramids), Amaury Johnen
(Bezier), Benjamin Ruard (Java wrappers). See comments in the sources for more
information. If we forgot to list your contributions please send us an email!
The AVL tree code (Common/avl.*) and the YUV image code (Graphics/gl2yuv.*) are
copyright (C) 1988-1993, 1995 The Regents of the University of
California. Permission to use, copy, modify, and distribute this software and
its documentation for any purpose and without fee is hereby granted, provided
that the above copyright notice appear in all copies and that both that
copyright notice and this permission notice appear in supporting documentation,
and that the name of the University of California not be used in advertising or
publicity pertaining to distribution of the software without specific, written
prior permission. The University of California makes no representations about
the suitability of this software for any purpose. It is provided "as is" without
express or implied warranty.
The trackball code (Graphics/Trackball.*) is copyright (C) 1993, 1994, Silicon
Graphics, Inc. ALL RIGHTS RESERVED. Permission to use, copy, modify, and
distribute this software for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that both the
copyright notice and this permission notice appear in supporting documentation,
and that the name of Silicon Graphics, Inc. not be used in advertising or
publicity pertaining to distribution of the software without specific, written
prior permission.
The GIF and PPM routines (Graphics/gl2gif.cpp) are based on code copyright (C)
1989, 1991, Jef Poskanzer. Permission to use, copy, modify, and distribute this
software and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in supporting
documentation. This software is provided "as is" without express or implied
warranty.
The colorbar widget (Fltk/Colorbar_Window.cpp) was inspired by code from the
Vis5d program for visualizing five dimensional gridded data sets, copyright (C)
1990-1995, Bill Hibbard, Brian Paul, Dave Santek, and Andre Battaiola.
This version of Gmsh may contain code (in the contrib/ANN subdirectory)
copyright (C) 1997-2005 University of Maryland and Sunil Arya and David Mount:
check the configuration options.
This version of Gmsh may contain code (in the contrib/Chaco subdirectory)
written by Bruce Hendrickson and Robert Leland at Sandia National Laboratories
under US Department of Energy contract DE-AC04-76DP00789 and is copyrighted by
Sandia Corporation: check the configuration options.
This version of Gmsh may contain code (in the contrib/gmm subdirectory)
copyright (C) 2002-2008 Yves Renard: check the configuration options.
This version of Gmsh may contain code (in the contrib/kbipack subdirectory)
copyright (C) 2005 Saku Suuriniemi: check the configuration options.
This version of Gmsh may contain code (in the contrib/MathEx subdirectory) based
in part on the work of the SSCILIB Library, copyright (C) 2000-2003 Sadao
Massago: check the configuration options.
This version of Gmsh may contain code (in the contrib/Metis subdirectory)
written by George Karypis (karypis at cs.umn.edu), copyright (C) 1998 Regents of
the University of Minnesota: check the configuration options.
This version of Gmsh may contain code (in the contrib/mpeg_encode subdirectory)
copyright (c) 1995 The Regents of the University of California: check the
configuration options.
This version of Gmsh may contain code (in the contrib/Netgen subdirectory)
copyright (C) 1994-2004 Joachim Sch"oberl: check the configuration options.
This version of Gmsh may contain code (in the contrib/Tetgen subdirectory)
copyright (C) 2002-2007 Hang Si: check the configuration options.
This version of Gmsh may contain code (in the contrib/Salome subdirectory)
copyright (C) 2003 OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN, CEDRAT, EDF R& D, LEG,
PRINCIPIA R& D, BUREAU VERITAS: check the configuration options.
This version of Gmsh may contain code (in the contrib/bamg subdirectory) from
Freefem++ copyright (C) Frederic Hecht: check the configuration options.
This version of Gmsh may contain code (in the contrib/lbfgs subdirectory) (C)
Sergey Bochkanov (ALGLIB project): check the configuration options.
This version of Gmsh may contain code (in the contrib/mmg3d subdirectory) from
MMG3D Version 4.0 (C) 2004-2011 Cecile Dobrzynski and Pascal Frey (IPB - UPMC -
INRIA): check the configuration options.
This version of Gmsh may contain code (in the contrib/Blossom subdirectory)
copyright (C) 1995-1997 Bill Cook et al.: check the configuration options.
Special thanks to Bill Spitzak, Michael Sweet, Matthias Melcher, Greg Ercolano
and others for the Fast Light Tool Kit on which Gmsh's GUI is based. See
http://www.fltk.org for more info on this excellent object-oriented,
cross-platform toolkit.
Special thanks also to EDF for funding the Open CASCADE and MED integration.
Thanks to the following folks who have contributed by providing fresh ideas on
theoretical or programming topics, who have sent patches, requests for changes
or improvements, or who gave us access to exotic machines for testing Gmsh: Juan
Abanto, Olivier Adam, Guillaume Alleon, Laurent Champaney, Pascal Dupuis,
Patrick Dular, Philippe Geuzaine, Johan Gyselinck, Francois Henrotte, Benoit
Meys, Nicolas Moes, Osamu Nakamura, Chad Schmutzer, Jean-Luc Fl'ejou, Xavier
Dardenne, Christophe Prud'homme, Sebastien Clerc, Jose Miguel Pasini, Philippe
Lussou, Jacques Kools, Bayram Yenikaya, Peter Hornby, Krishna Mohan Gundu,
Christopher Stott, Timmy Schumacher, Carl Osterwisch, Bruno Frackowiak, Philip
Kelleners, Romuald Conty, Renaud Sizaire, Michel Benhamou, Tom De Vuyst, Kris
Van den Abeele, Simon Vun, Simon Corbin, Thomas De-Soza, Marcus Drosson, Antoine
Dechaume, Jose Paulo Moitinho de Almeida, Thomas Pinchard, Corrado Chisari, Axel
Hackbarth, Peter Wainwright, Jiri Hnidek, Thierry Thomas, Konstantinos Poulios,
Laurent Van Miegroet, Shahrokh Ghavamian, Geordie McBain.
Gmsh is provided under the terms of the GNU General Public License
(GPL), Version 2 or later, with the following exception:
The copyright holders of Gmsh give you permission to combine Gmsh
with code included in the standard release of TetGen (from Hang Si),
Netgen (from Joachim Sch"oberl), Chaco (from Bruce Hendrickson and
Robert Leland at Sandia National Laboratories), METIS (from
George Karypis at the University of Minnesota) and OpenCASCADE (from
Open CASCADE S.A.S) under their respective licenses. You may copy
and distribute such a system following the terms of the GNU GPL
for Gmsh and the licenses of the other code concerned, provided
that you include the source code of that other code when and as the
GNU GPL requires distribution of source code.
Note that people who make modified versions of Gmsh are not
obligated to grant this special exception for their modified
versions; it is their choice whether to do so. The GNU General
Public License gives permission to release a modified version
without this exception; this exception also makes it possible to
release a modified version which carries forward this exception.
End of exception.
GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
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When we speak of free software, we are referring to freedom, not
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To protect your rights, we need to make restrictions that forbid
anyone to deny you these rights or to ask you to surrender the rights.
These restrictions translate to certain responsibilities for you if you
distribute copies of the software, or if you modify it.
For example, if you distribute copies of such a program, whether
gratis or for a fee, you must give the recipients all the rights that
you have. You must make sure that they, too, receive or can get the
source code. And you must show them these terms so they know their
rights.
