meshVertexNormals

MESHVERTEXNORMALS Compute normals to a mesh vertices.

   N = meshVertexNormals(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 20];
     [v f] = sphereMesh(s);
     figure; drawMesh(v, f);
     view(3);axis equal; light; lighting gouraud;
     normals = meshVertexNormals(v, f);
     drawVector3d(v, normals*2);

   See also
     meshes3d, meshFaceNormals, triangulateFaces

0001 function [normals, faceNormals] = meshVertexNormals(varargin)
0002 %MESHVERTEXNORMALS Compute normals to a mesh vertices.
0003 %
0004 %   N = meshVertexNormals(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 20];
0012 %     [v f] = sphereMesh(s);
0013 %     figure; drawMesh(v, f);
0014 %     view(3);axis equal; light; lighting gouraud;
0015 %     normals = meshVertexNormals(v, f);
0016 %     drawVector3d(v, normals*2);
0017 %
0018 %   See also
0019 %     meshes3d, meshFaceNormals, triangulateFaces
0020 %
0021 
0022 % ------
0023 % Author: David Legland
0024 % e-mail: david.legland@inra.fr
0025 % Created: 2011-12-19,    using Matlab 7.9.0.529 (R2009b)
0026 % Copyright 2011 INRA - Cepia Software Platform.
0027 
0028 [vertices, faces] = parseMeshData(varargin{:});
0029 
0030 nv = size(vertices, 1);
0031 nf = size(faces, 1);
0032 
0033 % unit normals to the faces
0034 faceNormals = normalizeVector3d(meshFaceNormals(vertices, faces));
0035 
0036 % compute normal of each vertex: sum of normals to each face
0037 normals = zeros(nv, 3);
0038 if isnumeric(faces)
0039     for i = 1:nf
0040         face = faces(i, :);
0041         for j = 1:length(face)
0042             v = face(j);
0043             normals(v, :) = normals(v,:) + faceNormals(i,:);
0044         end
0045     end
0046 else
0047     for i = 1:nf
0048         face = faces{i};
0049         for j = 1:length(face)
0050             v = face(j);
0051             normals(v, :) = normals(v,:) + faceNormals(i,:);
0052         end
0053     end
0054 end
0055 
0056 % normalize vertex normals to unit vectors
0057 normals = normalizeVector3d(normals);