# JSXGraph 1.10.0 Reference

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Class Index | File Index

Elements

- Angle
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- Axes3D
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- Circumcircle
- CircumcircleArc
- CircumcircleSector
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- CurveDifference
- CurveIntersection
- CurveUnion
- Derivative
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- Functiongraph
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- Glider
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- Incenter
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- Inequality
- Input
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- Intersection
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- Label
- Legend
- Line
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- MajorArc
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- MinorSector
- mirrorelement
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- NonReflexAngle
- Normal
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- OtherIntersection
- Parabola
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- PerpendicularPoint
- PerpendicularSegment
- Point
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- PolarLine
- PolePoint
- Polygon
- PolygonalChain
- RadicalAxis
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- RegularPolygon
- Riemannsum
- Sector
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- Semicircle
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- Smartlabel
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- Spline
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- Tangent
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- Tapemeasure
- Text
- Text3D
- Ticks
- Ticks3D
- Tracecurve
- Transformation
- Turtle
- Vectorfield
- Vectorfield3D
- View3D

Classes

- _global_
- JXG
- JXG.AbstractRenderer
- JXG.Board
- JXG.Board.infobox
- JXG.C
- JXG.CA
- JXG.CanvasRenderer
- JXG.Chart
- JXG.Circle
- JXG.Circle3D
- JXG.Complex
- JXG.Composition
- JXG.Coords
- JXG.CoordsElement
- JXG.Curve
- JXG.Curve3D
- JXG.Dump
- JXG.EventEmitter
- JXG.Expect
- JXG.ForeignObject
- JXG.GeometryElement
- JXG.GeometryElement3D
- JXG.GeonextParser
- JXG.Group
- JXG.Image
- JXG.JessieCode
- JXG.JSXGraph
- JXG.Legend
- JXG.Line
- JXG.Line3D
- JXG.Math
- JXG.Math.BoxQuadtree
- JXG.Math.Clip
- JXG.Math.Extrapolate
- JXG.Math.Geometry
- JXG.Math.ImplicitPlot
- JXG.Math.IntervalArithmetic
- JXG.Math.Metapost
- JXG.Math.Nlp
- JXG.Math.Numerics
- JXG.Math.Plot
- JXG.Math.Poly
- JXG.Math.Poly.Monomial
- JXG.Math.Poly.Polynomial
- JXG.Math.Poly.Ring
- JXG.Math.ProbFuncs
- JXG.Math.Quadtree
- JXG.Math.Statistics
- JXG.Math.Symbolic
- JXG.NoRenderer
- JXG.Options
- JXG.Plane3D
- JXG.Point
- JXG.Point3D
- JXG.Polygon
- JXG.Polygon3D
- JXG.PrefixParser
- JXG.Server
- JXG.Server.modules
- JXG.Sphere3D
- JXG.Surface3D
- JXG.SVGRenderer
- JXG.Text
- JXG.Text3D
- JXG.Ticks
- JXG.Transformation
- JXG.Turtle
- JXG.Util
- JXG.Util.Base64
- JXG.Util.Unzip
- JXG.Util.UTF8
- JXG.View3D
- JXG.VMLRenderer
- JXG.XML

# Namespace JXG.Math.Clip

↳ JXG.Math.Clip

Defined in: clip.js.

Namespace Summary
Constructor Attributes | Constructor Name and Description
--- | ---
| JXG.Math.Clip Math.Clip namespace definition.