We protect your rights with two steps: (1) copyright the software, and
(2) offer you this license which gives you legal permission to copy,
distribute and/or modify the software.
Also, for each author's protection and ours, we want to make certain
that everyone understands that there is no warranty for this free
software. If the software is modified by someone else and passed on, we
want its recipients to know that what they have is not the original, so
that any problems introduced by others will not reflect on the original
authors' reputations.
Finally, any free program is threatened constantly by software
patents. We wish to avoid the danger that redistributors of a free
program will individually obtain patent licenses, in effect making the
program proprietary. To prevent this, we have made it clear that any
patent must be licensed for everyone's free use or not licensed at all.
The precise terms and conditions for copying, distribution and
modification follow.
GNU GENERAL PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. This License applies to any program or other work which contains
a notice placed by the copyright holder saying it may be distributed
under the terms of this General Public License. The "Program", below,
refers to any such program or work, and a "work based on the Program"
means either the Program or any derivative work under copyright law:
that is to say, a work containing the Program or a portion of it,
either verbatim or with modifications and/or translated into another
language. (Hereinafter, translation is included without limitation in
the term "modification".) Each licensee is addressed as "you".
Activities other than copying, distribution and modification are not
covered by this License; they are outside its scope. The act of
running the Program is not restricted, and the output from the Program
is covered only if its contents constitute a work based on the
Program (independent of having been made by running the Program).
Whether that is true depends on what the Program does.
1. You may copy and distribute verbatim copies of the Program's
source code as you receive it, in any medium, provided that you
conspicuously and appropriately publish on each copy an appropriate
copyright notice and disclaimer of warranty; keep intact all the
notices that refer to this License and to the absence of any warranty;
and give any other recipients of the Program a copy of this License
along with the Program.
You may charge a fee for the physical act of transferring a copy, and
you may at your option offer warranty protection in exchange for a fee.
2. You may modify your copy or copies of the Program or any portion
of it, thus forming a work based on the Program, and copy and
distribute such modifications or work under the terms of Section 1
above, provided that you also meet all of these conditions:
a) You must cause the modified files to carry prominent notices
stating that you changed the files and the date of any change.
b) You must cause any work that you distribute or publish, that in
whole or in part contains or is derived from the Program or any
part thereof, to be licensed as a whole at no charge to all third
parties under the terms of this License.
c) If the modified program normally reads commands interactively
when run, you must cause it, when started running for such
interactive use in the most ordinary way, to print or display an
announcement including an appropriate copyright notice and a
notice that there is no warranty (or else, saying that you provide
a warranty) and that users may redistribute the program under
these conditions, and telling the user how to view a copy of this
License. (Exception: if the Program itself is interactive but
does not normally print such an announcement, your work based on
the Program is not required to print an announcement.)
These requirements apply to the modified work as a whole. If
identifiable sections of that work are not derived from the Program,
and can be reasonably considered independent and separate works in
themselves, then this License, and its terms, do not apply to those
sections when you distribute them as separate works. But when you
distribute the same sections as part of a whole which is a work based
on the Program, the distribution of the whole must be on the terms of
this License, whose permissions for other licensees extend to the
entire whole, and thus to each and every part regardless of who wrote it.
Thus, it is not the intent of this section to claim rights or contest
your rights to work written entirely by you; rather, the intent is to
exercise the right to control the distribution of derivative or
collective works based on the Program.
In addition, mere aggregation of another work not based on the Program
with the Program (or with a work based on the Program) on a volume of
a storage or distribution medium does not bring the other work under
the scope of this License.
3. You may copy and distribute the Program (or a work based on it,
under Section 2) in object code or executable form under the terms of
Sections 1 and 2 above provided that you also do one of the following:
a) Accompany it with the complete corresponding machine-readable
source code, which must be distributed under the terms of Sections
1 and 2 above on a medium customarily used for software interchange; or,
b) Accompany it with a written offer, valid for at least three
years, to give any third party, for a charge no more than your
cost of physically performing source distribution, a complete
machine-readable copy of the corresponding source code, to be
distributed under the terms of Sections 1 and 2 above on a medium
customarily used for software interchange; or,
c) Accompany it with the information you received as to the offer
to distribute corresponding source code. (This alternative is
allowed only for noncommercial distribution and only if you
received the program in object code or executable form with such
an offer, in accord with Subsection b above.)
The source code for a work means the preferred form of the work for
making modifications to it. For an executable work, complete source
code means all the source code for all modules it contains, plus any
associated interface definition files, plus the scripts used to
control compilation and installation of the executable. However, as a
special exception, the source code distributed need not include
anything that is normally distributed (in either source or binary
form) with the major components (compiler, kernel, and so on) of the
operating system on which the executable runs, unless that component
itself accompanies the executable.
If distribution of executable or object code is made by offering
access to copy from a designated place, then offering equivalent
access to copy the source code from the same place counts as
distribution of the source code, even though third parties are not
compelled to copy the source along with the object code.
4. You may not copy, modify, sublicense, or distribute the Program
except as expressly provided under this License. Any attempt
otherwise to copy, modify, sublicense or distribute the Program is
void, and will automatically terminate your rights under this License.
However, parties who have received copies, or rights, from you under
this License will not have their licenses terminated so long as such
parties remain in full compliance.
5. You are not required to accept this License, since you have not
signed it. However, nothing else grants you permission to modify or
distribute the Program or its derivative works. These actions are
prohibited by law if you do not accept this License. Therefore, by
modifying or distributing the Program (or any work based on the
Program), you indicate your acceptance of this License to do so, and
all its terms and conditions for copying, distributing or modifying
the Program or works based on it.
6. Each time you redistribute the Program (or any work based on the
Program), the recipient automatically receives a license from the
original licensor to copy, distribute or modify the Program subject to
these terms and conditions. You may not impose any further
restrictions on the recipients' exercise of the rights granted herein.
You are not responsible for enforcing compliance by third parties to
this License.
7. If, as a consequence of a court judgment or allegation of patent
infringement or for any other reason (not limited to patent issues),
conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License. If you cannot
distribute so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you
may not distribute the Program at all. For example, if a patent
license would not permit royalty-free redistribution of the Program by
all those who receive copies directly or indirectly through you, then
the only way you could satisfy both it and this License would be to
refrain entirely from distribution of the Program.
If any portion of this section is held invalid or unenforceable under
any particular circumstance, the balance of the section is intended to
apply and the section as a whole is intended to apply in other
circumstances.
It is not the purpose of this section to induce you to infringe any
patents or other property right claims or to contest validity of any
such claims; this section has the sole purpose of protecting the
integrity of the free software distribution system, which is
implemented by public license practices. Many people have made
generous contributions to the wide range of software distributed
through that system in reliance on consistent application of that
system; it is up to the author/donor to decide if he or she is willing
to distribute software through any other system and a licensee cannot
impose that choice.
This section is intended to make thoroughly clear what is believed to
be a consequence of the rest of this License.
8. If the distribution and/or use of the Program is restricted in
certain countries either by patents or by copyrighted interfaces, the
original copyright holder who places the Program under this License
may add an explicit geographical distribution limitation excluding
those countries, so that distribution is permitted only in or among
countries not thus excluded. In such case, this License incorporates
the limitation as if written in the body of this License.
9. The Free Software Foundation may publish revised and/or new versions
of the General Public License from time to time. Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.
