`alphaTriangulation`

Triangles or tetrahedra that make up an alpha shape, with the point coordinates.

Category: Mathematics > Computational Geometry

Syntax

tri = alphaTriangulation(shp)

Returns the connectivity list of the simplices inside the shape.

[tri, xyz] = alphaTriangulation(shp)

Also returns the coordinates of the points.

Description

The result is the part of the Delaunay triangulation of the points that is kept for the current Alpha. Raising alpha adds simplices; lowering it removes them. The rows of tri index into the rows of xyz, so the pair can be passed directly to a plotting call such as trisurf or triplot.

Input arguments

shp: An alphaShape object.

Output arguments

tri: Matrix of point indices: three columns per triangle for a 2-D shape, four per tetrahedron for a 3-D one.
xyz: The point coordinates, one row per point.

Example

Triangles of a 2-D alpha shape

x = [0 1 1 0 0.5]';
y = [0 0 1 1 0.5]';
shp = alphaShape(x, y, 1);
[tri, xyz] = alphaTriangulation(shp)

Output

tri = 4×3

     5     2     3
     1     2     5
     5     4     1
     3     4     5
xyz = 5×2

         0         0
    1.0000         0
    1.0000    1.0000
         0    1.0000
    0.5000    0.5000

alphaTriangulation