meshSurfaceArea

 Surface area of a polyhedral mesh.

   S = meshSurfaceArea(V, F)
   S = meshSurfaceArea(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 can be a NF-by-3 or NF-by-4 numeric array, or a Nf-by-1 cell
   array, containing vertex indices of each face.

   This functions iterates on faces, extract vertices of the current face,
   and computes the sum of face areas.

   This function assumes faces are coplanar and convex. If faces are all
   triangular, the function "trimeshSurfaceArea" should be more efficient.


   Example
     % compute the surface of a unit cube (should be equal to 6)
     [v f] = createCube;
     meshSurfaceArea(v, f)
     ans = 
         6

   See also
     meshes3d, trimeshSurfaceArea, meshVolume, meshFaceAreas,
     meshFacePolygons, polygonArea3d

0001 function area = meshSurfaceArea(varargin)
0002 % Surface area of a polyhedral mesh.
0003 %
0004 %   S = meshSurfaceArea(V, F)
0005 %   S = meshSurfaceArea(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 can be a NF-by-3 or NF-by-4 numeric array, or a Nf-by-1 cell
0009 %   array, containing vertex indices of each face.
0010 %
0011 %   This functions iterates on faces, extract vertices of the current face,
0012 %   and computes the sum of face areas.
0013 %
0014 %   This function assumes faces are coplanar and convex. If faces are all
0015 %   triangular, the function "trimeshSurfaceArea" should be more efficient.
0016 %
0017 %
0018 %   Example
0019 %     % compute the surface of a unit cube (should be equal to 6)
0020 %     [v f] = createCube;
0021 %     meshSurfaceArea(v, f)
0022 %     ans =
0023 %         6
0024 %
0025 %   See also
0026 %     meshes3d, trimeshSurfaceArea, meshVolume, meshFaceAreas,
0027 %     meshFacePolygons, polygonArea3d
0028 %
0029 
0030 % ------
0031 % Author: David Legland
0032 % e-mail: david.legland@inrae.fr
0033 % Created: 2010-10-13,    using Matlab 7.9.0.529 (R2009b)
0034 % Copyright 2010 INRA - Cepia Software Platform.
0035 
0036 % parse input arguments
0037 [vertices, faces] = parseMeshData(varargin{:});
0038 
0039 % pre-compute normals
0040 normals = normalizeVector3d(meshFaceNormals(vertices, faces));
0041 
0042 % init accumulator
0043 area = 0;
0044 
0045 
0046 if isnumeric(faces)
0047     % iterate on faces in a numeric array
0048     for i = 1:size(faces, 1)
0049         poly = vertices(faces(i, :), :);        
0050         area = area + polyArea3d(poly, normals(i,:));
0051     end
0052     
0053 else
0054     % iterate on faces in a cell array
0055     for i = 1:length(faces)
0056         poly = vertices(faces{i}, :);
0057         area = area + polyArea3d(poly, normals(i,:));
0058     end
0059 end
0060 
0061 
0062 function a = polyArea3d(v, normal)
0063 
0064 nv = size(v, 1);
0065 v0 = repmat(v(1,:), nv, 1);
0066 products = sum(cross(v-v0, v([2:end 1], :)-v0, 2), 1);
0067 a = abs(dot(products, normal, 2))/2;