Method Summary
Method Attributes | Method Name and Description
--- | ---
<private> <static> | JXG.Math.Clip._addVertex(path, vertex, DEBUG) Add a point to the clipping path and returns if the algorithms arrived at an intersection point which has already been visited.
<private> <static> | JXG.Math.Clip._classifyDegenerateIntersections(P) Determine the delayed status of degenerated intersection points.
<private> <static> | JXG.Math.Clip._countCrossingIntersections(intersections) Count intersection points of type 'X'.
<private> <static> | JXG.Math.Clip._getPath(obj, board) Create path from all sorts of input elements and convert it to a suitable input path for greinerHormann().
<private> <static> | JXG.Math.Clip._getPosition(q, p1, p2, p3) It is testedd if the point q lies to the left or right of the poylgonal chain [p1, p2, p3].
<private> <static> | JXG.Math.Clip._handleFullyDegenerateCase(S, C, board) Handle the case that all vertices of one path are contained in the other path.
<private> <static> | JXG.Math.Clip._handleIntersectionChains(P) At this point the degenerated intersections have been classified.
<private> <static> | JXG.Math.Clip._stayOnPath(P, isBackward)
<static> | JXG.Math.Clip.difference(subject, clip, board) Difference of two closed paths, i.e.
<private> <static> | JXG.Math.Clip.findIntersections(S, C, board) Find all intersections between two paths.
<static> | JXG.Math.Clip.greinerHormann(subject, clip, clip_type, board) Determine the intersection, union or difference of two closed paths.
<private> <static> | JXG.Math.Clip.handleEmptyIntersection(S, C, clip_type) Handle cases when there are no intersection points of the two paths.
<static> | JXG.Math.Clip.intersection(subject, clip, board) Intersection of two closed paths.
<private> <static> | JXG.Math.Clip.isEmptyCase(S, C, clip_type) Handle path clipping if one of the two paths is empty.
<private> <static> | JXG.Math.Clip.makeDoublyLinkedList(S) Add pointers to an array S such that it is a circular doubly-linked list.
<private> <static> | JXG.Math.Clip.markEntryExit(path1, path2, starters) Mark the intersection vertices of path1 as entry points or as exit points in respect to path2.
<private> <static> | JXG.Math.Clip.sortIntersections(P_crossings) Sort the intersection points into their path.
<private> <static> | JXG.Math.Clip.tracing(S, S_intersect, clip_type) Tracing phase of the Greiner-Hormann algorithm, see Greiner, Günther; Kai Hormann (1998).
<static> | JXG.Math.Clip.union(subject, clip, board) Union of two closed paths.
<private> <static> | JXG.Math.Clip.Vertex(coords, i, alpha, path, pathname, type) JavaScript object containing the intersection of two paths.

Namespace Detail
JXG.Math.Clip
Math.Clip namespace definition. This namespace contains algorithms for Boolean operations on paths, i.e. intersection, union and difference of paths. Base is the Greiner-Hormann algorithm.
Method Detail
<private> <static> {Boolean} JXG.Math.Clip._addVertex(path, vertex, DEBUG)
Add a point to the clipping path and returns if the algorithms arrived at an intersection point which has already been visited. In this case, true is returned.

Parameters:
{Array} path
  Resulting path
{JXG.Math.Clip.Vertex} vertex
  Point to be added
{Boolean} DEBUG
  debug output to console.log

Returns:
  {Boolean} true: point has been visited before, false otherwise

<private> <static> JXG.Math.Clip._classifyDegenerateIntersections(P)
Determine the delayed status of degenerated intersection points. It is of the form ['on|left|right', 'on|left|right']

If all four determinants are zero, we add random noise to the point.

Parameters:
{JXG.Math.Clip.Vertex} P
  Start of path

See:
  JXG.Math.Clip#markEntryExit
  JXG.Math.Clip#_handleIntersectionChains

<private> <static> JXG.Math.Clip._countCrossingIntersections(intersections)
Count intersection points of type 'X'.

Parameters:
{JXG.Mat.Clip.Vertex} intersections

Returns:
  Number

<private> <static> {Array} JXG.Math.Clip._getPath(obj, board)
Create path from all sorts of input elements and convert it to a suitable input path for greinerHormann().

Parameters:
{Object} obj
  Maybe curve, arc, sector, circle, polygon, array of points, array of JXG.Coords, array of coordinate pairs.
{JXG.Board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

Returns:
  {Array} Array of JXG.Coords elements containing a path.

See:
  JXG.Math.Clip#greinerHormann

<private> <static> JXG.Math.Clip._getPosition(q, p1, p2, p3)
It is testedd if the point q lies to the left or right of the poylgonal chain [p1, p2, p3].

Parameters:
{Array} q
  User coords array
{Array} p1
  User coords array
{Array} p2
  User coords array
{Array} p3
  User coords array

Returns:
  string 'left' or 'right'

<private> <static> JXG.Math.Clip._handleFullyDegenerateCase(S, C, board)
Handle the case that all vertices of one path are contained in the other path. In this case we search for a midpoint of an edge which is not contained in the other path and add it to the path. It will be used as starting point for the entry/exit algorithm.

