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| function B=SnakeInternalForceMatrix3D(FV,alpha,beta,gamma)
%
% B=SnakeInternalForceMatrix3D(F,alpha,beta,gamma)
%
% inputs,
% FV : Struct (Patch) with the triangulated surface
% alpha : membrame energy (first order)
% beta : thin plate energy (second order)
% gamma : Step Size (Time)
%
% outputs,
% B : The Snake Smoothness regulation matrix
%
% Function is written by D.Kroon University of Twente (July 2010)
Ne=VertexNeighbours(FV.faces,FV.vertices);
nV=size(FV.vertices,1);
% Matrix for umbrella mesh derivative function in (sparce) matrix form
NeMatrix = spalloc(nV,nV,nV*10);
for i=1:nV
Nc=Ne{i};
% Add the neighbours
NeMatrix(i,Nc)=1/length(Nc);
% Add the vertex it self
NeMatrix(i,i)=-1;
end
% Total internal force matrix
B=speye(nV,nV)+gamma*(alpha*NeMatrix-beta*NeMatrix*NeMatrix);
function Ne=VertexNeighbours(F,V)
% Function which return the neighbouring vertices of every vertex
% in a cell array list. (Basic version, not sorted by rotation)
% Neighbourh cell array
Ne=cell(1,size(V,1));
% Loop through all faces
for i=1:length(F)
% Add the neighbors of each vertice of a face
% to his neighbors list.
Ne{F(i,1)}=[Ne{F(i,1)} [F(i,2) F(i,3)]];
Ne{F(i,2)}=[Ne{F(i,2)} [F(i,3) F(i,1)]];
Ne{F(i,3)}=[Ne{F(i,3)} [F(i,1) F(i,2)]];
end
% Remove duplicate vertices
for i=1:size(V,1), Ne{i}=unique(Ne{i}); end |