Each version is given a distinguishing version number. If the Program
specifies a version number of this License which applies to it and "any
later version", you have the option of following the terms and conditions
either of that version or of any later version published by the Free
Software Foundation. If the Program does not specify a version number of
this License, you may choose any version ever published by the Free Software
Foundation.
10. If you wish to incorporate parts of the Program into other free
programs whose distribution conditions are different, write to the author
to ask for permission. For software which is copyrighted by the Free
Software Foundation, write to the Free Software Foundation; we sometimes
make exceptions for this. Our decision will be guided by the two goals
of preserving the free status of all derivatives of our free software and
of promoting the sharing and reuse of software generally.
NO WARRANTY
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
REPAIR OR CORRECTION.
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGES.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
convey the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this
when it starts in an interactive mode:
Gnomovision version 69, Copyright (C) year name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, the commands you use may
be called something other than `show w' and `show c'; they could even be
mouse-clicks or menu items--whatever suits your program.
You should also get your employer (if you work as a programmer) or your
school, if any, to sign a "copyright disclaimer" for the program, if
necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
<signature of Ty Coon>, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into
proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Library General
Public License instead of this License.
!: Operators!=: Operators%: Operators&&: Operators(): Operators*: Operators*=: General commands+: Operators++: Operators+=: General commands-: Operators-: Command-line options--: Operators-0: Command-line options-1, -2, -3: Command-line options-=: General commands-a, -g, -m, -s, -p: Command-line options-algo string: Command-line options-bgm file: Command-line options-bin: Command-line options-check file: Command-line options-clcurv: Command-line options-clmax float: Command-line options-clmin float: Command-line options-clscale float: Command-line options-combine: Command-line options-convert files: Command-line options-display string: Command-line options-fontsize int: Command-line options-format string: Command-line options-help: Command-line options-info: Command-line options-link int: Command-line options-listen: Command-line options-n: Command-line options-nodb: Command-line options-nopopup: Command-line options-o file: Command-line options-optimize[_netgen]: Command-line options-option file: Command-line options-order int: Command-line options-part int: Command-line options-pid: Command-line options-rand float: Command-line options-refine: Command-line options-saveall: Command-line options-smooth int: Command-line options-string "string": Command-line options-theme string: Command-line options-tol float: Command-line options-v int: Command-line options-version: Command-line options-watch: Command-line options/: Operators/*, */: Comments//: Comments/=: General commands:: Operators<: Operators<=: Operators=: General commands==: Operators>: Operators>=: Operators?: Operators^: OperatorsAbort;: General commandsAcos ( expression ): Built-in functionsAlias View[expression];: Post-processing commandsAliasWithOptions View[expression];: Post-processing commandsAsin ( expression ): Built-in functionsAtan ( expression ): Built-in functionsAtan2 ( expression, expression ): Built-in functionsAttractor: Specifying mesh element sizesAttractorAnisoCurve: Specifying mesh element sizesBackground Field = expression;: Specifying mesh element sizesBackground Mesh View[expression];: Post-processing commandsBoundary { transform-list }: TransformationsBoundaryLayer: Specifying mesh element sizesBoundingBox { expression, expression, expression, expression, expression, expression };: General commandsBoundingBox;: General commandsBox: Specifying mesh element sizesBSpline ( expression ) = { expression-list };: LinesCall string;: User-defined functionsCatmullRom ( expression ) = { expression-list };: LinesCeil ( expression ): Built-in functionsCenterline: Specifying mesh element sizes = char-expression;: General commandsCharacteristic Length { expression-list } = expression;: Specifying mesh element sizesCircle ( expression ) = { expression, expression, expression };: LinesCoherence Mesh;: Miscellaneous mesh commandsCoherence;: Miscellaneous geometry commandsCohomology ( { expression-list } ) { { expression-list } , { expression-list } };: Miscellaneous mesh commandsColor color-expression { Point | Line | Surface | Volume { expression-list }; ... }: Miscellaneous mesh commands = color-expression;: General commandsCombine ElementsByViewName;: Post-processing commandsCombine ElementsFromAllViews | Combine Views;: Post-processing commandsCombine ElementsFromVisibleViews;: Post-processing commandsCombine TimeStepsByViewName | Combine TimeSteps;: Post-processing commandsCombine TimeStepsFromAllViews;: Post-processing commandsCombine TimeStepsFromVisibleViews;: Post-processing commandsCombinedBoundary { transform-list }: TransformationsCompound Line ( expression ) = { expression-list };: LinesCompound Surface ( expression ) = { expression-list } < Boundary { { expression-list }, { expression-list }, { expression-list }, { expression-list } } > ;: SurfacesCompound Volume ( expression ) = { expression-list };: VolumesCos ( expression ): Built-in functionsCosh ( expression ): Built-in functionsCurvature: Specifying mesh element sizesCylinder: Specifying mesh element sizesDelete Empty Views;: Post-processing commandsDelete Model;: General commandsDelete Options;: General commandsDelete Physicals;: General commandsDelete string;: General commandsDelete Variables;: General commandsDelete View[expression];: Post-processing commandsDelete { Point | Line | Surface | Volume { expression-list }; ... }: Miscellaneous geometry commandsDilate { { expression-list }, expression } { transform-list }: TransformationsDraw;: General commandsEllipse ( expression ) = { expression, expression, expression, expression };: LinesEndFor: Loops and conditionalsEndIf: Loops and conditionalsError ( char-expression <, expression-list> );: General commandsExit;: General commandsExp ( expression ): Built-in functionsExtrude { expression-list } { extrude-list }: ExtrusionsExtrude { expression-list } { extrude-list layers }: Structured gridsExtrude { Surface { expression-list }; layers < Using Index[expr]; > < Using View[expr]; > }: Structured gridsExtrude { { expression-list }, { expression-list }, expression } { extrude-list layers }: Structured gridsExtrude { { expression-list }, { expression-list }, expression } { extrude-list }: ExtrusionsExtrude { { expression-list }, { expression-list }, { expression-list }, expression } { extrude-list layers }: Structured gridsExtrude { { expression-list }, { expression-list }, { expression-list }, expression } { extrude-list }: ExtrusionsFabs ( expression ): Built-in functionsField[expression] = string;: Specifying mesh element sizesField[expression].string = char-expression | expression | expression-list;: Specifying mesh element sizesFloor ( expression ): Built-in functionsFmod ( expression, expression ): Built-in functionsFor ( expression : expression ): Loops and