Parameters:
{Array} S
  Subject path
{Array} C
  Clip path
{JXG.board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

<private> <static> JXG.Math.Clip._handleIntersectionChains(P)
At this point the degenerated intersections have been classified. Now we decide if the intersection chains of the given path ultimatively cross the other path or bounce.

Parameters:
{JXG.Math.Clip.Vertex} P
  Start of path

See:
  JXG.Math.Clip#markEntryExit
  JXG.Math.Clip#_classifyDegenerateIntersections

<private> <static> {Boolean} JXG.Math.Clip._stayOnPath(P, isBackward)

Parameters:
{Array} P
{Boolean} isBackward

Returns:
  {Boolean} True, if the node is an intersection and is of type 'X'

<static> {Array} JXG.Math.Clip.difference(subject, clip, board)
Difference of two closed paths, i.e. path1 minus path2. The paths could be JSXGraph elements circle, curve, or polygon. Computed by the Greiner-Hormann algorithm.

Parameters:
{JXG.Circle|JXG.Curve|JXG.Polygon} subject
  First closed path.
{JXG.Circle|JXG.Curve|JXG.Polygon} clip
  Second closed path.
{JXG.Board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

Returns:
  {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of the resulting path.

See:
  JXG.Math.Clip#greinerHormann
  JXG.Math.Clip#intersection
  JXG.Math.Clip#union

Examples:

        var curve1 = board.create('polygon', [[-4, 4], [4, 4], [0, -1]],
                {strokeColor: 'blue', fillColor: 'none'});

        var curve2 = board.create('curve', [
                [-1, 1, 0, -1],
                [1, 1, 3, 1]
            ],
            {strokeColor: 'black', fillColor: 'none', fillOpacity: 0.8});

        var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.3});
        clip_path.updateDataArray = function() {
            var a = JXG.Math.Clip.difference(curve1, curve2, this.board);
            this.dataX = a[0];
            this.dataY = a[1];
        };

        board.update();

<private> <static> {Array} JXG.Math.Clip.findIntersections(S, C, board)
Find all intersections between two paths.

Parameters:
{Array} S
  Subject path
{Array} C
  Clip path
{JXG.Board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

Returns:
  {Array} Array containing two arrays. The first array contains the intersection vertices of the subject path and the second array contains the intersection vertices of the clip path.

See:
  JXG.Clip#Vertex

<static> {Array} JXG.Math.Clip.greinerHormann(subject, clip, clip_type, board)
Determine the intersection, union or difference of two closed paths.

This is an implementation of the Greiner-Hormann algorithm, see Günther Greiner and Kai Hormann (1998). "Efficient clipping of arbitrary polygons". ACM Transactions on Graphics. 17 (2): 71–83. and Erich, L. Foster, and Kai Hormann, Kai, and Romeo Traaian Popa (2019), "Clipping simple polygons with degenerate intersections", Computers & Graphics:X, 2.

It is assumed that the pathes are closed, whereby it does not matter if the last point indeed equals the first point. In contrast to the original Greiner-Hormann algorithm, this algorithm can cope with many degenerate cases. A degenerate case is a vertext of one path which is contained in the other path.

Problematic are:

- degenerate cases where one path additionally has self-intersections
- differences with one path having self-intersections.

Parameters:
{JXG.Circle|JXG.Curve|JXG.Polygon} subject
  First closed path, usually called 'subject'. Maybe curve, arc, sector, circle, polygon, array of points, array of JXG.Coords, array of coordinate pairs.
{JXG.Circle|JXG.Curve|JXG.Polygon} clip
  Second closed path, usually called 'clip'. Maybe curve, arc, sector, circle, polygon, array of points, array of JXG.Coords, array of coordinate pairs.
{String} clip_type
  Determines the type of boolean operation on the two paths. Possible values are 'intersection', 'union', or 'difference'.
{JXG.Board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

Returns:
  {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of the resulting path.

