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criticalAlpha

Alpha radius defining critical transition in shape

Description

example

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.

Examples

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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 object contains an object of type line.

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)

Figure contains an axes object. The axes object contains an object of type patch.

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)

Figure contains an axes object. The axes object contains an object of type patch.

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.

Introduced in R2014b