conditionalsFor ( expression : expression : expression ): Loops and conditionalsFor string In { expression : expression : expression }: Loops and conditionalsFor string In { expression : expression }: Loops and conditionalsFrustum: Specifying mesh element sizesFunction string: User-defined functionsGeneral.AlphaBlending: General options listGeneral.Antialiasing: General options listGeneral.ArrowHeadRadius: General options listGeneral.ArrowStemLength: General options listGeneral.ArrowStemRadius: General options listGeneral.Axes: General options listGeneral.AxesAutoPosition: General options listGeneral.AxesForceValue: General options listGeneral.AxesFormatX: General options listGeneral.AxesFormatY: General options listGeneral.AxesFormatZ: General options listGeneral.AxesLabelX: General options listGeneral.AxesLabelY: General options listGeneral.AxesLabelZ: General options listGeneral.AxesMaxX: General options listGeneral.AxesMaxY: General options listGeneral.AxesMaxZ: General options listGeneral.AxesMikado: General options listGeneral.AxesMinX: General options listGeneral.AxesMinY: General options listGeneral.AxesMinZ: General options listGeneral.AxesTicsX: General options listGeneral.AxesTicsY: General options listGeneral.AxesTicsZ: General options listGeneral.AxesValueMaxX: General options listGeneral.AxesValueMaxY: General options listGeneral.AxesValueMaxZ: General options listGeneral.AxesValueMinX: General options listGeneral.AxesValueMinY: General options listGeneral.AxesValueMinZ: General options listGeneral.BackgroundGradient: General options listGeneral.BackgroundImageFileName: General options listGeneral.BackgroundImagePositionX: General options listGeneral.BackgroundImagePositionY: General options listGeneral.Camera: General options listGeneral.CameraAperture: General options listGeneral.CameraEyeSeparationRatio: General options listGeneral.CameraFocalLengthRatio: General options listGeneral.Clip0A: General options listGeneral.Clip0B: General options listGeneral.Clip0C: General options listGeneral.Clip0D: General options listGeneral.Clip1A: General options listGeneral.Clip1B: General options listGeneral.Clip1C: General options listGeneral.Clip1D: General options listGeneral.Clip2A: General options listGeneral.Clip2B: General options listGeneral.Clip2C: General options listGeneral.Clip2D: General options listGeneral.Clip3A: General options listGeneral.Clip3B: General options listGeneral.Clip3C: General options listGeneral.Clip3D: General options listGeneral.Clip4A: General options listGeneral.Clip4B: General options listGeneral.Clip4C: General options listGeneral.Clip4D: General options listGeneral.Clip5A: General options listGeneral.Clip5B: General options listGeneral.Clip5C: General options listGeneral.Clip5D: General options listGeneral.ClipFactor: General options listGeneral.ClipOnlyDrawIntersectingVolume: General options listGeneral.ClipOnlyVolume: General options listGeneral.ClipPositionX: General options listGeneral.ClipPositionY: General options listGeneral.ClipWholeElements: General options listGeneral.Color.AmbientLight: General options listGeneral.Color.Axes: General options listGeneral.Color.Background: General options listGeneral.Color.BackgroundGradient: General options listGeneral.Color.DiffuseLight: General options listGeneral.Color.Foreground: General options listGeneral.Color.SmallAxes: General options listGeneral.Color.SpecularLight: General options listGeneral.Color.Text: General options listGeneral.ColorScheme: General options listGeneral.ConfirmOverwrite: General options listGeneral.ContextPositionX: General options listGeneral.ContextPositionY: General options listGeneral.DefaultFileName: General options listGeneral.DetachedMenu: General options listGeneral.Display: General options listGeneral.DisplayBorderFactor: General options listGeneral.DoubleBuffer: General options listGeneral.DrawBoundingBoxes: General options listGeneral.ErrorFileName: General options listGeneral.ExpertMode: General options listGeneral.ExtraHeight: General options listGeneral.ExtraPositionX: General options listGeneral.ExtraPositionY: General options listGeneral.ExtraWidth: General options listGeneral.FastRedraw: General options listGeneral.FieldHeight: General options listGeneral.FieldPositionX: General options listGeneral.FieldPositionY: General options listGeneral.FieldWidth: General options listGeneral.FileChooserPositionX: General options listGeneral.FileChooserPositionY: General options listGeneral.FileName: General options listGeneral.FltkTheme: General options listGeneral.FontSize: General options listGeneral.GraphicsFont: General options listGeneral.GraphicsFontSize: General options listGeneral.GraphicsFontSizeTitle: General options listGeneral.GraphicsFontTitle: General options listGeneral.GraphicsHeight: General options listGeneral.GraphicsPositionX: General options listGeneral.GraphicsPositionY: General options listGeneral.GraphicsWidth: General options listGeneral.InitialModule: General options listGeneral.Light0: General options listGeneral.Light0W: General options listGeneral.Light0X: General options listGeneral.Light0Y: General options listGeneral.Light0Z: General options listGeneral.Light1: General options listGeneral.Light1W: General options listGeneral.Light1X: General options listGeneral.Light1Y: General options listGeneral.Light1Z: General options listGeneral.Light2: General options listGeneral.Light2W: General options listGeneral.Light2X: General options listGeneral.Light2Y: General options listGeneral.Light2Z: General options listGeneral.Light3: General options listGeneral.Light3W: General options listGeneral.Light3X: General options listGeneral.Light3Y: General options listGeneral.Light3Z: General options listGeneral.Light4: General options listGeneral.Light4W: General options listGeneral.Light4X: General options listGeneral.Light4Y: General options listGeneral.Light4Z: General options listGeneral.Light5: General options listGeneral.Light5W: General options listGeneral.Light5X: General options listGeneral.Light5Y: General options listGeneral.Light5Z: General options listGeneral.LineWidth: General options listGeneral.ManipulatorPositionX: General options listGeneral.ManipulatorPositionY: General options listGeneral.MaxX: General options listGeneral.MaxY: General options listGeneral.MaxZ: General options listGeneral.MenuHeight: General options listGeneral.MenuPositionX: General options listGeneral.MenuPositionY: General options listGeneral.MenuWidth: General options listGeneral.MessageHeight: General options listGeneral.MinX: General options listGeneral.MinY: General options listGeneral.MinZ: General options listGeneral.MouseHoverMeshes: General options listGeneral.MouseSelection: General options listGeneral.NonModalWindows: General options listGeneral.NoPopup: General options listGeneral.OptionsFileName: General options listGeneral.OptionsPositionX: General options listGeneral.OptionsPositionY: General options listGeneral.Orthographic: General options listGeneral.PluginHeight: General options listGeneral.PluginPositionX: General options listGeneral.PluginPositionY: General options listGeneral.PluginWidth: General options listGeneral.PointSize: General options listGeneral.PolygonOffsetAlwaysOn: General options listGeneral.PolygonOffsetFactor: General options listGeneral.PolygonOffsetUnits: General options listGeneral.ProgressMeterStep: General options listGeneral.QuadricSubdivisions: General options listGeneral.RecentFile0: General options listGeneral.RecentFile1: General options listGeneral.RecentFile2: General options listGeneral.RecentFile3: General options listGeneral.RecentFile4: