/
compute_mesh_weight.m
104 lines (90 loc) · 2.75 KB
/
compute_mesh_weight.m
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function W = compute_mesh_weight(vertex,face,type,options)
% compute_mesh_weight - compute a weight matrix
%
% W = compute_mesh_weight(vertex,face,type,options);
%
% W is sparse weight matrix and W(i,j)=0 is vertex i and vertex j are not
% connected in the mesh.
%
% type is either
% 'combinatorial': W(i,j)=1 is vertex i is conntected to vertex j.
% 'distance': W(i,j) = 1/d_ij^2 where d_ij is distance between vertex
% i and j.
% 'conformal': W(i,j) = cot(alpha_ij)+cot(beta_ij) where alpha_ij and
% beta_ij are the adjacent angle to edge (i,j)
%
% If options.normalize=1, the the rows of W are normalize to sum to 1.
%
% Copyright (c) 2007 Gabriel Peyre
options.null = 0;
[vertex,face] = check_face_vertex(vertex,face);
nface = size(face,1);
n = max(max(face));
if isfield(options, 'verb')
verb = options.verb;
else
verb = n>5000;
end
if nargin<3
type = 'conformal';
end
switch lower(type)
case 'combinatorial'
W = triangulation2adjacency(face);
case 'distance'
W = my_euclidean_distance(triangulation2adjacency(face),vertex);
W(W>0) = 1./W(W>0);
W = (W+W')/2;
case 'conformal'
% conformal laplacian
W = sparse(n,n);
ring = compute_vertex_face_ring(face);
for i = 1:n
if verb
progressbar(i,n);
end
for b = ring{i}
% b is a face adjacent to a
bf = face(:,b);
% compute complementary vertices
if bf(1)==i
v = bf(2:3);
elseif bf(2)==i
v = bf([1 3]);
elseif bf(3)==i
v = bf(1:2);
else
error('Problem in face ring.');
end
j = v(1); k = v(2);
vi = vertex(:,i);
vj = vertex(:,j);
vk = vertex(:,k);
% angles
alpha = myangle(vk-vi,vk-vj);
beta = myangle(vj-vi,vj-vk);
% add weight
W(i,j) = W(i,j) + cot( alpha );
W(i,k) = W(i,k) + cot( beta );
end
end
otherwise
error('Unknown type.')
end
if isfield(options, 'normalize') && options.normalize==1
W = diag(sum(W,2).^(-1)) * W;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function beta = myangle(u,v);
du = sqrt( sum(u.^2) );
dv = sqrt( sum(v.^2) );
du = max(du,eps); dv = max(dv,eps);
beta = acos( sum(u.*v) / (du*dv) );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function W = my_euclidean_distance(A,vertex)
if size(vertex,1)<size(vertex,2)
vertex = vertex';
end
[i,j,s] = find(sparse(A));
d = sum( (vertex(i,:) - vertex(j,:)).^2, 2);
W = sparse(i,j,d);