alphaSpectrum

Alpha values giving distinct alpha shapes

Syntax

a = alphaSpectrum(shp)

Description

a = alphaSpectrum(shp) returns the values of the alpha radius that produce distinct alpha shapes. a is in descending sorted order. Each element in a represents a value of the alpha radius that results in a distinct shape. The length of a is equal to the number of unique shapes. Values of alpha that lie between the values in a do not produce unique alpha shapes.

example

Examples

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Find Alpha Spectrum for 2-D Point Cloud

Open Live Script

Create and plot a set of 2-D points.

th = (pi/12:pi/12:2*pi)';
x1 = [reshape(cos(th)*(1:5), numel(cos(th)*(1:5)),1); 0];
y1 = [reshape(sin(th)*(1:5), numel(sin(th)*(1:5)),1); 0];
x = [x1; x1+15;];
y = [y1; y1];
plot(x,y,'.')
axis equal

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

Create an alpha shape for the point cloud using the default alpha radius.

shp = alphaShape(x,y);

Find the spectrum of critical alpha values that produce unique alpha shapes for the point cloud.

alphaspec = alphaSpectrum(shp);

Plot four of the unique alpha shapes generated by alpha values in the spectrum.

for k = 1:4
    alpha = alphaspec(8*k-7); 
    shp.Alpha = alpha; 
    subplot(2,2,k)
    plot(shp)
    title("Alpha = "+alpha)
end

Figure contains 4 axes objects. Axes object 1 with title Alpha = 52.5066 contains an object of type patch. Axes object 2 with title Alpha = 7.3917 contains an object of type patch. Axes object 3 with title Alpha = 3.2274 contains an object of type patch. Axes object 4 with title Alpha = 0.77523 contains an object of type patch.