General options listGeneral.RotationCenterGravity: General options listGeneral.RotationCenterX: General options listGeneral.RotationCenterY: General options listGeneral.RotationCenterZ: General options listGeneral.RotationX: General options listGeneral.RotationY: General options listGeneral.RotationZ: General options listGeneral.SaveOptions: General options listGeneral.SaveSession: General options listGeneral.ScaleX: General options listGeneral.ScaleY: General options listGeneral.ScaleZ: General options listGeneral.SessionFileName: General options listGeneral.Shininess: General options listGeneral.ShininessExponent: General options listGeneral.SmallAxes: General options listGeneral.SmallAxesPositionX: General options listGeneral.SmallAxesPositionY: General options listGeneral.SmallAxesSize: General options listGeneral.StatisticsPositionX: General options listGeneral.StatisticsPositionY: General options listGeneral.Stereo: General options listGeneral.SystemMenuBar: General options listGeneral.Terminal: General options listGeneral.TextEditor: General options listGeneral.TmpFileName: General options listGeneral.Tooltips: General options listGeneral.Trackball: General options listGeneral.TrackballHyperbolicSheet: General options listGeneral.TrackballQuaternion0: General options listGeneral.TrackballQuaternion1: General options listGeneral.TrackballQuaternion2: General options listGeneral.TrackballQuaternion3: General options listGeneral.TranslationX: General options listGeneral.TranslationY: General options listGeneral.TranslationZ: General options listGeneral.VectorType: General options listGeneral.Verbosity: General options listGeneral.VisibilityPositionX: General options listGeneral.VisibilityPositionY: General options listGeneral.WatchFilePattern: General options listGeneral.WebBrowser: General options listGeneral.ZoomFactor: General options listGeometry.AutoCoherence: Geometry options listGeometry.Clip: Geometry options listGeometry.Color.HighlightOne: Geometry options listGeometry.Color.HighlightTwo: Geometry options listGeometry.Color.HighlightZero: Geometry options listGeometry.Color.Lines: Geometry options listGeometry.Color.Normals: Geometry options listGeometry.Color.Points: Geometry options listGeometry.Color.Projection: Geometry options listGeometry.Color.Selection: Geometry options listGeometry.Color.Surfaces: Geometry options listGeometry.Color.Tangents: Geometry options listGeometry.Color.Volumes: Geometry options listGeometry.CopyMeshingMethod: Geometry options listGeometry.ExactExtrusion: Geometry options listGeometry.ExtrudeReturnLateralEntities: Geometry options listGeometry.ExtrudeSplinePoints: Geometry options listGeometry.HideCompounds: Geometry options listGeometry.HighlightOrphans: Geometry options listGeometry.LabelType: Geometry options listGeometry.Light: Geometry options listGeometry.LightTwoSide: Geometry options listGeometry.LineNumbers: Geometry options listGeometry.Lines: Geometry options listGeometry.LineSelectWidth: Geometry options listGeometry.LineType: Geometry options listGeometry.LineWidth: Geometry options listGeometry.MatchGeomAndMesh: Geometry options listGeometry.Normals: Geometry options listGeometry.NumSubEdges: Geometry options listGeometry.OCCConnectFaces: Geometry options listGeometry.OCCFixDegenerated: Geometry options listGeometry.OCCFixSmallEdges: Geometry options listGeometry.OCCFixSmallFaces: Geometry options listGeometry.OCCSewFaces: Geometry options listGeometry.OffsetX: Geometry options listGeometry.OffsetY: Geometry options listGeometry.OffsetZ: Geometry options listGeometry.OldCircle: Geometry options listGeometry.OldNewReg: Geometry options listGeometry.PointNumbers: Geometry options listGeometry.Points: Geometry options listGeometry.PointSelectSize: Geometry options listGeometry.PointSize: Geometry options listGeometry.PointType: Geometry options listGeometry.ScalingFactor: Geometry options listGeometry.SnapX: Geometry options listGeometry.SnapY: Geometry options listGeometry.SnapZ: Geometry options listGeometry.SurfaceNumbers: Geometry options listGeometry.Surfaces: Geometry options listGeometry.SurfaceType: Geometry options listGeometry.Tangents: Geometry options listGeometry.Tolerance: Geometry options listGeometry.Transform: Geometry options listGeometry.TransformXX: Geometry options listGeometry.TransformXY: Geometry options listGeometry.TransformXZ: Geometry options listGeometry.TransformYX: Geometry options listGeometry.TransformYY: Geometry options listGeometry.TransformYZ: Geometry options listGeometry.TransformZX: Geometry options listGeometry.TransformZY: Geometry options listGeometry.TransformZZ: Geometry options listGeometry.VolumeNumbers: Geometry options listGeometry.Volumes: Geometry options listGMSH_MAJOR_VERSION: General commandsGMSH_MINOR_VERSION: General commandsGMSH_PATCH_VERSION: General commandsGradient: Specifying mesh element sizesHide char-expression;: Miscellaneous mesh commandsHide char-expression;: Miscellaneous geometry commandsHide { Point | Line | Surface | Volume { expression-list }; ... }: Miscellaneous mesh commandsHide { Point | Line | Surface | Volume { expression-list }; ... }: Miscellaneous geometry commandsHomology ( { expression-list } ) { { expression-list } , { expression-list } };: Miscellaneous mesh commandsHypot ( expression, expression ): Built-in functionsIf ( expression ): Loops and conditionalsInclude char-expression;: General commandsLaplacian: Specifying mesh element sizesLine ( expression ) = { expression, expression };: LinesLine Loop ( expression ) = { expression-list };: LinesLog ( expression ): Built-in functionsLog10 ( expression ): Built-in functionsLonLat: Specifying mesh element sizesMathEval: Specifying mesh element sizesMathEvalAniso: Specifying mesh element sizesMax: Specifying mesh element sizesMaxEigenHessian: Specifying mesh element sizesMean: Specifying mesh element sizesMerge char-expression;: General commandsMesh expression;: General commandsMesh.Algorithm: Mesh options listMesh.Algorithm3D: Mesh options listMesh.AllowSwapAngle: Mesh options listMesh.AngleSmoothNormals: Mesh options listMesh.AnisoMax: Mesh options listMesh.BdfFieldFormat: Mesh options listMesh.Binary: Mesh options listMesh.Bunin: Mesh options listMesh.CgnsImportOrder: Mesh options listMesh.ChacoArchitecture: Mesh options listMesh.ChacoEigensolver: Mesh options listMesh.ChacoEigTol: Mesh options listMesh.ChacoGlobalMethod: Mesh options listMesh.ChacoHypercubeDim: Mesh options listMesh.ChacoLocalMethod: Mesh options listMesh.ChacoMeshDim1: Mesh options listMesh.ChacoMeshDim2: Mesh options listMesh.ChacoMeshDim3: Mesh options listMesh.ChacoParamINTERNAL_VERTICES: Mesh options listMesh.ChacoParamREFINE_MAP: Mesh options listMesh.ChacoParamREFINE_PARTITION: Mesh options listMesh.ChacoParamTERMINAL_PROPOGATION: Mesh options listMesh.ChacoPartitionSection: Mesh options listMesh.ChacoSeed: Mesh options listMesh.ChacoVMax: Mesh options listMesh.CharacteristicLengthExtendFromBoundary: Mesh options listMesh.CharacteristicLengthFactor: Mesh options listMesh.CharacteristicLengthFromCurvature: Mesh options listMesh.CharacteristicLengthFromPoints: Mesh options listMesh.CharacteristicLengthMax: Mesh options listMesh.CharacteristicLengthMin: Mesh options listMesh.Clip: Mesh options listMesh.Color.Eight: Mesh options listMesh.Color.Eighteen: Mesh options listMesh.Color.Eleven: Mesh options listMesh.Color.Fifteen: Mesh options listMesh.Color.Five: Mesh options listMesh.Color.Four: Mesh options listMesh.Color.Fourteen: Mesh options listMesh.Color.Hexahedra: Mesh options listMesh.Color.Lines: Mesh options listMesh.Color.Nine: