Regina Calculation Engine
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A saturated block that is a three-tetrahedron triangular prism. More...
#include <nsatblocktypes.h>
Public Member Functions | |
NSatTriPrism (const NSatTriPrism &cloneMe) | |
Constructs a clone of the given block structure. | |
bool | isMajor () const |
Is this prism of major type or minor type? See the class notes for further details. | |
virtual NSatBlock * | clone () const |
Returns a newly created clone of this saturated block structure. | |
virtual void | adjustSFS (NSFSpace &sfs, bool reflect) const |
Adjusts the given Seifert fibred space to insert the contents of this saturated block. | |
virtual void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. | |
virtual void | writeAbbr (std::ostream &out, bool tex=false) const |
Writes an abbreviated name or symbol for this block to the given output stream. | |
Static Public Member Functions | |
static NSatTriPrism * | isBlockTriPrism (const NSatAnnulus &annulus, TetList &avoidTets) |
Determines whether the given annulus is a boundary annulus for a block of this type (triangular prism). | |
static NSatTriPrism * | insertBlock (NTriangulation &tri, bool major) |
Inserts a new copy of a triangular prism block into the given triangulation, and returns the corresponding block structure. | |
Protected Member Functions | |
NSatTriPrism (bool major) | |
Constructs a partially initialised block. |
A saturated block that is a three-tetrahedron triangular prism.
Such a prism may be of major type or of minor type. In a major type prism, the horizontal edges of the boundary annuli are all major (degree three) edges of the prism. Likewise, in a minor type prism, the horizontal boundary edges are all minor (degree two) edges of the prism. See the NSatAnnulus class notes for a definition of "horizontal" and the NTriSolidTorus class notes for further details regarding "major" and "minor".
regina::NSatTriPrism::NSatTriPrism | ( | const NSatTriPrism & | cloneMe | ) | [inline] |
Constructs a clone of the given block structure.
cloneMe | the block structure to clone. |
regina::NSatTriPrism::NSatTriPrism | ( | bool | major | ) | [inline, protected] |
Constructs a partially initialised block.
The boundary annuli will remain uninitialised, and must be initialised before this block can be used.
major | true if this block is of major type, or false if it is of minor type. |
virtual void regina::NSatTriPrism::adjustSFS | ( | NSFSpace & | sfs, |
bool | reflect | ||
) | const [virtual] |
Adjusts the given Seifert fibred space to insert the contents of this saturated block.
In particular, the space should be adjusted as though an ordinary solid torus (base orbifold a disc, no twists or exceptional fibres) had been replaced by this block. This description does not make sense for blocks with twisted boundary; the twisted case is discussed below.
If the argument reflect is true
, it should be assumed that this saturated block is being reflected before being inserted into the larger Seifert fibred space. That is, any twists or exceptional fibres should be negated before being added.
Regarding the signs of exceptional fibres: Consider a saturated block containing a solid torus whose meridinal curve runs p times horizontally around the boundary in order through annuli 0,1,... and follows the fibres q times from bottom to top (as depicted in the diagram in the NSatBlock class notes). Then this saturated block adds a positive (p, q) fibre to the underlying Seifert fibred space.
If the ring of saturated annuli bounding this block is twisted then the situation becomes more complex. It can be proven that such a block must contain a twisted reflector boundary in the base orbifold (use Z_2 homology with fibre-reversing paths to show that the base orbifold must contain another twisted boundary component, and then recall that real boundaries are not allowed inside blocks).
In this twisted boundary case, it should be assumed that the twisted reflector boundary is already stored in the given Seifert fibred space. This routine should make any further changes that are required (there may well be none). That is, the space should be adjusted as though a trivial Seifert fibred space over the annulus with one twisted reflector boundary (and one twisted puncture corresponding to the block boundary) had been replaced by this block. In particular, this routine should not add the reflector boundary itself.
sfs | the Seifert fibred space to adjust. |
reflect | true if this block is to be reflected, or false if it should be inserted directly. |
Implements regina::NSatBlock.
NSatBlock * regina::NSatTriPrism::clone | ( | ) | const [inline, virtual] |
Returns a newly created clone of this saturated block structure.
A clone of the correct subclass of NSatBlock will be returned. For this reason, each subclass of NSatBlock must implement this routine.
Implements regina::NSatBlock.
static NSatTriPrism* regina::NSatTriPrism::insertBlock | ( | NTriangulation & | tri, |
bool | major | ||
) | [static] |
Inserts a new copy of a triangular prism block into the given triangulation, and returns the corresponding block structure.
The given triangulation will not be emptied before the new tetrahedra are inserted.
tri | the triangulation into which the new block should be inserted. |
major | true if a block of major type should be inserted, or false if a block of minor type should be inserted. |
static NSatTriPrism* regina::NSatTriPrism::isBlockTriPrism | ( | const NSatAnnulus & | annulus, |
TetList & | avoidTets | ||
) | [static] |
Determines whether the given annulus is a boundary annulus for a block of this type (triangular prism).
This routine is a specific case of NSatBlock::isBlock(); see that routine for further details.
annulus | the proposed boundary annulus that should form part of the new saturated block. |
avoidTets | the list of tetrahedra that should not be considered, and to which any new tetrahedra will be added. |
null
if none was found. bool regina::NSatTriPrism::isMajor | ( | ) | const [inline] |
Is this prism of major type or minor type? See the class notes for further details.
Note that this routine cannot be called major(), since on some compilers that name clashes with a macro for isolating major/minor bytes.
true
if this prism is of major type, or false
if it is of minor type. void regina::NSatTriPrism::writeAbbr | ( | std::ostream & | out, |
bool | tex = false |
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) | const [inline, virtual] |
Writes an abbreviated name or symbol for this block to the given output stream.
This name should reflect the particular block type, but need not provide thorough details.
The output should be no more than a handful of characters long, and no newline should be written. In TeX mode, no leading or trailing dollar signs should be written.
out | the output stream to which to write. |
tex | true if the output should be formatted for TeX, or false if it should be in plain text format. |
Implements regina::NSatBlock.
void regina::NSatTriPrism::writeTextShort | ( | std::ostream & | out | ) | const [inline, virtual] |
Writes this object in short text format to the given output stream.
The output should fit on a single line and no newline should be written.
out | the output stream to which to write. |
Implements regina::ShareableObject.