Use the delaunayTriangulation
class to create
a 2D or 3D triangulation from a set of points. When your points
are in 2D, you can specify edge constraints .
You can perform a variety of topological and geometric queries
on a delaunayTriangulation
, including any triangulation
query.
For example, locate a facet that contains a specific point, find the
vertices of the convex hull, or compute the Voronoi Diagram.
creates
a Delaunay triangulation from the points in DT
= delaunayTriangulation(P
)P
.
Matrix P
has 2 or 3 columns, depending on whether
your points are in 2D or 3D space.
specifies
the edge constraints in matrix DT
= delaunayTriangulation(P
,C
)C
. In this case, P
specifies
points in 2D. Each row of C
defines the start
and end vertex IDs of a constrained edge.
creates
a 2D Delaunay triangulation from the point coordinates in the column
vectors, DT
= delaunayTriangulation(x
,y
)x
and y
.
specifies
the edge constraints in matrix DT
= delaunayTriangulation(x
,y
,C
)C
.
creates
a 3D Delaunay triangulation from the point coordinates in the column
vectors, DT
= delaunayTriangulation(x
,y
,z
)x
, y
, and z
.
creates
an empty Delaunay triangulation.DT
= delaunayTriangulation()

Input points, specified as a matrix whose columns are the x, y,
(and possibly z) coordinates of the triangulation
points. The row numbers of 

xcoordinates vector, specified as a column vector containing the xcoordinates of the triangulation points. 

ycoordinates vector, specified as a column vector containing the ycoordinates of the triangulation points. 

zcoordinates vector, specified as a column vector containing the zcoordinates of the triangulation points. 

Vertex IDs of constrained edges, specified as a 2column matrix.
Each row of
You can specify edge constraints for 2D triangulations only. 

Points in the triangulation, represented as a matrix containing the following information:


Triangulation connectivity list, represented as a matrix. This matrix contains the following information:


Constrained edges, represented as a twocolumn matrix of vertex
IDs. Each row of

convexHull  Convex hull 
isInterior  Test if triangle is in interior of 2D constrained Delaunay triangulation 
voronoiDiagram  Voronoi diagram 
barycentricToCartesian  Converts point coordinates from barycentric to Cartesian 
cartesianToBarycentric  Converts point coordinates from Cartesian to barycentric 
circumcenter  Circumcenter of triangle or tetrahedron 
edgeAttachments  Triangles or tetrahedra attached to specified edge 
edges  Triangulation edges 
faceNormal  Triangulation face normal 
featureEdges  Triangulation sharp edges 
freeBoundary  Triangulation facets referenced by only one triangle or tetrahedron 
incenter  Incenter of triangle or tetrahedron 
isConnected  Test if two vertices are connected by edge 
nearestNeighbor  Vertex closest to specified location 
neighbors  Neighbors to specified triangle or tetrahedron 
pointLocation  Triangle or tetrahedron containing specified point 
size  Size of triangulation connectivity list 
vertexAttachments  Triangles or tetrahedra attached to specified vertex 
vertexNormal  Triangulation vertex normal 
In a 2D Delaunay triangulation, the circumcircle associated
with each triangle does not contain any points in its interior. Similarly,
a 3D Delaunay triangulation does not have any points in the interior
of the circumsphere associated with each tetrahedron. This definition
extends to ND, although delaunayTriangulation
supports
only 2D and 3D.
A row number of the matrix, DT.Points
. Use
this ID to refer a specific vertex in the triangulation.
A row number of the matrix, DT.ConnectivityList
.
Use this ID to refer a specific triangle or tetrahedron.
Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB^{®} documentation.