vertexNormal

VERTEXNORMAL Compute normals to a mesh vertices.

   N = vertexNormal(V, F)
   Computes vertex normals of the mesh given by vertices V and F. 
   V is a vertex array with 3 columns, F is either a NF-by-3 or NF-by-4
   index array, or a cell array with NF elements.

   Example
     % Draw the vertex normals of a sphere
     s = [10 20 30 40];
     [v f] = sphereMesh(s);
     drawMesh(v, f);
     view(3);axis equal; light; lighting gouraud;
     normals = vertexNormal(v, f);
     drawVector3d(v, normals);

   See also
     meshes3d, meshFaceNormals, triangulateFaces

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2011-12-19,    using Matlab 7.9.0.529 (R2009b)
 Copyright 2011 INRA - Cepia Software Platform.

0001 function normals = vertexNormal(vertices, faces)
0002 %VERTEXNORMAL Compute normals to a mesh vertices.
0003 %
0004 %   N = vertexNormal(V, F)
0005 %   Computes vertex normals of the mesh given by vertices V and F.
0006 %   V is a vertex array with 3 columns, F is either a NF-by-3 or NF-by-4
0007 %   index array, or a cell array with NF elements.
0008 %
0009 %   Example
0010 %     % Draw the vertex normals of a sphere
0011 %     s = [10 20 30 40];
0012 %     [v f] = sphereMesh(s);
0013 %     drawMesh(v, f);
0014 %     view(3);axis equal; light; lighting gouraud;
0015 %     normals = vertexNormal(v, f);
0016 %     drawVector3d(v, normals);
0017 %
0018 %   See also
0019 %     meshes3d, meshFaceNormals, triangulateFaces
0020 %
0021 % ------
0022 % Author: David Legland
0023 % e-mail: david.legland@grignon.inra.fr
0024 % Created: 2011-12-19,    using Matlab 7.9.0.529 (R2009b)
0025 % Copyright 2011 INRA - Cepia Software Platform.
0026 
0027 
0028 nv = size(vertices, 1);
0029 nf = size(faces, 1);
0030 
0031 % unit normals to the faces
0032 faceNormals = normalizeVector3d(meshFaceNormals(vertices, faces));
0033 
0034 % compute normal of each vertex: sum of normals to each face
0035 normals = zeros(nv, 3);
0036 if isnumeric(faces)
0037     for i = 1:nf
0038         face = faces(i, :);
0039         for j = 1:length(face)
0040             v = face(j);
0041             normals(v, :) = normals(v,:) + faceNormals(i,:);
0042         end
0043     end
0044 else
0045     for i = 1:nf
0046         face = faces{i};
0047         for j = 1:length(face)
0048             v = face(j);
0049             normals(v, :) = normals(v,:) + faceNormals(i,:);
0050         end
0051     end
0052 end
0053 
0054 % normalize vertex normals to unit vectors
0055 normals = normalizeVector3d(normals);
0056 
0057