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Classes


Namespace JXG.Math.Geometry


Defined in: MathGeometry.js.

Namespace Summary
Constructor Attributes Constructor Name and Description
 
Math.Geometry namespace definition
Field Summary
Field Attributes Field Name and Description
<static>  
JXG.Math.Geometry.circumcenterMidpoint
Method Summary
Method Attributes Method Name and Description
<static>  
JXG.Math.Geometry.affineDistance(array1, array2)
Calculates euclidean distance for two given arrays of the same length.
<static>  
JXG.Math.Geometry.angle(A, B, C)
Calculates the angle defined by the points A, B, C.
<static>  
JXG.Math.Geometry.angleBisector(A, B, C, board)
Calculates the bisection between the three points A, B, C.
<static>  
JXG.Math.Geometry.calcStraight(el, point1, point2, margin)
A line can be a segment, a straight, or a ray.
<static>  
JXG.Math.Geometry.circumcenter(point1, point2, point3, board)
Calculates the center of the circumcircle of the three given points.
<static>  
JXG.Math.Geometry.distance(array1, array2)
Calculates euclidean norm for two given arrays of the same length.
<static>  
JXG.Math.Geometry.distPointLine(point, line)
Calculates the distance of a point to a line.
<static>  
JXG.Math.Geometry.intersectCircleCircle(circle1, circle2, board)
Calculates the coordinates of the intersection of the given circles.
<static>  
JXG.Math.Geometry.intersectCircleLine(circle, line, board)
Calculates the coordinates of the intersection of the given line and circle.
<static>  
JXG.Math.Geometry.intersectLineLine(line1, line2, board)
Calculates the coordinates of the intersection of the given lines.
<static>  
JXG.Math.Geometry.isSameDir(p1, p2, i1, i2)
The vectors p2-p1 and i2-i1 are supposed to be collinear.
<static>  
JXG.Math.Geometry.isSameDirection(start, p, s)
If you're looking from point "start" towards point "s" and can see the point "p", true is returned.
<static>  
JXG.Math.Geometry.meet(el1, el2, i, board)
Computes the intersection of a pair of lines, circles or both.
<static>  
JXG.Math.Geometry.meetCircleCircle(circ1, circ2, i, board)
Intersection of two circles using the stdform.
<static>  
JXG.Math.Geometry.meetCurveCurve(c1, c2, t1ini, t2ini, board)
Compute an intersection of the curves c1 and c2 with a generalized Newton method.
<static>  
JXG.Math.Geometry.meetCurveLine(el1, el2, nr, board, pointObj)
Intersection of curve with line, Order of input does not matter for el1 and el2.
<static>  
JXG.Math.Geometry.meetCurveLineContinuous(cu, li, nr, board)
Intersection of line and curve, continuous case.
<static>  
JXG.Math.Geometry.meetCurveLineDiscrete(cu, li, nr, board, pointObj)
Intersection of line and curve, continuous case.
<static>  
JXG.Math.Geometry.meetLineCircle(lin, circ, i, board)
Intersection of line and circle using the stdform.
<static>  
JXG.Math.Geometry.meetLineLine(l1, l2, i, board)
Intersection of two lines using the stdform.
<static>  
JXG.Math.Geometry.meetSegmentSegment(p1, p2, q1, q2, board)
Intersection of two segments.
<static>  
JXG.Math.Geometry.perpendicular(line, point, board)
Calculates the coordinates of a point on the perpendicular to the given line through the given point.
<static>  
JXG.Math.Geometry.projectCoordsToCurve(x, y, t, curve, board)
Calculates the coordinates of the projection of a coordinates pair on a given curve.
<static>  
JXG.Math.Geometry.projectCoordsToSegment(p1, q1, q2)
Calculates the coordinates of the orthogonal projection of a given coordinate array on a given line segment defined by two coordinate arrays.
<static>  
JXG.Math.Geometry.projectPointToCircle(point, circle, board)
Calculates the coordinates of the projection of a given point on a given circle.
<static>  
JXG.Math.Geometry.projectPointToCurve(point, curve, board)
Calculates the coordinates of the projection of a given point on a given curve.
<static>  
JXG.Math.Geometry.projectPointToLine(point, line, board)
Calculates the coordinates of the orthogonal projection of a given point on a given line.
<static>  
JXG.Math.Geometry.projectPointToPoint(point, dest, board)
Trivial projection of a point to another point.
<static>  
JXG.Math.Geometry.projectPointToTurtle(point, turtle, board)
Calculates the coordinates of the projection of a given point on a given turtle.
<static>  
JXG.Math.Geometry.rad(A, B, C)
Calculates the internal angle defined by the three points A, B, C if you're going from A to C around B counterclockwise.
<static>  
JXG.Math.Geometry.reflection(line, point, board)
Reflects the point along the line.
<static>  
JXG.Math.Geometry.rotation(rotpoint, point, phi, board)
Computes the new position of a point which is rotated around a second point (called rotpoint) by the angle phi.
<static>  
JXG.Math.Geometry.trueAngle(A, B, C)
Calculates the angle defined by the three points A, B, C if you're going from A to C around B counterclockwise.
Namespace Detail
JXG.Math.Geometry
Math.Geometry namespace definition
Field Detail
<static> JXG.Math.Geometry.circumcenterMidpoint
Deprecated:
Please use JXG.Math.Geometry#circumcenter instead.
Method Detail
<static> {Number} JXG.Math.Geometry.affineDistance(array1, array2)
Calculates euclidean distance for two given arrays of the same length. If one of the arrays contains a zero in the first coordinate, and the euclidean distance is different from zero it is a point at infinity and we return Infinity.
Parameters:
{Array} array1
Array containing elements of number.
{Array} array2
Array containing elements of type number.
Returns:
{Number} Euclidean (affine) distance of the given vectors.

