surfaceArea

Surface area of a 3-D alpha shape.

Category: Mathematics > Computational Geometry

Syntax

SA = surfaceArea(shp)

Description

The result is the sum of the areas of the triangular boundary facets listed by boundaryFacets. For the regular corner tetrahedron with legs of length 1, three faces are right triangles of area 0.5 and the fourth is an equilateral triangle of area about 0.866, so the total is about 2.366. The matching volume is returned by volume.

Input arguments

shp

A 3-D alphaShape object. A 2-D one raises an error; use perimeter for it.

Output arguments

SA

Scalar surface area.

Example

Surface area and volume of a tetrahedron

P = [0 0 0; 1 0 0; 0 1 0; 0 0 1];
shp = alphaShape(P(:,1), P(:,2), P(:,3));
surfaceArea(shp)
volume(shp)

ans = 2.3660
ans = 0.1667

See also

alphaShape volume boundaryFacets perimeter area