criticalAlpha

R2026b

Alpha radius defining critical transition in shape

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Syntax

a = criticalAlpha(shp,type)

Description

a = criticalAlpha(shp,type) returns the critical alpha radius that produces a notable transition in the alpha shape. Specifying type as "all-points" returns the smallest alpha radius producing an alpha shape that encloses all points. Specifying type as "one-region" returns the smallest alpha radius producing an alpha shape that encloses all points and has only one region.

example

Examples

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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

Two clusters of 2-D points arranged in concentric circles, centered at (0,0) and (15,0)

Create an alpha shape using the default alpha radius.

shp = alphaShape(x,y);

Compute the smallest alpha radius that produces an alpha shape enclosing all of the points and plot the corresponding alpha shape.

pc = criticalAlpha(shp,"all-points");
shp.Alpha = pc;
plot(shp)

Alpha shape enclosing all points with two separate regions showing irregular boundaries

Compute the smallest alpha radius that produces an alpha shape enclosing all of the points and having only one region.

shp = alphaShape(x,y);
pc = criticalAlpha(shp,"one-region");
shp.Alpha = pc;
plot(shp)

Alpha shape with one region connecting both point clusters via a narrow bridge

Input Arguments

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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.

Type of critical transition, specified as either "all-points" or "one-region".

  • "all-points" corresponds to the smallest alpha radius producing an alpha shape that encloses all points.

  • "one-region" corresponds to the smallest alpha radius producing an alpha shape that encloses all points and has only one region.

Data Types: char

Output Arguments

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Critical alpha radius, returned as a scalar. a is the value of the alpha radius that produces an alpha shape, which either encloses all points (if type is "all-points"), or encloses all points within a single region (if type is "one-region").

After using criticalAlpha to find a, you can make the alpha radius of shp equal to a by typing shp.Alpha = a.

Version History

Introduced in R2014b

See Also

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