tri = alphaTriangulation(shp)
returns a triangulation that defines the domain of the alpha shape. Each row in
tri specifies a triangle or tetrahedron defined by vertex
IDs (the row numbers of the shp.Points matrix).

tri = alphaTriangulation(shp,RegionID)
returns a triangulation for a region of the alpha shape.
RegionID is the ID for the region and
1 ≤ RegionID ≤
numRegions(shp).

[tri,P]
= alphaTriangulation(___)
also returns a matrix of vertex coordinates, P, using any of
the previous syntaxes.

Alpha shape, specified as an alphaShape object.
For more information, see alphaShape.

Example: shp = alphaShape(x,y) creates a 2-D alphaShape object
from the (x,y) point coordinates.

RegionID — ID number for a region in the alpha shape positive integer scalar

ID number for region in alpha shape, specified as a positive
integer scalar between 1 and numRegions(shp).

An alpha shape can contain several smaller regions, depending
on the point set and parameters. Each of these smaller regions is
assigned a unique RegionID, which numbers the regions
from the largest area or volume to the smallest. For example, consider
a 3-D alpha shape with two regions. The region with the largest volume
has a RegionID of 1, and the smaller region has
a RegionID of 2.

Example: shp.RegionThreshold = area(shp,numRegions(shp)-2); suppresses
the two smallest regions in 2-D alpha shape shp.

Triangulation, returned as a matrix. tri is of size
mtri-by-nv, where
mtri is the number of triangles or tetrahedra in the
alpha shape and nv is the number of vertices. The value
of nv is 3 for 2-D alpha shapes and
4 for 3-D alpha shapes.

P — Vertex coordinates matrix

Vertex coordinates, returned as a matrix. P is of size
N-by-dim, where
N is the number of points in the alpha shape and
dim is either 2 or
3 (for either a 2-D or 3-D alpha shape).

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