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214 | function [phi]=CreateFiniteElementBasis3D(mesh_file,sizeim,pscale,selected_nodes,GaussPts,full_size,selected_elts)
load(mesh_file,'rint','xo','yo','zo','Nnodes','Nelems','Smesh');
if nargin < 3 , pscale=1;end
if nargin < 4 , selected_nodes=[];end
if nargin < 5 , GaussPts='pixels';end
if nargin < 6 , full_size=false;end
if nargin < 7 , selected_elts=[];end
xo=(xo-0.5)*pscale+0.5;
yo=(yo-0.5)*pscale+0.5;
zo=(zo-0.5)*pscale+0.5;
load(mesh_file,'conn','elt','ng','ns');
incp(1)=1;incp(2)=incp(1)*sizeim(1)*pscale;incp(3)=incp(2)*sizeim(2)*pscale;
if strcmp(GaussPts,'rpixels')
GaussPts='pixels';
ng=0;
end
if strcmp(GaussPts,'pixels') ,ngte=ng*prod(ns)*2;ngt=ng*prod(ns)*2;ngq=ng*prod(ns);st=1+(prod(ns)==1);
elseif strcmp(GaussPts,'Gauss_points'),ngte=1;ngt=1+(~rint);ngq=1+7*(~rint);ng=1;ns=1;st=1;
elseif strcmp(GaussPts,'sub_cells'), ngte=1*prod(ns)*2;ngt=2*prod(ns)*2;ngq=1*prod(ns);ng=1;st=1+(prod(ns)==1);
end
if ng>0
if isempty(selected_nodes)
if isempty(selected_elts)
npts=4*ngte*sum(elt==4)/st+6*ngt*sum(elt==6)/st+8*ngq*sum(elt==8);
else
npts=4*ngte*sum(elt(selected_elts)==4)/st+6*ngt*sum(elt(selected_elts)==6)/st+8*ngq*sum(elt(selected_elts)==8);
end
else
if isempty(selected_elts)
selected_elts=GetEltsFromNodes(conn,elt,selected_nodes);
end
npts=4*ngte*sum(elt(selected_elts)==4)/st+6*ngt*sum(elt(selected_elts)==6)/st+8*ngq*sum(elt(selected_elts)==8);
end
nx=ngte*sum(elt==4)/st+ngt*sum(elt==6)/st+ngq*sum(elt==8);
else
npts=ceil(mean(elt))*ceil(prod(Smesh))*pscale^3;nx=prod(sizeim*pscale);
end
if isempty(selected_nodes)||full_size
ny=prod(Nnodes);
else
ny=length(selected_nodes);
end
indn=zeros(npts,1);
indp=zeros(npts,1);
val=zeros(npts,1);
if ng>0
if any(elt==4)
[xgte,ygte,zgte,wgte]=GetGaussPointsTetrahedron(ngte,ns);
Selte=length(xgte);
Nte=[1-xgte-ygte-zgte,xgte,ygte,zgte];
end
if any(elt==6)
[xgt,ygt,zgt,wgt]=GetGaussPointsWedge(ngt/(2*prod(ns)),ns);
Selt=length(xgt);
Nt=[0.5*(1-xgt-ygt).*(1-zgt),0.5*(xgt).*(1-zgt),0.5*(ygt).*(1-zgt),...
0.5*(1-xgt-ygt).*(1+zgt),0.5*(xgt).*(1+zgt),0.5*(ygt).*(1+zgt)];
end
if any(elt==8)
[xgq,ygq,zgq,wgq]=GetGaussPointsHexaedron(ngq/prod(ns),ns);
Selq=length(xgq);
Nq=[0.125*(1-xgq).*(1-ygq).*(1-zgq),0.125*(1+xgq).*(1-ygq).*(1-zgq),0.125*(1+xgq).*(1+ygq).*(1-zgq),0.125*(1-xgq).*(1+ygq).*(1-zgq),...
