TV_operator_3D

PURPOSE ^

L=TV_operator_3D( msh )

SYNOPSIS ^

function L=TV_operator_3D( msh )

DESCRIPTION ^

 L=TV_operator_3D( msh )
 construct Total Variation operator for a 3D mesh

 INPUTS:
 msh = a 3D scaip msh structure with .msh.vtx_c_c, .elem_c defined
 OUTPUTS:
 L = TV operator (generally used for regularisation)

 Copyright 2004 Andrea Borsic, SC-AIP s.a.s.
 Scientific Computing & Applied Inverse Problems  www.sc-aip.com
 Modifications (C) 2005 Andy Adler.
 License: GPL version 2 or version 3
 $Id: TV_operator_3D.m 3039 2012-06-06 14:58:10Z bgrychtol $

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function L=TV_operator_3D( msh )
0002 % L=TV_operator_3D( msh )
0003 % construct Total Variation operator for a 3D mesh
0004 %
0005 % INPUTS:
0006 % msh = a 3D scaip msh structure with .msh.vtx_c_c, .elem_c defined
0007 % OUTPUTS:
0008 % L = TV operator (generally used for regularisation)
0009 %
0010 % Copyright 2004 Andrea Borsic, SC-AIP s.a.s.
0011 % Scientific Computing & Applied Inverse Problems  www.sc-aip.com
0012 % Modifications (C) 2005 Andy Adler.
0013 % License: GPL version 2 or version 3
0014 % $Id: TV_operator_3D.m 3039 2012-06-06 14:58:10Z bgrychtol $
0015 
0016 %global SP3D % Sparse 3D matrix used in the computations
0017 %SP3D=[];
0018 
0019 num_vtx=size(msh.vtx_c,1);
0020 num_tet=size(msh.elem_c,1);
0021 
0022 list=[]; % List is an auxiliary variable which will hold for each row the two facing thetrahydra and the shared face area
0023 
0024 %We build a selection array, to index the T matrix
0025 
0026 SEL=[ 1 1 1 2; 2 3 4 4; 3 4 2 3];
0027 
0028 % allocate_3Dsparse(num_vtx,num_vtx,num_vtx,num_tet*4);
0029 SP3D=spalloc(num_vtx,num_vtx^2,num_tet*4);
0030 
0031 for k=1:num_tet
0032     
0033     for j=1:4 % cycle on the faces of each thetrahydra
0034         
0035         face_vtx(1)=msh.elem_c(k,SEL(1,j)); % face_vtx are the varticies on a face of thetrahydra k
0036         face_vtx(2)=msh.elem_c(k,SEL(2,j));
0037         face_vtx(3)=msh.elem_c(k,SEL(3,j));
0038         
0039         face_vtx=sort(face_vtx); % faces must be unique
0040         
0041 %       simplex=read_from_3Dsparse(face_vtx,num_vtx,num_vtx,num_vtx);
0042 %function val=read_from_3Dsparse(mnp,M,N,P);
0043 %
0044 %global SP3D
0045         %val=SP3D(mnp(1),(mnp(2)-1)*N+mnp(3));
0046         simplex=SP3D(face_vtx(1),(face_vtx(2)-1)*num_vtx+face_vtx(3));
0047         
0048         if (simplex==0)
0049             
0050 %         write_to_3Dsparse(mnp,M,N,P,val);
0051 %           SP3D(mnp(1),(mnp(2)-1)*N+mnp(3))=val;
0052 %
0053 %           write_to_3Dsparse(face_vtx,num_vtx,num_vtx,num_vtx,k);
0054             SP3D(face_vtx(1),(face_vtx(2)-1)*num_vtx+face_vtx(3))=k;
0055             
0056         else
0057             
0058             vec1=msh.vtx_c(face_vtx(1),:)-msh.vtx_c(face_vtx(2),:);  % vec1,vec2 are vectors along edgs, used for the area calculation as cross prod.
0059             vec2=msh.vtx_c(face_vtx(1),:)-msh.vtx_c(face_vtx(3),:);
0060             facearea=0.5*norm(cross(vec1,vec2));
0061             list=[list;[k,simplex,facearea]]; % Triangles and length of the shared edge are written into the list
0062             
0063         end % if then else
0064         
0065     end % for j
0066     
0067 end % for k
0068 
0069 L=spalloc(length(list),num_tet,2*length(list));
0070 
0071 for i=1:length(list)
0072     
0073     L(i,list(i,1))=list(i,3);
0074     L(i,list(i,2))=-list(i,3);
0075     
0076 end % for
0077 
0078 %clear SP3D;
0079 
0080 
0081 %%%%%%%%%% Auxiliary functions for handling the 3D sparse matrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0082 
0083 %%%%%%%%%% mnp is a vector of 3 indexes into the matrix, and M,N,P the matrix size along the three dimensions
0084 % - removed these functions for inclusion with EIDORS -aa Dec05
0085 %
0086 %function allocate_3Dsparse(M,N,P,max_elements);
0087 %
0088 %global SP3D
0089 %SP3D=spalloc(M,N*P,max_elements);
0090 %
0091 %function write_to_3Dsparse(mnp,M,N,P,val);
0092 %
0093 %global SP3D
0094 %SP3D(mnp(1),(mnp(2)-1)*N+mnp(3))=val;
0095 %
0096 %function val=read_from_3Dsparse(mnp,M,N,P);
0097 %
0098 %global SP3D
0099 %val=SP3D(mnp(1),(mnp(2)-1)*N+mnp(3));
0100 %

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