Mesh options listMesh.Color.Nineteen: Mesh options listMesh.Color.Normals: Mesh options listMesh.Color.One: Mesh options listMesh.Color.Points: Mesh options listMesh.Color.PointsSup: Mesh options listMesh.Color.Prisms: Mesh options listMesh.Color.Pyramids: Mesh options listMesh.Color.Quadrangles: Mesh options listMesh.Color.Seven: Mesh options listMesh.Color.Seventeen: Mesh options listMesh.Color.Six: Mesh options listMesh.Color.Sixteen: Mesh options listMesh.Color.Tangents: Mesh options listMesh.Color.Ten: Mesh options listMesh.Color.Tetrahedra: Mesh options listMesh.Color.Thirteen: Mesh options listMesh.Color.Three: Mesh options listMesh.Color.Triangles: Mesh options listMesh.Color.Twelve: Mesh options listMesh.Color.Two: Mesh options listMesh.Color.Zero: Mesh options listMesh.ColorCarousel: Mesh options listMesh.CpuTime: Mesh options listMesh.DrawSkinOnly: Mesh options listMesh.Dual: Mesh options listMesh.ElementOrder: Mesh options listMesh.Explode: Mesh options listMesh.Format: Mesh options listMesh.Hexahedra: Mesh options listMesh.HighOrderNumLayers: Mesh options listMesh.HighOrderOptimize: Mesh options listMesh.HighOrderPoissonRatio: Mesh options listMesh.HighOrderSmoothingThreshold: Mesh options listMesh.IgnorePartitionBoundary: Mesh options listMesh.LabelSampling: Mesh options listMesh.LabelType: Mesh options listMesh.LcIntegrationPrecision: Mesh options listMesh.Light: Mesh options listMesh.LightLines: Mesh options listMesh.LightTwoSide: Mesh options listMesh.LineNumbers: Mesh options listMesh.Lines: Mesh options listMesh.LineWidth: Mesh options listMesh.MeshOnlyVisible: Mesh options listMesh.MetisAlgorithm: Mesh options listMesh.MetisEdgeMatching: Mesh options listMesh.MetisRefinementAlgorithm: Mesh options listMesh.MinimumCirclePoints: Mesh options listMesh.MinimumCurvePoints: Mesh options listMesh.MshFilePartitioned: Mesh options listMesh.MshFileVersion: Mesh options listMesh.MultiplePassesMeshes: Mesh options listMesh.NbHexahedra: Mesh options listMesh.NbNodes: Mesh options listMesh.NbPartitions: Mesh options listMesh.NbPrisms: Mesh options listMesh.NbPyramids: Mesh options listMesh.NbQuadrangles: Mesh options listMesh.NbTetrahedra: Mesh options listMesh.NbTriangles: Mesh options listMesh.Normals: Mesh options listMesh.NumSubEdges: Mesh options listMesh.Optimize: Mesh options listMesh.OptimizeNetgen: Mesh options listMesh.Partitioner: Mesh options listMesh.PartitionHexWeight: Mesh options listMesh.PartitionPrismWeight: Mesh options listMesh.PartitionPyramidWeight: Mesh options listMesh.PartitionQuadWeight: Mesh options listMesh.PartitionTetWeight: Mesh options listMesh.PartitionTriWeight: Mesh options listMesh.PointNumbers: Mesh options listMesh.Points: Mesh options listMesh.PointSize: Mesh options listMesh.PointType: Mesh options listMesh.Prisms: Mesh options listMesh.Pyramids: Mesh options listMesh.Quadrangles: Mesh options listMesh.QualityInf: Mesh options listMesh.QualitySup: Mesh options listMesh.QualityType: Mesh options listMesh.RadiusInf: Mesh options listMesh.RadiusSup: Mesh options listMesh.RandomFactor: Mesh options listMesh.RecombinationAlgorithm: Mesh options listMesh.RecombineAll: Mesh options listMesh.RefineSteps: Mesh options listMesh.RemeshAlgorithm: Mesh options listMesh.RemeshParametrization: Mesh options listMesh.Remove4Triangles: Mesh options listMesh.ReverseAllNormals: Mesh options listMesh.SaveAll: Mesh options listMesh.SaveElementTagType: Mesh options listMesh.SaveGroupsOfNodes: Mesh options listMesh.SaveParametric: Mesh options listMesh.ScalingFactor: Mesh options listMesh.SecondOrderExperimental: Mesh options listMesh.SecondOrderIncomplete: Mesh options listMesh.SecondOrderLinear: Mesh options listMesh.Smoothing: Mesh options listMesh.SmoothNormals: Mesh options listMesh.SmoothRatio: Mesh options listMesh.SubdivisionAlgorithm: Mesh options listMesh.SurfaceEdges: Mesh options listMesh.SurfaceFaces: Mesh options listMesh.SurfaceNumbers: Mesh options listMesh.SwitchElementTags: Mesh options listMesh.Tangents: Mesh options listMesh.Tetrahedra: Mesh options listMesh.ToleranceEdgeLength: Mesh options listMesh.Triangles: Mesh options listMesh.VolumeEdges: Mesh options listMesh.VolumeFaces: Mesh options listMesh.VolumeNumbers: Mesh options listMesh.Voronoi: Mesh options listMesh.ZoneDefinition: Mesh options listMin: Specifying mesh element sizesMinAniso: Specifying mesh element sizesModulo ( expression, expression ): Built-in functionsMPI_Rank: General commandsMPI_Size: General commandsnewl: General commandsnewll: General commandsnewp: General commandsnewreg: General commandsnews: General commandsnewsl: General commandsnewv: General commandsNonBlockingSystemCall char-expression;: General commandsParam: Specifying mesh element sizesPeriodic Line { expression-list } = { expression-list };: Miscellaneous mesh commandsPeriodic Surface expression { expression-list } = expression { expression-list };: Miscellaneous mesh commandsPhysical Line ( expression | char-expression ) = { expression-list };: LinesPhysical Point ( expression | char-expression ) = { expression-list };: PointsPhysical Surface ( expression | char-expression ) = { expression-list };: SurfacesPhysical Volume ( expression | char-expression ) = { expression-list };: VolumesPi: General commandsPlane Surface ( expression ) = { expression-list };: SurfacesPlugin (string) . Run;: Post-processing commandsPlugin (string) . string = expression | char-expression;: Post-processing commandsPlugin(AnalyseCurvedMesh): Post-processing pluginsPlugin(Annotate): Post-processing pluginsPlugin(Bubbles): Post-processing pluginsPlugin(Curl): Post-processing pluginsPlugin(CutBox): Post-processing pluginsPlugin(CutGrid): Post-processing pluginsPlugin(CutParametric): Post-processing pluginsPlugin(CutPlane): Post-processing pluginsPlugin(CutSphere): Post-processing pluginsPlugin(DiscretizationError): Post-processing pluginsPlugin(Distance): Post-processing pluginsPlugin(Divergence): Post-processing pluginsPlugin(Eigenvalues): Post-processing pluginsPlugin(Eigenvectors): Post-processing pluginsPlugin(ExtractEdges): Post-processing pluginsPlugin(ExtractElements): Post-processing pluginsPlugin(FieldFromAmplitudePhase): Post-processing pluginsPlugin(Gradient): Post-processing pluginsPlugin(GSHHS): Post-processing pluginsPlugin(HarmonicToTime): Post-processing pluginsPlugin(HomologyComputation): Post-processing pluginsPlugin(HomologyPostProcessing): Post-processing pluginsPlugin(Integrate): Post-processing pluginsPlugin(Isosurface): Post-processing pluginsPlugin(Lambda2): Post-processing pluginsPlugin(LongitudeLatitude): Post-processing pluginsPlugin(MakeSimplex): Post-processing pluginsPlugin(MathEval): Post-processing pluginsPlugin(MinMax): Post-processing pluginsPlugin(ModifyComponent): Post-processing pluginsPlugin(ModulusPhase): Post-processing pluginsPlugin(NearestNeighbor): Post-processing pluginsPlugin(NearToFarField): Post-processing pluginsPlugin(NewView): Post-processing pluginsPlugin(Particles): Post-processing pluginsPlugin(Probe): Post-processing pluginsPlugin(Remove): Post-processing pluginsPlugin(Scal2Vec): Post-processing pluginsPlugin(Skin): Post-processing pluginsPlugin(Smooth): Post-processing pluginsPlugin(SphericalRaise): Post-processing pluginsPlugin(StreamLines): Post-processing pluginsPlugin(Tetrahedralize): Post-processing pluginsPlugin(Transform): Post-processing pluginsPlugin(Triangulate): Post-processing pluginsPlugin(Warp): Post-processing pluginsPoint ( expression ) = { expression, expression, expression <, expression > };: PointsPoint | Line { expression-list } In Surface { expression };: Miscellaneous