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DelaunayTri class

Superclasses: TriRep

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


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.


The 2-D Delaunay triangulation of a set of points is the triangulation in which no point of the set is contained in the circumcircle for any triangle in the triangulation. The definition extends naturally to higher dimensions.


DelaunayTri(Not recommended) Construct Delaunay triangulation


convexHull(Not recommended) Convex hull
inOutStatus(Not recommended) Status of triangles in 2-D constrained Delaunay triangulation
nearestNeighbor(Not recommended) Point closest to specified location
pointLocation(Not recommended) Simplex containing specified location
voronoiDiagram(Not recommended) Voronoi diagram

Inherited methods

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
edgeAttachments(Not recommended) Simplices attached to specified edges
edges(Not recommended) Triangulation edges
faceNormals(Not recommended) Unit normals to specified triangles
featureEdges(Not recommended) Sharp edges of surface triangulation
freeBoundary(Not recommended) Facets referenced by only one simplex
incenters(Not recommended) Incenters of specified simplices
isEdge(Not recommended) Test if vertices are joined by edge
neighbors(Not recommended) Simplex neighbor information
size(Not recommended) Size of triangulation matrix
vertexAttachments(Not recommended) Return simplices attached to specified vertices



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 data.

This feature is only supported for 2-D triangulations.

XThe 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.
TriangulationTriangulation is a matrix representing the set of simplices (triangles or tetrahedra etc.) 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.

Instance Hierarchy

DelaunayTri is a subclass of TriRep.

Copy Semantics

Value. To learn how this affects your use of the class, see Comparing Handle and Value Classes in the MATLAB® Object-Oriented Programming documentation.

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