See:
  JXG.Math.Clip#intersection
  JXG.Math.Clip#union
  JXG.Math.Clip#difference

Examples:

        var curve1 = board.create('curve', [
                [-3, 3, 0, -3],
                [3, 3, 0, 3]
            ],
            {strokeColor: 'black'});

        var curve2 = board.create('curve', [
                [-4, 4, 0, -4],
                [2, 2, 4, 2]
            ],
            {strokeColor: 'blue'});

        var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.6});
        clip_path.updateDataArray = function() {
            var a = JXG.Math.Clip.greinerHormann(curve2, curve1, 'intersection', this.board);

            this.dataX = a[0];
            this.dataY = a[1];
        };

        board.update();

        var curve1 = board.create('curve', [
                [-3, 3, 0, -3],
                [3, 3, 0, 3]
            ],
            {strokeColor: 'black', fillColor: 'none', fillOpacity: 0.8});

        var curve2 = board.create('polygon', [[3, 4], [-4, 0], [-4, 4]],
                {strokeColor: 'blue', fillColor: 'none'});

        var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.6});
        clip_path.updateDataArray = function() {
            var a = JXG.Math.Clip.greinerHormann(curve1, curve2, 'union', this.board);
            this.dataX = a[0];
            this.dataY = a[1];
        };

        board.update();

        var curve1 = board.create('curve', [
                [-4, 4, 0, -4],
                [4, 4, -2, 4]
            ],
            {strokeColor: 'black', fillColor: 'none', fillOpacity: 0.8});

        var curve2 = board.create('circle', [[0, 0], [0, -2]],
                {strokeColor: 'blue', strokeWidth: 1, fillColor: 'red', fixed: true, fillOpacity: 0.3,
                center: {visible: true, size: 5}, point2: {size: 5}});

        var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.6});
        clip_path.updateDataArray = function() {
            var a = JXG.Math.Clip.greinerHormann(curve1, curve2, 'difference', this.board);

            this.dataX = a[0];
            this.dataY = a[1];
        };

        board.update();

    var clip_path = board.create('curve', [[], []], {strokeWidth: 1, fillColor: 'yellow', fillOpacity: 0.6});
    clip_path.updateDataArray = function() {
        var bbox = this.board.getBoundingBox(),
            canvas, triangle;

        canvas = [[bbox[0], bbox[1]], // ul
             [bbox[0], bbox[3]], // ll
             [bbox[2], bbox[3]], // lr
             [bbox[2], bbox[1]], // ur
             [bbox[0], bbox[1]]] // ul
        triangle = [[-1,1], [1,1], [0,-1], [-1,1]];

        var a = JXG.Math.Clip.greinerHormann(canvas, triangle, 'difference', this.board);
        this.dataX = a[0];
        this.dataY = a[1];
    };

<private> <static> {Array} JXG.Math.Clip.handleEmptyIntersection(S, C, clip_type)
Handle cases when there are no intersection points of the two paths. This is the case if the paths are disjoint or one is contained in the other.

Parameters:
{Array} S
  First path, array of JXG.Coords
{Array} C
  Second path, array of JXG.Coords
{String} clip_type
  Type of Boolean operation: 'intersection', 'union', 'differrence'.

Returns:
  {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of the resulting path.

<static> {Array} JXG.Math.Clip.intersection(subject, clip, board)
Intersection of two closed paths. The paths could be JSXGraph elements circle, curve, or polygon. Computed by the Greiner-Hormann algorithm.

Parameters:
{JXG.Circle|JXG.Curve|JXG.Polygon} subject
  First closed path.
{JXG.Circle|JXG.Curve|JXG.Polygon} clip
  Second closed path.
{JXG.Board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

Returns:
  {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of the resulting path.

See:
  JXG.Math.Clip#greinerHormann
  JXG.Math.Clip#union
  JXG.Math.Clip#difference

Examples:

    var p = [];
    p.push(board.create('point', [0, -5]));
    p.push(board.create('point', [-5, 0]));
    p.push(board.create('point', [-3, 3]));

    var curve1 = board.create('ellipse', p,
                    {strokeColor: 'black'});

    var curve2 = board.create('curve', [function(phi){return 4 * Math.cos(2*phi); },
                                        [0, 0],
                                        0, 2 * Math.PI],
                          {curveType:'polar', strokeColor: 'blue', strokewidth:1});

    var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.3});
    clip_path.updateDataArray = function() {
        var a = JXG.Math.Clip.intersection(curve2, curve1, this.board);

        this.dataX = a[0];
        this.dataY = a[1];
    };

    board.update();

<private> <static> {Boolean} JXG.Math.Clip.isEmptyCase(S, C, clip_type)
Handle path clipping if one of the two paths is empty.

