DelaunayTriangulation - Maple Help
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GraphTheory

  

DelaunayTriangulation

  

find the Delaunay triangulation for a given list of points

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DelaunayTriangulation(points)

Parameters

points

-

list of 2-element lists representing n coordinates

Description

• 

This function computes a Delaunay triangulation of the region bounded by the sequence of line segments connecting the outermost of the input points, returning a sequence of two outputs: the set of triangles and an edge adjacency Matrix.

• 

The Delaunay triangulation is a triangulation that maximizes the smallest angle of the triangles in the triangulation (i.e. it avoids thin triangles).

• 

The triangles are returned in a set containing the three vertices of each triangle as integer references to the input points list.

• 

The adjacency matrix is an n by n symmetric Matrix that contains a  in entry  if one of the triangle edges is from  to , and  otherwise.

Examples

For this example we first construct a point list containing all points at coordinates (i,j) for i=0..4,j=0..4, and the center points of all enclosed squares (that is, (1/2,1/2)..(7/2,7/2)).

(1)

Use the DelaunayTriangulation command to get the set of triangles (tris) and the adjacency matrix (amat) for the point list pts.

Build and display a plot of all triangles.

Note that in the preceding plot, many of the triangles are chosen randomly because there are two optimal choices for many of the subdivisions. A slight shift of the points will make the optimal triangulation unique:

(2)

Compatibility

• 

The GraphTheory[DelaunayTriangulation] command was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

ComputationalGeometry[DelaunayTriangulation]

GraphTheory

plot

seq

 


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