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ComputationalGeometry

  

PolygonTriangulation

  

triangulate a simple polygon

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

PolygonTriangulation(polygon)

PolygonTriangulation(polygon,option)

Parameters

polygon

-

a list of two element lists or an n by 2 Matrix representing a simple polygon in either clockwise or counterclockwise order

option

-

(optional) keyword option of the form method=name

Description

• 

The PolygonTriangulation command computes a triangulation of a simple polygon.

• 

The method option specifies the triangulation algorithm used. method can be either earclipping or monotone. The default method is earclipping.

• 

The monotone method is faster for large polygons, but the earclipping method is more likely to produce better quality triangulations.

• 

The triangles are returned as a list of three element lists; each inner list specifies the three vertices of a triangle as integer references into the input polygon list or Matrix.

• 

Except for the first vertex and the last vertex, the polygon should not contain duplicate vertices.

Examples

with(ComputationalGeometry):

xy:=[[391,374],[240,431],[252, 340],[374, 320],[289, 214],[134, 390],[68, 186],[154, 259],[161, 107],[435, 108],[208, 148],[295, 160],[421, 212],[441, 303]];

xy391,374,240,431,252,340,374,320,289,214,134,390,68,186,154,259,161,107,435,108,208,148,295,160,421,212,441,303

(1)

plots:-display(plottools:-polygon(xy,style=line));

t:=PolygonTriangulation(xy,method=monotone);

t3,1,2,4,3,1,14,4,1,5,14,4,13,5,14,5,8,6,12,13,5,12,5,8,11,12,8,9,10,11,9,11,8,7,8,6

(2)

plots:-display(map(x->plottools:-polygon(xy[x],style=line),t));

Compatibility

• 

The ComputationalGeometry[PolygonTriangulation] command was introduced in Maple 2018.

• 

For more information on Maple 2018 changes, see Updates in Maple 2018.

See Also

ComputationalGeometry