<static> {Number} JXG.Math.Geometry.angle(A, B, C)
Calculates the angle defined by the points A, B, C.
Parameters:
{JXG.Point} A
A point or [x,y] array.
{JXG.Point} B
Another point or [x,y] array.
{JXG.Point} C
A circle - no, of course the third point or [x,y] array.
Deprecated:
Use JXG.Math.Geometry#rad instead.
Returns:
{Number} The angle in radian measure.
See:
#rad
#trueAngle

<static> {JXG.Coords} JXG.Math.Geometry.angleBisector(A, B, C, board)
Calculates the bisection between the three points A, B, C. The bisection is defined by two points: Parameter B and a point with the coordinates calculated in this function.
Parameters:
{JXG.Point} A
Point
{JXG.Point} B
Point
{JXG.Point} C
Point
board Optional, Default: A.board
Reference to the board
Returns:
{JXG.Coords} Coordinates of the second point defining the bisection.

<static> JXG.Math.Geometry.calcStraight(el, point1, point2, margin)
A line can be a segment, a straight, or a ray. so it is not always delimited by point1 and point2 calcStraight determines the visual start point and end point of the line. A segment is only drawn from start to end point, a straight line is drawn until it meets the boards boundaries.
Parameters:
{JXG.Line} el
Reference to a line object, that needs calculation of start and end point.
{JXG.Coords} point1
Coordinates of the point where line drawing begins. This value is calculated and set by this method.
{JXG.Coords} point2
Coordinates of the point where line drawing ends. This value is calculated and set by this method.
{Number} margin
Optional margin, to avoid the display of the small sides of lines.
See:
Line
JXG.Line

<static> {JXG.Coords} JXG.Math.Geometry.circumcenter(point1, point2, point3, board)
Calculates the center of the circumcircle of the three given points.
Parameters:
{JXG.Point} point1
Point
{JXG.Point} point2
Point
{JXG.Point} point3
Point
{JXG.Board} board Optional, Default: point1.board
Reference to the board
Returns:
{JXG.Coords} Coordinates of the center of the circumcircle of the given points.

<static> {Number} JXG.Math.Geometry.distance(array1, array2)
Calculates euclidean norm for two given arrays of the same length.
Parameters:
{Array} array1
Array of float or integer.
{Array} array2
Array of float or integer.
Returns:
{Number} Euclidean distance of the given vectors.

<static> {Number} JXG.Math.Geometry.distPointLine(point, line)
Calculates the distance of a point to a line. The point and the line are given by homogeneous coordinates. For lines this can be line.stdform.
Parameters:
{Array} point
Homogeneous coordinates of a point.
{Array} line
Homogeneous coordinates of a line ([C,A,B] where A*x+B*y+C*z=0).
Returns:
{Number} Distance of the point to the line.

