Main Content


Alpha values giving distinct alpha shapes



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.


collapse all

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];
axis equal

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; 
    title("Alpha = "+alpha)

Input Arguments

collapse all

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.

Output Arguments

collapse all

Alpha values for distinct alpha shapes, returned as a column vector in descending sorted order.

Version History

Introduced in R2014b

See Also