locan.data.hulls.alpha_shape

Alpha shape

This module provides methods for computing the alpha complex and specific alpha shapes together with related properties for LocData objects.

Alpha shape is a hull object that defines a group of localizations bordering a concave hull (which does not have to be connected and might have holes) [1]. It depends on a single parameter alpha (here defined to be a distance with a unit equal to the coordinate units of the given localization data). For alpha approaching infinity the alpha shape is equal to the convex hull.

In this context we call an alpha-complex the subgroup of simplexes of a Delaunay triangulation that is computed according to Edelsbrunner algorithm. All localizations that lie on the boundary of the alpha-complex make up the alpha shape.

Internally we also work with an alpha-independent representation of the alpha-complex that allows efficient computation of alpha shapes for arbitrary alpha values.

Simplices are classified as exterior (not part of the alpha complex), interior (not part of the boundary), regular (part of the boundary but not singular), and singular (part of the boundary but all simplices of higher dimension they are incident to are exterior).

References

[1]

H. Edelsbrunner and E. P. Mücke, Three-dimensional alpha shapes. ACM Trans. Graph. 13(1):43-72, 1994.

Classes

AlphaComplex(points[, delaunay])	Class for an alpha-independent representation of the alpha complex of the given points.
AlphaShape(alpha[, points, alpha_complex, ...])	Class for the alpha shape of points for a specific alpha value.