<static> {Array} JXG.Math.Geometry.intersectCircleCircle(circle1, circle2, board)
Calculates the coordinates of the intersection of the given circles.
Parameters:
{JXG.Circle} circle1
Circle.
{JXG.Circle} circle2
Circle.
{JXG.Board} board Optional, Default: circle1.board
Reference to the board
Returns:
{Array} Coordinates of the intersection points of the given circles and the amount of intersection points in the first component of the array.

<static> {Array} JXG.Math.Geometry.intersectCircleLine(circle, line, board)
Calculates the coordinates of the intersection of the given line and circle.
Parameters:
{JXG.Circle} circle
Circle.
{JXG.Line} line
Line.
{JXG.Board} board Optional, Default: line.board
Reference to the board
Returns:
{Array} The coordinates of the intersection points of the given circle with the given line and the amount of intersection points in the first component of the array.

<static> {JXG.Coords} JXG.Math.Geometry.intersectLineLine(line1, line2, board)
Calculates the coordinates of the intersection of the given lines.
Parameters:
{JXG.Line} line1
Line.
{JXG.Line} line2
Line.
{JXG.Board} board Optional, Default: line1.board
Reference to the board
Returns:
{JXG.Coords} Coordinates of the intersection point of the given lines.

<static> {Boolean} JXG.Math.Geometry.isSameDir(p1, p2, i1, i2)
The vectors p2-p1 and i2-i1 are supposed to be collinear. If their cosine is positive they point into the same direction otherwise they point in opposite direction
Parameters:
{JXG.Coords} p1
{JXG.Coords} p2
{JXG.Coords} i1
{JXG.Coords} i2
Returns:
{Boolean} True, if p2-p1 and i2-i1 point into the same direction

<static> {Boolean} JXG.Math.Geometry.isSameDirection(start, p, s)
If you're looking from point "start" towards point "s" and can see the point "p", true is returned. Otherwise false.
Parameters:
{JXG.Coords} start
The point you're standing on.
{JXG.Coords} p
The point in which direction you're looking.
{JXG.Coords} s
The point that should be visible.
Returns:
{Boolean} True, if from start the point p is in the same direction as s is, that means s-start = k*(p-start) with k>=0.

<static> {JXG.Coords} JXG.Math.Geometry.meet(el1, el2, i, board)
Computes the intersection of a pair of lines, circles or both. It uses the internal data array stdform of these elements.
Parameters:
{Array} el1
stdform of the first element (line or circle)
{Array} el2
stdform of the second element (line or circle)
{Number} i
Index of the intersection point that should be returned.
board
Reference to the board.
Returns:
{JXG.Coords} Coordinates of one of the possible two or more intersection points. Which point will be returned is determined by i.

<static> {JXG.Coords} JXG.Math.Geometry.meetCircleCircle(circ1, circ2, i, board)
Intersection of two circles using the stdform.
Parameters:
{Array} circ1
stdform of the first circle
{Array} circ2
stdform of the second circle
{number} i
number of the returned intersection point. i==0: use the positive square root, i==1: use the negative square root.
{JXG.Board} board
Reference to the board.
Returns:
{JXG.Coords} Coordinates of the intersection point

<static> {JXG.Coords} JXG.Math.Geometry.meetCurveCurve(c1, c2, t1ini, t2ini, board)
Compute an intersection of the curves c1 and c2 with a generalized Newton method. We want to find values t1, t2 such that c1(t1) = c2(t2), i.e. (c1_x(t1)-c2_x(t2),c1_y(t1)-c2_y(t2)) = (0,0). We set (e,f) := (c1_x(t1)-c2_x(t2),c1_y(t1)-c2_y(t2)) The Jacobian J is defined by J = (a, b) (c, d) where a = c1_x'(t1) b = -c2_x'(t2) c = c1_y'(t1) d = -c2_y'(t2) The inverse J^(-1) of J is equal to (d, -b)/ (-c, a) / (ad-bc) Then, (t1new, t2new) := (t1,t2) - J^(-1)*(e,f). If the function meetCurveCurve possesses the properties t1memo and t2memo then these are taken as start values for the Newton algorithm. After stopping of the Newton algorithm the values of t1 and t2 are stored in t1memo and t2memo.
Parameters:
{JXG.Curve} c1
Curve, Line or Circle
{JXG.Curve} c2
Curve, Line or Circle
{Number} t1ini
start value for t1
{Number} t2ini
start value for t2
{JXG.Board} board Optional, Default: c1.board
Reference to a board object.
Returns:
{JXG.Coords} intersection point