Parameters:
{Array} S
  First path, array of JXG.Coords
{Array} C
  Second path, array of JXG.Coords
{String} clip_type
  Type of Boolean operation: 'intersection', 'union', 'differrence'.

Returns:
  {Boolean} true, if one of the input paths is empty, false otherwise.

<private> <static> {Array} JXG.Math.Clip.makeDoublyLinkedList(S)
Add pointers to an array S such that it is a circular doubly-linked list.

Parameters:
{Array} S
  Array

Returns:
  {Array} return containing the starter indices of each component.

<private> <static> JXG.Math.Clip.markEntryExit(path1, path2, starters)
Mark the intersection vertices of path1 as entry points or as exit points in respect to path2.

This is the simple algorithm as in Greiner, Günther; Kai Hormann (1998). "Efficient clipping of arbitrary polygons". ACM Transactions on Graphics. 17 (2): 71–83

The algorithm handles also "delayed crossings" from Erich, L. Foster, and Kai Hormann, Kai, and Romeo Traaian Popa (2019), "Clipping simple polygons with degenerate intersections", Computers & Graphics:X, 2. and - as an additional improvement - handles self intersections of delayed crossings (A.W. 2021).

Parameters:
{Array} path1
  First path
{Array} path2
  Second path
starters

<private> <static> {Array} JXG.Math.Clip.sortIntersections(P_crossings)
Sort the intersection points into their path.

Parameters:
{Array} P_crossings
  Array of arrays. Each array contains the intersections of the path with one segment of the other path.

Returns:
  {Array} Array of intersection points ordered by first occurrence in the path.

<private> <static> {Array} JXG.Math.Clip.tracing(S, S_intersect, clip_type)
Tracing phase of the Greiner-Hormann algorithm, see Greiner, Günther; Kai Hormann (1998). "Efficient clipping of arbitrary polygons". ACM Transactions on Graphics. 17 (2): 71–83 Boolean operations on polygons are distinguished: 'intersection', 'union', 'difference'.

Parameters:
{Array} S
  Subject path
{Array} S_intersect
  Array containing the intersection vertices of the subject path
{String} clip_type
  contains the Boolean operation: 'intersection', 'union', or 'difference'

Returns:
  {Array} Array consisting of two arrays containing the x-coordinates and the y-coordintaes of the resulting path.

<static> {Array} JXG.Math.Clip.union(subject, clip, board)
Union of two closed paths. The paths could be JSXGraph elements circle, curve, or polygon. Computed by the Greiner-Hormann algorithm.

Parameters:
{JXG.Circle|JXG.Curve|JXG.Polygon} subject
  First closed path.
{JXG.Circle|JXG.Curve|JXG.Polygon} clip
  Second closed path.
{JXG.Board} board
  JSXGraph board object. It is needed to convert between user coordinates and screen coordinates.

Returns:
  {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of the resulting path.

See:
  JXG.Math.Clip#greinerHormann
  JXG.Math.Clip#intersection
  JXG.Math.Clip#difference

Examples:

        var curve1 = board.create('curve', [
                [-3, 3, 0, -3],
                [3, 3, 0, 3]
            ],
            {strokeColor: 'black'});

        var curve2 = board.create('polygon', [[3, 4], [-4, 0], [-4, 4]],
                {strokeColor: 'blue', fillColor: 'none'});

        var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.3});
        clip_path.updateDataArray = function() {
            var a = JXG.Math.Clip.union(curve1, curve2, this.board);
            this.dataX = a[0];
            this.dataY = a[1];
        };

        board.update();

<private> <static> JXG.Math.Clip.Vertex(coords, i, alpha, path, pathname, type)
JavaScript object containing the intersection of two paths. Every intersection point is on one path, but comes with a neighbour point having the same coordinates and being on the other path. The intersection point is inserted into the doubly linked list of the path.

Parameters:
{JXG.Coords} coords
  JSXGraph Coords object containing the coordinates of the intersection
{Number} i
  Number of the segment of the subject path (first path) containing the intersection.
{Number} alpha
  The intersection is a p_1 + alpha*(p_2 - p_1), where p_1 and p_2 are the end points of the i-th segment.
{Array} path
  Pointer to the path containing the intersection point
{String} pathname
  Name of the path: 'S' or 'C'.
type

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