meshFaceCentroids

MESHFACECENTROIDS Compute centroids of faces in a mesh.

   CENTROIDS = meshFaceCentroids(VERTICES, FACES)
   VERTICES is a set of 3D points  (as a N-by-3 array), and FACES is
   either a N-by-3 index array or a cell array of indices. The function
   computes the centroid of each face, and returns a Nf-by-3 array
   containing their coordinates.

   Example
     [v, e, f] = createIcosahedron;
     normals1 = meshFaceNormals(v, f);
     centros1 = meshFaceCentroids(v, f);
     figure; hold on; axis equal; view(3);
     drawMesh(v, f); 
     drawVector3d(centros1, normals1);


   See also
     meshes3d, drawMesh, meshFaceNormals, meshFaceAreas, convhull

0001 function centroids = meshFaceCentroids(varargin)
0002 %MESHFACECENTROIDS Compute centroids of faces in a mesh.
0003 %
0004 %   CENTROIDS = meshFaceCentroids(VERTICES, FACES)
0005 %   VERTICES is a set of 3D points  (as a N-by-3 array), and FACES is
0006 %   either a N-by-3 index array or a cell array of indices. The function
0007 %   computes the centroid of each face, and returns a Nf-by-3 array
0008 %   containing their coordinates.
0009 %
0010 %   Example
0011 %     [v, e, f] = createIcosahedron;
0012 %     normals1 = meshFaceNormals(v, f);
0013 %     centros1 = meshFaceCentroids(v, f);
0014 %     figure; hold on; axis equal; view(3);
0015 %     drawMesh(v, f);
0016 %     drawVector3d(centros1, normals1);
0017 %
0018 %
0019 %   See also
0020 %     meshes3d, drawMesh, meshFaceNormals, meshFaceAreas, convhull
0021 %
0022 
0023 % ------
0024 % Author: David Legland
0025 % E-mail: david.legland@inrae.fr
0026 % Created: 2006-07-05
0027 % Copyright 2006-2024 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
0028 
0029 % parse input data
0030 [vertices, faces] = parseMeshData(varargin{:});
0031 
0032 if isnumeric(faces)
0033     % trimesh or quadmesh
0034     nf = size(faces, 1);
0035     centroids = zeros(nf, size(vertices, 2));
0036     if size(vertices, 2) == 2
0037         % planar case
0038         for f = 1:nf
0039             centroids(f,:) = polygonCentroid(vertices(faces(f,:), :));
0040         end
0041     else
0042         % 3D case
0043         if size(faces, 2) == 3
0044             % For triangular meshes, uses accelerated method
0045             % (taken from https://github.com/alecjacobson/gptoolbox)
0046             for ff = 1:3
0047                 centroids = centroids + 1/3 * vertices(faces(:,ff),:);
0048             end
0049         else
0050             % for quad (or larger) meshes, use slower but more precise method
0051             for f = 1:nf
0052                 centroids(f,:) = polygonCentroid3d(vertices(faces(f,:), :));
0053             end
0054         end
0055     end        
0056 else
0057     % mesh with faces stored as cell array
0058     nf = length(faces);
0059     centroids = zeros(nf, size(vertices, 2));
0060     if size(vertices, 2) == 2
0061         % planar case
0062         for f = 1:nf
0063             centroids(f,:) = polygonCentroid(vertices(faces{f}, :));
0064         end
0065     else
0066         % 3D case
0067         for f = 1:nf
0068             centroids(f,:) = polygonCentroid3d(vertices(faces{f}, :));
0069         end
0070     end
0071 end
0072