<static> {JXG.Coords} JXG.Math.Geometry.meetCurveLine(el1, el2, nr, board, pointObj)
Intersection of curve with line, Order of input does not matter for el1 and el2.
Parameters:
{JXG.Curve|JXG.Line} el1
Curve or Line
{JXG.Curve|JXG.Line} el2
Curve or Line
{Number} nr
the nr-th intersection point will be returned.
{JXG.Board} board Optional, Default: el1.board
Reference to a board object.
pointObj
Returns:
{JXG.Coords} Intersection point. In case no intersection point is detected, the ideal point [0,1,0] is returned.

<static> JXG.Math.Geometry.meetCurveLineContinuous(cu, li, nr, board)
Intersection of line and curve, continuous case. Segments are treated as lines. Finding the nr-the intersection point works for nr=0,1 only. BUG: does not respect cu.minX() and cu.maxX()
Parameters:
cu
li
nr
board

<static> JXG.Math.Geometry.meetCurveLineDiscrete(cu, li, nr, board, pointObj)
Intersection of line and curve, continuous case. Segments are treated as lines. Finding the nr-the intersection point should work for all nr.
Parameters:
cu
li
nr
board
pointObj

<static> {JXG.Coords} JXG.Math.Geometry.meetLineCircle(lin, circ, i, board)
Intersection of line and circle using the stdform.
Parameters:
{Array} lin
stdform of the line
{Array} circ
stdform of the circle
{number} i
number of the returned intersection point. i==0: use the positive square root, i==1: use the negative square root.
{JXG.Board} board
Reference to a board.
Returns:
{JXG.Coords} Coordinates of the intersection point

<static> {JXG.Coords} JXG.Math.Geometry.meetLineLine(l1, l2, i, board)
Intersection of two lines using the stdform.
Parameters:
{Array} l1
stdform of the first line
{Array} l2
stdform of the second line
{number} i
unused
{JXG.Board} board
Reference to the board.
Returns:
{JXG.Coords} Coordinates of the intersection point.

<static> {Array} JXG.Math.Geometry.meetSegmentSegment(p1, p2, q1, q2, board)
Intersection of two segments.
Parameters:
{Array} p1
First point of segment 1 using homogeneous coordinates [z,x,y]
{Array} p2
Second point of segment 1 using homogeneous coordinates [z,x,y]
{Array} q1
First point of segment 2 using homogeneous coordinates [z,x,y]
{Array} q2
Second point of segment 2 using homogeneous coordinates [z,x,y]
board
Returns:
{Array} [Intersection point, t, u] The first entry contains the homogeneous coordinates of the intersection point. The second and third entry gives the position of the intersection between the two defining points. For example, the second entry t is defined by: interestion point = t*p1 + (1-t)*p2.

<static> {JXG.Coords} JXG.Math.Geometry.perpendicular(line, point, board)
Calculates the coordinates of a point on the perpendicular to the given line through the given point.
Parameters:
{JXG.Line} line
A line.
{JXG.Point} point
Intersection point of line to perpendicular.
{JXG.Board} board Optional, Default: point.board
Reference to the board
Returns:
{JXG.Coords} Coordinates of a point on the perpendicular to the given line through the given point.

<static> {JXG.Coords} JXG.Math.Geometry.projectCoordsToCurve(x, y, t, curve, board)
Calculates the coordinates of the projection of a coordinates pair on a given curve. In case of function graphs this is the intersection point of the curve and the parallel to y-axis through the given point.
Parameters:
{Number} x
coordinate to project.
{Number} y
coordinate to project.
{Number} t
start value for newtons method
{JXG.Curve} curve
Curve on that the point is projected.
{JXG.Board} board Optional, Default: curve.board
Reference to a board.
Returns:
{JXG.Coords} Array containing the coordinates of the projection of the given point on the given graph and the position on the curve.
See:
#projectPointToCurve

<static> {Array} JXG.Math.Geometry.projectCoordsToSegment(p1, q1, q2)
Calculates the coordinates of the orthogonal projection of a given coordinate array on a given line segment defined by two coordinate arrays.
Parameters:
{Array} p1
Point to project.
{Array} q1
Start point of the line segment on that the point is projected.
{Array} q2
End point of the line segment on that the point is projected.
Returns:
{Array} The coordinates of the projection of the given point on the given segment and the factor that determines the projected point as a convex combination of the two endpoints q1 and q2 of the segment.

