Bounding Regions

Compute convex hull, alpha shape, or boundaries around points

A bounding region encloses a set of points within a defined boundary. The boundary function enables you to specify how tightly the boundary fits around the points, while the convhull and convhulln functions return the smallest convex boundary. For more control over defining bounding regions, alphaShape objects have adjustable boundary settings that are based on the alpha radius. You can compute geometric quantities of alphaShape objects using their object functions.

Functions

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Create Basic Bounding Regions

`boundary`	Boundary around a set of points in 2-D or 3-D
`convhull`	Convex hull
`convhulln`	N-D convex hull

Create and Manipulate Alpha Shapes

`alphaShape`	Polygons and polyhedra from points in 2-D and 3-D
`alphaSpectrum`	Alpha values giving distinct alpha shapes
`criticalAlpha`	Alpha radius defining critical transition in shape
`numRegions`	Number of regions in alpha shape
`inShape`	Determine if point is inside alpha shape
`alphaTriangulation`	Triangulation that fills alpha shape
`boundaryFacets`	Boundary facets of alpha shape
`perimeter`	Perimeter of 2-D alpha shape
`area`	Area of 2-D alpha shape
`surfaceArea`	Surface area of 3-D alpha shape
`volume`	Volume of 3-D alpha shape
`plot`	Plot alpha shape
`nearestNeighbor`	Determine nearest alpha shape boundary point

Topics

Convex Hulls

Convex Hulls vs. Nonconvex Polygons
Define convex and nonconvex regions for a set of points.
Approaches for Computing the Convex Hull
Consider different approaches for computing the convex hull for a set of points.
Convex Hull Computation with convhull
Compute the convex hull of sets of points in 2-D and 3-D by using the convhull function.
Convex Hull Computation with delaunayTriangulation
Compute the convex hull of a set of points in 2-D by using the convexHull method of the delaunayTriangulation class.

Alpha Shapes

Alpha Shapes
Find the alpha shape of a 2-D point set using the alphaShape function.