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Boundary facets of alpha shape



bf = boundaryFacets(shp) returns a matrix representing the facets that make up the boundary of the alpha shape. The facets represent edge segments in 2-D and triangles in 3-D. The vertices of the facets index into the shp.Points matrix.

bf = boundaryFacets(shp,RegionID) returns the boundary facets for a region of the alpha shape. RegionID is the ID for the region and 1RegionIDnumRegions(shp).

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


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Create a set of 3-D points.

[x1, y1, z1] = sphere(24);
x1 = x1(:);
y1 = y1(:);
z1 = z1(:);
x2 = x1+5;
P = [x1 y1 z1; x2 y1 z1];
P = unique(P,'rows');

Create and plot an alpha shape using an alpha radius of 1.5.

shp = alphaShape(P,1.5);
axis equal

Compute and plot only the boundary of the alpha shape.

[tri, xyz] = boundaryFacets(shp);
axis equal

Input Arguments

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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.

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.

Data Types: double

Output Arguments

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Boundary facets, returned as a matrix. bf is of size m-by-n, where m is the number of boundary facets and n is the number of vertices per facet.

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

Version History

Introduced in R2014b