`alphaSpectrum`

Alpha values at which the alpha shape changes its set of triangles or tetrahedra.

Category: Mathematics > Computational Geometry

Syntax

spec = alphaSpectrum(shp)

Returns the alpha values that change the shape, in ascending order.

Description

Each simplex of the Delaunay triangulation of the points has a circumradius. The alpha shape includes a simplex when alpha is at least that radius, so the sorted radii mark every alpha at which the shape actually changes. Values outside the spectrum only repeat a neighbouring shape.

This is useful to pick an alpha systematically, for instance by plotting area against the spectrum.

Input arguments

shp: An alphaShape object.

Output arguments

spec: Column vector of alpha values. Setting shp.Alpha between two consecutive entries gives the same shape.

Example

Spectrum of a small point set

x = [0 1 1 0 0.5]';
y = [0 0 1 1 0.5]';
shp = alphaShape(x, y);
spec = alphaSpectrum(shp)

Output

spec = 0.5000

alphaSpectrum