interpolate_cortex

 INTERPOLATE_CORTEX Interpolate current density from a sparse tesselation to a dense tesselation
 function InterpMatrix = interpolate_cortex(sparseFV,denseFV,vertConn);
 sparseFV is the sparse Faces/Vertices structure
 denseFV is the dense Faces/Vertices structure
 vertConn is the vertices connectivity of the dense Faces/Vertices structure

 InterpMatrix returned is a sparse matrix (nDenseVertices x nSparseVertices) used for interpolation,
 where nDenseVertices in the number of vertices in the dense structure and nSparseVertices is the
 number of vertices in the sparse structure
 Interpolated current density is given by DenseCurrentDensity = InterpMatrix * SparseCurrentDensity

 Remarks: Every vertex in sparseFV should have a corresponding one in denseFV (i.e. same coordinates)
 sparseFV=reducepatch(denseFV) matlab function produces such tesselations
 Surfaces should be connected, i.e. there should exist a path through triangles connecting every pair
 of vertices on the surface
 interpolate_cortex performs interpolation in terms of surface neighbours and not in terms of volume
 neighbours

 See also REDUCEPATCH VERTICES_CONNECTIVITY PATCH_SWELL

0001 function [InterpMatrix] = interpolate_cortex(sparseFV,denseFV,vertConn)
0002 % INTERPOLATE_CORTEX Interpolate current density from a sparse tesselation to a dense tesselation
0003 % function InterpMatrix = interpolate_cortex(sparseFV,denseFV,vertConn);
0004 % sparseFV is the sparse Faces/Vertices structure
0005 % denseFV is the dense Faces/Vertices structure
0006 % vertConn is the vertices connectivity of the dense Faces/Vertices structure
0007 %
0008 % InterpMatrix returned is a sparse matrix (nDenseVertices x nSparseVertices) used for interpolation,
0009 % where nDenseVertices in the number of vertices in the dense structure and nSparseVertices is the
0010 % number of vertices in the sparse structure
0011 % Interpolated current density is given by DenseCurrentDensity = InterpMatrix * SparseCurrentDensity
0012 %
0013 % Remarks: Every vertex in sparseFV should have a corresponding one in denseFV (i.e. same coordinates)
0014 % sparseFV=reducepatch(denseFV) matlab function produces such tesselations
0015 % Surfaces should be connected, i.e. there should exist a path through triangles connecting every pair
0016 % of vertices on the surface
0017 % interpolate_cortex performs interpolation in terms of surface neighbours and not in terms of volume
0018 % neighbours
0019 %
0020 % See also REDUCEPATCH VERTICES_CONNECTIVITY PATCH_SWELL
0021 
0022 % Dimitrios Pantazis, Ph.D.
0023 % 11-Apr-02
0024 % <copyright>
0025 % <copyright>
0026 
0027 
0028 %choose whether to display bars
0029 if(~exist('VERBOSE','var')),
0030    VERBOSE = 1; % default non-silent running of waitbars
0031 end
0032 
0033 %Initialize variables
0034 nDenseVertices=size(denseFV.vertices,1);
0035 nSparseVertices=size(sparseFV.vertices,1);
0036 existInSparse=zeros(nDenseVertices,1);
0037 InterpMatrix=sparse(nDenseVertices,nSparseVertices);
0038 
0039 
0040 %find vertices that have been preserved in sparse patch
0041 %iDense: index of common vertices in denseFV
0042 %iSparse: index of common vertices in sparseFV
0043 [ignore,iDense,iSparse]=intersect(denseFV.vertices,sparseFV.vertices,'rows');
0044 existInSparse(iDense) =iSparse; %helpful vector
0045 
0046 %For a strange reason it takes awful time if I write InterpMatrix(iDense,iSparse)=1;
0047 for i=1:length(iDense)
0048     InterpMatrix(iDense(i),iSparse(i))=1;
0049 end
0050 
0051 %interpolate the rest of the vertices
0052 if(VERBOSE)
0053     hwait = waitbar(0,sprintf('Interpolating the %.0f remaining vertices...',nDenseVertices-nSparseVertices));
0054     drawnow %flush the display
0055     step=round(nDenseVertices/20);
0056 end
0057 for i=1:nDenseVertices
0058     if(VERBOSE)
0059        if(~rem(i,step)) % twenty updates
0060           waitbar(i/nDenseVertices,hwait);
0061           drawnow %flush the display
0062        end
0063     end
0064     if(~existInSparse(i))
0065         startPatch=i;
0066         nLayer=0;
0067         neighboursKnown=[];
0068         neighboursKnownScale=[];
0069         while(length(neighboursKnown)<3 & nLayer <10 )
0070             swelledPatch=patch_swell(startPatch,vertConn); %swell patch to find know vertices
0071             if(isempty(swelledPatch))
0072                 %disp('surface not closed');
0073                 break;
0074             end         
0075             temp=existInSparse(swelledPatch);
0076             neighboursNew=temp(temp>0)';
0077             nLayer=nLayer+1;
0078             neighboursKnown=[neighboursKnown neighboursNew];
0079             neighboursKnownScale=[neighboursKnownScale nLayer*ones(1,length(neighboursNew))];
0080             startPatch=[swelledPatch startPatch];
0081         end
0082         %update InterpMatrix
0083         InterpMatrix(i,neighboursKnown)=(1./neighboursKnownScale)/sum(1./neighboursKnownScale);
0084     end
0085 end
0086 if(VERBOSE)
0087     close(hwait);
0088 end