trimeshSurfaceArea

TRIMESHSURFACEAREA Surface area of a triangular mesh.

   S = trimeshSurfaceArea(V, F)
   S = trimeshSurfaceArea(V, E, F)
   Computes the surface area of the mesh specified by vertex array V and
   face array F. Vertex array is a NV-by-3 array of coordinates. 
   Face array is a NF-by-3, containing vertex indices of each face.

   Example
     % Compute area of an octahedron (equal to 2*sqrt(3)*a*a, with 
     % a = sqrt(2) in this case)
     [v f] = createOctahedron;
     trimeshSurfaceArea(v, f)
     ans = 
         6.9282

     % triangulate a compute area of a unit cube
     [v f] = createCube;
     f2 = triangulateFaces(f);
     trimeshSurfaceArea(v, f2)
     ans =
         6

   See also
   meshes3d, meshSurfaceArea, trimeshMeanBreadth, triangulateFaces

0001 function area = trimeshSurfaceArea(v, e, f)
0002 %TRIMESHSURFACEAREA Surface area of a triangular mesh.
0003 %
0004 %   S = trimeshSurfaceArea(V, F)
0005 %   S = trimeshSurfaceArea(V, E, F)
0006 %   Computes the surface area of the mesh specified by vertex array V and
0007 %   face array F. Vertex array is a NV-by-3 array of coordinates.
0008 %   Face array is a NF-by-3, containing vertex indices of each face.
0009 %
0010 %   Example
0011 %     % Compute area of an octahedron (equal to 2*sqrt(3)*a*a, with
0012 %     % a = sqrt(2) in this case)
0013 %     [v f] = createOctahedron;
0014 %     trimeshSurfaceArea(v, f)
0015 %     ans =
0016 %         6.9282
0017 %
0018 %     % triangulate a compute area of a unit cube
0019 %     [v f] = createCube;
0020 %     f2 = triangulateFaces(f);
0021 %     trimeshSurfaceArea(v, f2)
0022 %     ans =
0023 %         6
0024 %
0025 %   See also
0026 %   meshes3d, meshSurfaceArea, trimeshMeanBreadth, triangulateFaces
0027 
0028 % ------
0029 % Author: David Legland
0030 % e-mail: david.legland@inra.fr
0031 % Created: 2011-08-26,    using Matlab 7.9.0.529 (R2009b)
0032 % Copyright 2011 INRA - Cepia Software Platform.
0033 
0034 % check input number
0035 if nargin == 2
0036     f = e;
0037 end
0038 
0039 % compute two direction vectors, using first vertex of each face as origin
0040 v1 = v(f(:, 2), :) - v(f(:, 1), :);
0041 v2 = v(f(:, 3), :) - v(f(:, 1), :);
0042 
0043 % area of each triangle is half the cross product norm
0044 vn = vectorNorm3d(crossProduct3d(v1, v2));
0045 
0046 % sum up and normalize
0047 area = sum(vn) / 2;