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Area of 2-D alpha shape



A = area(shp) returns the area of 2-D alpha shape shp.


A = area(shp,RegionID) returns the area of a region of the alpha shape. RegionID is the ID for the region and 1RegionIDnumRegions(shp).


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Create 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];

Create and plot an alpha shape using an alpha radius of 2.5.

shp = alphaShape(x,y,2.5);

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

Compute the area of the alpha shape.

totalarea = area(shp)
totalarea = 155.2914

Compute the areas of each of the two regions separately.

regionareas = area(shp, 1:numRegions(shp))
regionareas = 1×2

   77.6457   77.6457

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.

ID number for region in alpha shape, specified as a positive integer scalar between 1 and numRegions(shp).

An alpha shape can contain several smaller regions, depending on the point set and parameters. Each of these smaller regions is assigned a unique RegionID, which numbers the regions from the largest area or volume to the smallest. For example, consider a 3-D alpha shape with two regions. The region with the largest volume has a RegionID of 1, and the smaller region has a RegionID of 2.

Example: shp.RegionThreshold = area(shp,numRegions(shp)-2); suppresses the two smallest regions in 2-D alpha shape shp.

Data Types: double

Introduced in R2014b