mesh commandsPostProcessing.AnimationCycle: Post-processing options listPostProcessing.AnimationDelay: Post-processing options listPostProcessing.AnimationStep: Post-processing options listPostProcessing.CombineRemoveOriginal: Post-processing options listPostProcessing.Format: Post-processing options listPostProcessing.HorizontalScales: Post-processing options listPostProcessing.Link: Post-processing options listPostProcessing.NbViews: Post-processing options listPostProcessing.Plugins: Post-processing options listPostProcessing.Smoothing: Post-processing options listPostView: Specifying mesh element sizesPrint char-expression;: General commandsPrint.Background: General options listPrint.CompositeWindows: General options listPrint.DeleteTemporaryFiles: General options listPrint.EpsBestRoot: General options listPrint.EpsCompress: General options listPrint.EpsLineWidthFactor: General options listPrint.EpsOcclusionCulling: General options listPrint.EpsPointSizeFactor: General options listPrint.EpsPS3Shading: General options listPrint.EpsQuality: General options listPrint.Format: General options listPrint.GeoLabels: General options listPrint.GeoOnlyPhysicals: General options listPrint.GifDither: General options listPrint.GifInterlace: General options listPrint.GifSort: General options listPrint.GifTransparent: General options listPrint.Height: General options listPrint.JpegQuality: General options listPrint.JpegSmoothing: General options listPrint.PostDisto: General options listPrint.PostElement: General options listPrint.PostElementary: General options listPrint.PostEta: General options listPrint.PostGamma: General options listPrint.PostRho: General options listPrint.TexAsEquation: General options listPrint.Text: General options listPrint.Width: General options listPrintf ( char-expression , expression-list ) > char-expression;: General commandsPrintf ( char-expression , expression-list ) >> char-expression;: General commandsPrintf ( char-expression <, expression-list> );: General commandsRand ( expression ): Built-in functions *= expression;: General commands += expression;: General commands -= expression;: General commands /= expression;: General commands = expression;: General commandsRecombine Surface { expression-list } | "*" < = expression >;: Miscellaneous mesh commandsRefineMesh;: General commandsRestrict: Specifying mesh element sizesReturn: User-defined functionsRotate { { expression-list }, { expression-list }, expression } { transform-list }: TransformationsRuled Surface ( expression ) = { expression-list } < In Sphere { expression } >;: SurfacesSave char-expression;: Miscellaneous mesh commandsSave View[expression] char-expression;: Post-processing commandsSetName char-expression;: General commandsShow char-expression;: Miscellaneous mesh commandsShow char-expression;: Miscellaneous geometry commandsShow { Point | Line | Surface | Volume { expression-list }; ... }: Miscellaneous mesh commandsShow { Point | Line | Surface | Volume { expression-list }; ... }: Miscellaneous geometry commandsSin ( expression ): Built-in functionsSinh ( expression ): Built-in functionsSleep expression;: General commandsSmoother Surface { expression-list } = expression;: Miscellaneous mesh commandsSolver.AlwaysListen: Solver options listSolver.AutoArchiveOutputFiles: Solver options listSolver.AutoCheck: Solver options listSolver.AutoHideNewViews: Solver options listSolver.AutoMergeFile: Solver options listSolver.AutoMesh: Solver options listSolver.AutoSaveDatabase: Solver options listSolver.AutoShowLastStep: Solver options listSolver.Executable0: Solver options listSolver.Executable1: Solver options listSolver.Executable2: Solver options listSolver.Executable3: Solver options listSolver.Executable4: Solver options listSolver.Name0: Solver options listSolver.Name1: Solver options listSolver.Name2: Solver options listSolver.Name3: Solver options listSolver.Name4: Solver options listSolver.Plugins: Solver options listSolver.RemoteLogin0: Solver options listSolver.RemoteLogin1: Solver options listSolver.RemoteLogin2: Solver options listSolver.RemoteLogin3: Solver options listSolver.RemoteLogin4: Solver options listSolver.SocketName: Solver options listSolver.Timeout: Solver options listSpline ( expression ) = { expression-list };: LinesSqrt ( expression ): Built-in functions *= expression;: General commands += expression;: General commands += { expression-list };: General commands -= expression;: General commands -= { expression-list };: General commands /= expression;: General commands = char-expression;: General commands = expression;: General commands = { expression-list };: General commands = { };: General commands [ { expression-list } ] *= { expression-list };: General commands [ { expression-list } ] += { expression-list };: General commands [ { expression-list } ] -= { expression-list };: General commands [ { expression-list } ] /= { expression-list };: General commands [ { expression-list } ] = { expression-list };: General commandsStructured: Specifying mesh element sizesSurface Loop ( expression ) = { expression-list };: SurfacesSymmetry { expression-list } { transform-list }: TransformationsSyncModel;: General commandsSystemCall char-expression;: General commandsTan ( expression ): Built-in functionsTanh ( expression ): Built-in functionsThreshold: Specifying mesh element sizesTransfinite Line { expression-list } | "*" = expression < Using Progression | Bump expression >;: Structured gridsTransfinite Surface { expression-list } | "*" < = { expression-list } > < Left | Right | Alternate > ;: Structured gridsTransfinite Volume { expression-list } | "*" < = { expression-list } > ;: Structured gridsTranslate { expression-list } { transform-list }: TransformationsUTM: Specifying mesh element sizesView "string" { string < ( expression-list ) > { expression-list }; ... };: Post-processing commandsView.AbscissaRangeType: Post-processing options listView.AdaptVisualizationGrid: Post-processing options listView.AngleSmoothNormals: Post-processing options listView.ArrowSizeMax: Post-processing options listView.ArrowSizeMin: Post-processing options listView.Attributes: Post-processing options listView.AutoPosition: Post-processing options listView.Axes: Post-processing options listView.AxesAutoPosition: Post-processing options listView.AxesFormatX: Post-processing options listView.AxesFormatY: Post-processing options listView.AxesFormatZ: Post-processing options listView.AxesLabelX: Post-processing options listView.AxesLabelY: Post-processing options listView.AxesLabelZ: Post-processing options listView.AxesMaxX: Post-processing options listView.AxesMaxY: Post-processing options listView.AxesMaxZ: Post-processing options listView.AxesMikado: Post-processing options listView.AxesMinX: Post-processing options listView.AxesMinY: Post-processing options listView.AxesMinZ: Post-processing options listView.AxesTicsX: Post-processing options listView.AxesTicsY: Post-processing options listView.AxesTicsZ: Post-processing options listView.Boundary: Post-processing options listView.CenterGlyphs: Post-processing options listView.Clip: Post-processing options listView.Color.Axes: Post-processing options listView.Color.Background2D: Post-processing options listView.Color.Hexahedra: Post-processing options listView.Color.Lines: Post-processing options listView.Color.Normals: Post-processing options listView.Color.Points: Post-processing options listView.Color.Prisms: Post-processing options listView.Color.Pyramids: Post-processing options listView.Color.Quadrangles: Post-processing options listView.Color.Tangents: Post-processing