mesh_vertex_spacing

 [FV] = mesh_vertex_spacing(FV)

 FV.vertices - Nx3
 FV.faces - Nx3
 FV.edges - NxN, see mesh_edges

 This function shifts vertex location toward the center of its
 neighbouring vertices.  It is useful to maintain vertex spacing.

 This code is developed on the basis of Smith (2002, fig 4).

 Smith, S. (2002). Fast robust automated brain extraction. 
    Human Brain Mapping, 17(3): 143-155.

0001 function [FV] = mesh_vertex_spacing(FV),
0002 
0003 % [FV] = mesh_vertex_spacing(FV)
0004 %
0005 % FV.vertices - Nx3
0006 % FV.faces - Nx3
0007 % FV.edges - NxN, see mesh_edges
0008 %
0009 % This function shifts vertex location toward the center of its
0010 % neighbouring vertices.  It is useful to maintain vertex spacing.
0011 %
0012 % This code is developed on the basis of Smith (2002, fig 4).
0013 %
0014 % Smith, S. (2002). Fast robust automated brain extraction.
0015 %    Human Brain Mapping, 17(3): 143-155.
0016 
0017 
0018 if isfield(FV,'edges'),
0019     if isempty(FV.edges),
0020         FV.edges = mesh_edges(FV);
0021     end
0022 else
0023     FV.edges = mesh_edges(FV);
0024 end
0025 
0026 %[normals,unit_normals] = mesh_vertex_normals(FV);
0027 
0028 % get surface normals
0029 hf = figure('Visible','off');
0030 hp = patch('faces',FV.faces,'vertices',FV.vertices);
0031 normals = get(hp,'VertexNormals');
0032 close(hf); clear hf hp
0033 %Convert to unit normals
0034 [normals,unit_normals] = colnorm(normals');
0035 unit_normals = unit_normals';
0036 clear normals
0037 
0038 
0039 Nvertices = size(FV.vertices,1);
0040 
0041 for index = 1:Nvertices,
0042 
0043     v = FV.vertices(index,:);
0044     x = FV.vertices(index,1);
0045     y = FV.vertices(index,2);
0046     z = FV.vertices(index,3);
0047 
0048     unit_normal = unit_normals(index,:);
0049 
0050     % Find neighbouring vertex coordinates
0051     vi = find(FV.edges(index,:));  % the indices
0052     neighbour_vertices = FV.vertices(vi,:);
0053     X = neighbour_vertices(:,1);
0054     Y = neighbour_vertices(:,2);
0055     Z = neighbour_vertices(:,3);
0056 
0057     % Find neighbour mean location; this is 'mean position of A and B' in
0058     % figure 4 of Smith (2002)
0059     Xmean = mean(X);
0060     Ymean = mean(Y);
0061     Zmean = mean(Z);
0062 
0063     % Find difference in distance between the vertex of interest and its
0064     % neighbours; this value is 's' and 'sn' in figure 4 of
0065     % Smith (2002, eq. 1 to 4)
0066     s = [ Xmean - x, Ymean - y, Zmean - z]; % inward toward mean
0067 
0068     % Find the vector sn
0069     % the projection of s in the direction of the surface normal
0070     sn = dot( s, unit_normal ) * unit_normal;
0071 
0072     % Find the vector st, the component of s orthogonal to the
0073     % surface normal vector.
0074     st = s - sn; % absolute value
0075 
0076     
0077     S(index,:) = s;
0078     Sn(index,:) = sn;
0079     St(index,:) = st;
0080 
0081 end
0082 
0083 % We can now use St to move the vertex toward the mean location of the
0084 % neighbour vertices
0085 
0086 FV.vertices = FV.vertices + St;
0087 
0088 return