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DelaunayTri

(Not recommended) Delaunay triangulation in 2-D and 3-D

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DelaunayTri is not recommended. Use delaunayTriangulation instead.

Description

DelaunayTri creates a Delaunay triangulation object from a set of points. You can incrementally modify the triangulation by adding or removing points. In 2-D triangulations you can impose edge constraints. You can perform topological and geometric queries, and compute the Voronoi diagram and convex hull.

Creation

Syntax

DT = DelaunayTri
DT = DelaunayTri(X)
DT = DelaunayTri(x,y)
DT = DelaunayTri(x,y,z)
DT = DelaunayTri(___,C)

Description

DT = DelaunayTri creates an empty Delaunay triangulation.

DT = DelaunayTri(X), DT = DelaunayTri(x,y) and DT = DelaunayTri(x,y,z) create a Delaunay triangulation from a set of points. The points can be specified as an mpts-by-ndim matrix X, where mpts is the number of points and ndim is the dimension of the space where the points reside (ndim is 2 or 3). Alternatively, the points can be specified as column vectors (x,y) or (x,y,z) for 2-D and 3-D input.

example

DT = DelaunayTri(___,C) creates a constrained Delaunay triangulation. This feature is only supported for 2-D triangulations.

Input Arguments

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Points to triangulate, specified as a matrix. X is an mpts-by-ndim matrix, where mpts is the number of points and ndim is the dimension of the space where the points reside (ndim is 2 or 3).

Points to triangulate, specified as separate vector arguments. Specify column vectors (x,y) or (x,y,z) for 2-D and 3-D input, respectively.

Edge constraints, specified as a matrix. The edge constraints C are defined by an numc-by-2 matrix, numc being the number of constrained edges. Each row of C defines a constrained edge in terms of its endpoint indices into the point set X.

Properties

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Vertex coordinates, specified as a matrix. The dimension of X is mpts-by-ndim, where mpts is the number of points and ndim is the dimension of the space where the points reside. If column vectors of x,y or x,y,z coordinates are used to construct the triangulation, the data is consolidated into a single matrix X.

Triangulation connectivity, specified as a matrix. Triangulation is a matrix representing the set of simplices (triangles, tetrahedra, and so on) that make up the triangulation. The matrix is of size mtri-by-nv, where mtri is the number of simplices and nv is the number of vertices per simplex. The triangulation is represented by standard simplex-vertex format; each row specifies a simplex defined by indices into X, where X is the array of point coordinates.

Constrained edges, specified as a matrix. Constraints is a numc-by-2 matrix that defines the constrained edge data in the triangulation, where numc is the number of constrained edges. Each constrained edge is defined in terms of its endpoint indices into X.

The constraints can be specified when the triangulation is constructed or can be imposed afterwards by directly editing the Constraints property.

This feature is only supported for 2-D triangulations.

Object Functions

In addition to the below object functions, DelaunayTri objects support indexing into the triangulation using parentheses (). The syntax is the same as for arrays.

baryToCart(Not recommended) Convert point coordinates from barycentric to Cartesian
cartToBary(Not recommended) Convert point coordinates from Cartesian to barycentric
circumcenters(Not recommended) Circumcenters of specified simplices
convexHull(Not recommended) Convex hull of Delaunay triangulation
edgeAttachments(Not recommended) Triangles or tetrahedra attached to specified edge
edges(Not recommended) Triangulation edges
faceNormals(Not recommended) Unit normals to specified triangles
featureEdges(Not recommended) Sharp edges of surface triangulation
freeBoundary(Not recommended) Free boundary facets
incenters(Not recommended) Incenters of specified simplices
inOutStatus(Not recommended) Status of triangles in 2-D constrained Delaunay triangulation
isEdge(Not recommended) Test if vertices are joined by edge
nearestNeighbor(Not recommended) Vertex closest to specified point
neighbors(Not recommended) Triangle or tetrahedron neighbors
pointLocation(Not recommended) Triangle or tetrahedron enclosing point
size(Not recommended) Size of triangulation matrix
vertexAttachments(Not recommended) Triangles or tetrahedra attached to vertex
voronoiDiagram(Not recommended) Voronoi diagram of Delaunay triangulation

Examples

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Open Live Script

Compute the Delaunay triangulation of twenty random points located within a unit square and then plot the triangulation.

rng default
x = rand(20,1);
y = rand(20,1);
dt = DelaunayTri(x,y);
triplot(dt)

Figure contains an axes object. The axes object contains an object of type line.

More About

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Tips

  • DelaunayTri can produce incorrect or inconsistent results when boundary constraints intersect or overlap. To avoid this behavior, use constraints that form one or multiple closed boundaries that do not intersect or overlap.

Version History

Introduced in R2009a

See Also

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