0.125*(1-xgq).*(1-ygq).*(1+zgq),0.125*(1+xgq).*(1-ygq).*(1+zgq),0.125*(1+xgq).*(1+ygq).*(1+zgq),0.125*(1-xgq).*(1+ygq).*(1+zgq)];
end
end
nel=0;
npix=0;
for i1=1:prod(Nelems)
if isempty(selected_nodes)
if isempty(selected_elts)
go=1;
else
go=any(selected_elts==i1);
end
else
if any(selected_elts==i1)
go=1;
else
go=0;
end
end
if go
inods=conn(i1,1:elt(i1));
if ng==0
xn=xo(inods);
yn=yo(inods);
zn=zo(inods);
[ypix,xpix,zpix]=meshgrid(ceil(min(yn)):floor(max(yn)),ceil(min(xn)):floor(max(xn)),ceil(min(zn)):floor(max(zn)));
if elt(i1)==4
if pscale==1
[xg,yg,zg,wg]=GetGaussPointsTetrahedron(ngte,ns,xn,yn,zn,xpix(:),ypix(:),zpix(:));
else
xg=(xpix-min(xn))/(max(xn)-min(xn));
yg=(ypix-min(yn))/(max(yn)-min(yn));
zg=(zpix-min(zn))/(max(zn)-min(zn));
wg=~(abs(xg)>1|abs(yg)>1|abs(zg)>1|(1-xg-yg-zg<0));
end
N=[1-xg-yg-zg,xg,yg,zg];
elseif elt(i1)==6
if pscale==1
[xg,yg,zg,wg]=GetGaussPointsWedge(ngt,ns,xn,yn,zn,xpix(:),ypix(:),zpix(:));
else
xg=-1+2*(xpix-min(xn))/(max(xn)-min(xn));
yg=-1+2*(ypix-min(yn))/(max(yn)-min(yn));
zg=-1+2*(zpix-min(zn))/(max(zn)-min(zn));
wg=~(abs(xg)>1|abs(yg)>1|abs(zg)>1);
end
N=[0.5*(1-xg-yg).*(1-zg),0.5*(xg).*(1-zg),0.5*(yg).*(1-zg),...
0.5*(1-xg-yg).*(1+zg),0.5*(xg).*(1+zg),0.5*(yg).*(1+zg)];
elseif elt(i1)==8
if pscale==1
[xg,yg,zg,wg]=GetGaussPointsHexaedron(ngt,ns,xn,yn,zn,xpix(:),ypix(:),zpix(:));
else
xg=-1+2*(xpix(:)-min(xn))/(max(xn)-min(xn));
yg=-1+2*(ypix(:)-min(yn))/(max(yn)-min(yn));
zg=-1+2*(zpix(:)-min(zn))/(max(zn)-min(zn));
wg=~(abs(xg)>1|abs(yg)>1|abs(zg)>1);
end
N=[0.125*(1-xg).*(1-yg).*(1-zg),0.125*(1+xg).*(1-yg).*(1-zg),0.125*(1+xg).*(1+yg).*(1-zg),0.125*(1-xg).*(1+yg).*(1-zg),...
0.125*(1-xg).*(1-yg).*(1+zg),0.125*(1+xg).*(1-yg).*(1+zg),0.125*(1+xg).*(1+yg).*(1+zg),0.125*(1-xg).*(1+yg).*(1+zg)];
end
Sel=length(xg);
npix=1+incp(1)*(xpix-1)+incp(2)*(ypix-1)+incp(3)*(zpix-1);
for in=1:elt(i1)
if isempty(selected_nodes)||full_size
id=inods(in);
else
id=find(selected_nodes==inods(in));
end
if ~isempty(id)
indn(nel+(1:Sel))=id;
indp(nel+(1:Sel))=npix;
val(nel+(1:Sel))=wg.*N(:,in);
nel=nel+Sel;
end
end
else
if elt(i1)==4
for in=1:4
if isempty(selected_nodes)||full_size
id=inods(in);
else
id=find(selected_nodes==inods(in));
end
if ~isempty(id)
indn(nel+(1:Selte))=id;
indp(nel+(1:Selte))=npix+(1:Selte);
val(nel+(1:Selte))=Nte(:,in);
nel=nel+Selte;
end
end
elseif elt(i1)==6
for in=1:6
if isempty(selected_nodes)||full_size
id=inods(in);
else
id=find(selected_nodes==inods(in));
end
if ~isempty(id)
indn(nel+(1:Selt))=id;
indp(nel+(1:Selt))=npix+(1:Selt);
val(nel+(1:Selt))=Nt(:,in);
nel=nel+Selt;
end
end
% npix=npix+Selt;
elseif elt(i1)==8
for in=1:8
if isempty(selected_nodes)||full_size
id=inods(in);
else
id=find(selected_nodes==inods(in));
end
if ~isempty(id)
indn(nel+(1:Selq))=id;
indp(nel+(1:Selq))=npix+(1:Selq);
val(nel+(1:Selq))=Nq(:,in);
nel=nel+Selq;
end
end
% npix=npix+Selq;
end
end
end
if ng>0
switch elt(i1)
case 4
npix=npix+Selte;
case 6
npix=npix+Selt;
case 8
npix=npix+Selq;
end
end
end
if nel<length(indn)
indn=indn(1:nel);
indp=indp(1:nel);
val=val(1:nel);
end
phi=sparse(indp,indn,val,nx,ny);
end
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