options listView.Color.Tetrahedra: Post-processing options listView.Color.Text2D: Post-processing options listView.Color.Text3D: Post-processing options listView.Color.Triangles: Post-processing options listView.ColormapAlpha: Post-processing options listView.ColormapAlphaPower: Post-processing options listView.ColormapBeta: Post-processing options listView.ColormapBias: Post-processing options listView.ColormapCurvature: Post-processing options listView.ColormapInvert: Post-processing options listView.ColormapNumber: Post-processing options listView.ColormapRotation: Post-processing options listView.ColormapSwap: Post-processing options listView.ColorTable: Post-processing options listView.ComponentMap0: Post-processing options listView.ComponentMap1: Post-processing options listView.ComponentMap2: Post-processing options listView.ComponentMap3: Post-processing options listView.ComponentMap4: Post-processing options listView.ComponentMap5: Post-processing options listView.ComponentMap6: Post-processing options listView.ComponentMap7: Post-processing options listView.ComponentMap8: Post-processing options listView.CustomAbscissaMax: Post-processing options listView.CustomAbscissaMin: Post-processing options listView.CustomMax: Post-processing options listView.CustomMin: Post-processing options listView.DisplacementFactor: Post-processing options listView.DrawHexahedra: Post-processing options listView.DrawLines: Post-processing options listView.DrawPoints: Post-processing options listView.DrawPrisms: Post-processing options listView.DrawPyramids: Post-processing options listView.DrawQuadrangles: Post-processing options listView.DrawScalars: Post-processing options listView.DrawSkinOnly: Post-processing options listView.DrawStrings: Post-processing options listView.DrawTensors: Post-processing options listView.DrawTetrahedra: Post-processing options listView.DrawTriangles: Post-processing options listView.DrawVectors: Post-processing options listView.Explode: Post-processing options listView.ExternalView: Post-processing options listView.FakeTransparency: Post-processing options listView.FileName: Post-processing options listView.ForceNumComponents: Post-processing options listView.Format: Post-processing options listView.GeneralizedRaiseFactor: Post-processing options listView.GeneralizedRaiseView: Post-processing options listView.GeneralizedRaiseX: Post-processing options listView.GeneralizedRaiseY: Post-processing options listView.GeneralizedRaiseZ: Post-processing options listView.GlyphLocation: Post-processing options listView.Height: Post-processing options listView.IntervalsType: Post-processing options listView.Light: Post-processing options listView.LightLines: Post-processing options listView.LightTwoSide: Post-processing options listView.LineType: Post-processing options listView.LineWidth: Post-processing options listView.Max: Post-processing options listView.MaxRecursionLevel: Post-processing options listView.MaxX: Post-processing options listView.MaxY: Post-processing options listView.MaxZ: Post-processing options listView.Min: Post-processing options listView.MinX: Post-processing options listView.MinY: Post-processing options listView.MinZ: Post-processing options listView.Name: Post-processing options listView.NbIso: Post-processing options listView.NbTimeStep: Post-processing options listView.NormalRaise: Post-processing options listView.Normals: Post-processing options listView.OffsetX: Post-processing options listView.OffsetY: Post-processing options listView.OffsetZ: Post-processing options listView.PointSize: Post-processing options listView.PointType: Post-processing options listView.PositionX: Post-processing options listView.PositionY: Post-processing options listView.RaiseX: Post-processing options listView.RaiseY: Post-processing options listView.RaiseZ: Post-processing options listView.RangeType: Post-processing options listView.Sampling: Post-processing options listView.SaturateValues: Post-processing options listView.ScaleType: Post-processing options listView.ShowElement: Post-processing options listView.ShowScale: Post-processing options listView.ShowTime: Post-processing options listView.SmoothNormals: Post-processing options listView.Stipple: Post-processing options listView.Stipple0: Post-processing options listView.Stipple1: Post-processing options listView.Stipple2: Post-processing options listView.Stipple3: Post-processing options listView.Stipple4: Post-processing options listView.Stipple5: Post-processing options listView.Stipple6: Post-processing options listView.Stipple7: Post-processing options listView.Stipple8: Post-processing options listView.Stipple9: Post-processing options listView.Tangents: Post-processing options listView.TargetError: Post-processing options listView.TensorType: Post-processing options listView.TimeStep: Post-processing options listView.TransformXX: Post-processing options listView.TransformXY: Post-processing options listView.TransformXZ: Post-processing options listView.TransformYX: Post-processing options listView.TransformYY: Post-processing options listView.TransformYZ: Post-processing options listView.TransformZX: Post-processing options listView.TransformZY: Post-processing options listView.TransformZZ: Post-processing options listView.Type: Post-processing options listView.UseGeneralizedRaise: Post-processing options listView.VectorType: Post-processing options listView.Visible: Post-processing options listView.Width: Post-processing options listVolume ( expression ) = { expression-list };: Volumes||: Operators[1] Note that mixing structured volume grids with unstructured volume grids generated with the default 3D Delaunay algorithm can result, in certain cases, to non-conform surface meshes on their shared boundary. If this happens, you may consider using the frontal algorithm for the unstructured part.
[2] Nearly all the interactive commands have shortcuts: see Keyboard shortcuts, or select `Help->Keyboard Shortcuts' in the menu. For example, to quickly save a mesh, you can press Ctrl+Shift+s.
[3] If you compile Gmsh without the GUI, this is the only mode you have access to.
[4] The affectation operators are introduced in General commands.
[5] For compatibility with GetDP
(http://geuz.org/getdp/), parentheses can be replaced by brackets
[].
[6] For
compatibility purposes, the behavior of newl, news,
newv and newreg can be modified with the
Geometry.OldNewReg option (see Geometry options list).
[7] R. A. Dwyer, A simple divide-and-conquer algorithm for computing Delaunay triangulations in O(n log n) expected time, In Proceedings of the second annual symposium on computational geometry, Yorktown Heights, 2–4 June 1986.
[8] N. P. Weatherill, The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation, Commun. Appl. Numer. Methods 6(2), pp. 101–109, 1990.
[9] C. Geuzaine and J.-F. Remacle, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, International Journal for Numerical Methods in Engineering 79(11), pp. 1309–1331, 2009.
[10] P.-L. George and P. Frey, Mesh generation, Hermes, Lyon, 2000.
[11] S. Rebay, Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm, J. Comput. Phys. 106, pp. 25–138, 1993.
[12] H. Si, Tetgen: a quality tetrahedral mesh generator and three-dimensional Delaunay triangulator, 2004.
[13] J. Schoeberl, Netgen, an advancing front 2d/3d-mesh generator based on abstract rules, Comput. Visual. Sci., 1, pp. 41–52, 1997.
[14] This behaviour was introduced in Gmsh 2.0. In older versions, both the elementary and the physical region numbers would be set to the identification number of the elementary region.