<static> {JXG.Coords} JXG.Math.Geometry.projectPointToCircle(point, circle, board)
Calculates the coordinates of the projection of a given point on a given circle. I.o.w. the nearest one of the two intersection points of the line through the given point and the circles center.
Parameters:
{JXG.Point_JXG.Coords} point
Point to project or coords object to project.
{JXG.Circle} circle
Circle on that the point is projected.
{JXG.Board} board Optional, Default: point.board
Reference to the board
Returns:
{JXG.Coords} The coordinates of the projection of the given point on the given circle.

<static> {JXG.Coords} JXG.Math.Geometry.projectPointToCurve(point, curve, board)
Calculates the coordinates of the projection of a given point on a given curve. Uses #projectCoordsToCurve.
Parameters:
{JXG.Point} point
Point to project.
{JXG.Curve} curve
Curve on that the point is projected.
{JXG.Board} board Optional, Default: point.board
Reference to a board.
Returns:
{JXG.Coords} The coordinates of the projection of the given point on the given graph.
See:
#projectCoordsToCurve

<static> {JXG.Coords} JXG.Math.Geometry.projectPointToLine(point, line, board)
Calculates the coordinates of the orthogonal projection of a given point on a given line. I.o.w. the intersection point of the given line and its perpendicular through the given point.
Parameters:
{JXG.Point} point
Point to project.
{JXG.Line} line
Line on that the point is projected.
{JXG.Board} board Optional, Default: point.board
Reference to a board.
Returns:
{JXG.Coords} The coordinates of the projection of the given point on the given line.

<static> {JXG.Coords} JXG.Math.Geometry.projectPointToPoint(point, dest, board)
Trivial projection of a point to another point.
Parameters:
{JXG.Point} point
Point to project (not used).
{JXG.Point} dest
Point on that the point is projected.
{JXG.Board} board Optional, Default: point.board
Reference to the board (not used).
Returns:
{JXG.Coords} The coordinates of the projection of the given point on the given circle.

<static> {JXG.Coords} JXG.Math.Geometry.projectPointToTurtle(point, turtle, board)
Calculates the coordinates of the projection of a given point on a given turtle. A turtle consists of one or more curves of curveType 'plot'. Uses #projectPointToCurve.
Parameters:
{JXG.Point} point
Point to project.
{JXG.Turtle} turtle
on that the point is projected.
{JXG.Board} board Optional, Default: point.board
Reference to a board.
Returns:
{JXG.Coords} The coordinates of the projection of the given point on the given turtle.

<static> {Number} JXG.Math.Geometry.rad(A, B, C)
Calculates the internal angle defined by the three points A, B, C if you're going from A to C around B counterclockwise.
Parameters:
{JXG.Point} A
Point or [x,y] array
{JXG.Point} B
Point or [x,y] array
{JXG.Point} C
Point or [x,y] array
Returns:
{Number} Angle in radians.
See:
#trueAngle

<static> {JXG.Coords} JXG.Math.Geometry.reflection(line, point, board)
Reflects the point along the line.
Parameters:
{JXG.Line} line
Axis of reflection.
{JXG.Point} point
Point to reflect.
board Optional, Default: point.board
Reference to the board
Returns:
{JXG.Coords} Coordinates of the reflected point.

<static> {JXG.Coords} JXG.Math.Geometry.rotation(rotpoint, point, phi, board)
Computes the new position of a point which is rotated around a second point (called rotpoint) by the angle phi.
Parameters:
{JXG.Point} rotpoint
Center of the rotation
{JXG.Point} point
point to be rotated
{number} phi
rotation angle in arc length
{JXG.Board} board Optional, Default: point.board
Reference to the board
Returns:
{JXG.Coords} Coordinates of the new position.

<static> {Number} JXG.Math.Geometry.trueAngle(A, B, C)
Calculates the angle defined by the three points A, B, C if you're going from A to C around B counterclockwise.
Parameters:
{JXG.Point} A
Point or [x,y] array
{JXG.Point} B
Point or [x,y] array
{JXG.Point} C
Point or [x,y] array
Returns:
{Number} The angle in degrees.
See:
#rad

Documentation generated by JsDoc Toolkit 2.4.0 on Fri May 31 2013 05:21:37 GMT-0000 (UTC)