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| R2012a Documentation → MATLAB | |
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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 | Construct Delaunay triangulation |
| convexHull | Convex hull |
| inOutStatus | Status of triangles in 2-D constrained Delaunay triangulation |
| nearestNeighbor | Point closest to specified location |
| pointLocation | Simplex containing specified location |
| voronoiDiagram | Voronoi diagram |
| baryToCart | Convert point coordinates from barycentric to Cartesian |
| cartToBary | Convert point coordinates from cartesian to barycentric |
| circumcenters | Circumcenters of specified simplices |
| edgeAttachments | Simplices attached to specified edges |
| edges | Triangulation edges |
| faceNormals | Unit normals to specified triangles |
| featureEdges | Sharp edges of surface triangulation |
| freeBoundary | Facets referenced by only one simplex |
| incenters | Incenters of specified simplices |
| isEdge | Test if vertices are joined by edge |
| neighbors | Simplex neighbor information |
| size | Size of triangulation matrix |
| vertexAttachments | Return simplices attached to specified vertices |
| Constraints | 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. |
| X | 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 | Triangulation 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. |
DelaunayTri is a subclass of TriRep.
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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