function [dphidx,dphidy,dphidz,Xi,Yi,Zi,wgi]=CreateGradNURBSBasis3D(mesh_file,p,GaussPts,pscale,frame)
if nargin < 3 , GaussPts='Gauss_points';end
if nargin < 4 , pscale=1;end
if nargin < 5 , frame='parametric';end
[pp,filname,ext]=fileparts(mesh_file);
if isempty(ext)
mesh_file=[mesh_file,'.mat'];
end
load(mesh_file,'Px','Py','Pz','uo','vo','wo','Nbselems','-mat');
uo=(uo-0.5)*pscale+0.5;
vo=(vo-0.5)*pscale+0.5;
wo=(wo-0.5)*pscale+0.5;
switch GaussPts
case 'pixels'
error('Not allowed in 3D');
case 'knot'
[Yi,Xi,Zi]=meshgrid(vo,uo,wo);
Xi=Xi(:);Yi=Yi(:);Zi=Zi(:);
wgi=1;
case 'nodes'
load(mesh_file,'ui','vi','wi','-mat');
Yi=vi;
Xi=ui;
Zi=wi;
wgi=1;
case 'Gauss_points'
[xgi,wxgi]=GetGaussPointsLine(1+p(1));
[ygi,wygi]=GetGaussPointsLine(1+p(2));
[zgi,wzgi]=GetGaussPointsLine(1+p(3));
[yg,xg,zg]=meshgrid(ygi,xgi,zgi);
wg=wxgi*wygi';
wg=wg(:)*wzgi';
xg=xg(:);yg=yg(:);zg=zg(:);wg=wg(:);
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)];
N_r=[-0.125*(1-yg).*(1-zg),0.125*(1-yg).*(1-zg),0.125*(1+yg).*(1-zg),-0.125*(1+yg).*(1-zg),...
-0.125*(1-yg).*(1+zg),0.125*(1-yg).*(1+zg),0.125*(1+yg).*(1+zg),-0.125*(1+yg).*(1+zg)];
N_s=[-0.125*(1-xg).*(1-zg),-0.125*(1+xg).*(1-zg),0.125*(1+xg).*(1-zg),0.125*(1-xg).*(1-zg),...
-0.125*(1-xg).*(1+zg),-0.125*(1+xg).*(1+zg),0.125*(1+xg).*(1+zg),0.125*(1-xg).*(1+zg)];
N_t=[-0.125*(1-xg).*(1-yg),-0.125*(1+xg).*(1-yg),-0.125*(1+xg).*(1+yg),-0.125*(1-xg).*(1+yg),...
0.125*(1-xg).*(1-yg),0.125*(1+xg).*(1-yg),0.125*(1+xg).*(1+yg),0.125*(1-xg).*(1+yg)];
Xi=zeros(prod(Nbselems)*prod(p+1),1);
Yi=zeros(prod(Nbselems)*prod(p+1),1);
Zi=zeros(prod(Nbselems)*prod(p+1),1);
wgi=zeros(prod(Nbselems)*prod(p+1),1);
Sel=prod(p+1);
np=0;
for ix=1:Nbselems(1)
for iy=1:Nbselems(2)
for iz=1:Nbselems(3)
inods=ix+p(1)+[0,1,1,0,0,1,1,0];
jnods=iy+p(2)+[0,0,1,1,0,0,1,1];
knods=iz+p(3)+[0,0,0,0,1,1,1,1];
ui=uo(inods(:))';
vi=vo(jnods(:))';
wi=wo(knods(:))';
dxdr=N_r*ui;
dydr=N_r*vi;
dzdr=N_r*wi;
dxds=N_s*ui;
dyds=N_s*vi;
dzds=N_s*wi;
dxdt=N_t*ui;
dydt=N_t*vi;
dzdt=N_t*wi;
detJ =dxdr.*dyds.*dzdt + dxdt .*dydr.*dzds +...
dxds.*dydt.*dzdr - dxdt .*dyds.*dzdr -...
dxdr.*dydt.*dzds - dxds .*dydr.*dzdt;
indp=np+(1:Sel);
Xi(indp)=N*ui;
Yi(indp)=N*vi;
Zi(indp)=N*wi;
wgi(indp)=detJ.*wg;
np=np+Sel;
end
end
end
end
npt=numel(Xi);
indp=zeros((p(1)+1)*npt,1);
indn=zeros((p(1)+1)*npt,1);
val=zeros((p(1)+1)*npt,1);
dval=zeros((p(1)+1)*npt,1);
Nnx=Nbselems(1)+p(1);
nel=0;
for ix=1:Nbselems(1)
if ix==Nbselems(1)
found=find((Xi>=uo(ix+p(1)))&(Xi<=uo(ix+p(1)+1)));
else
found=find((Xi>=uo(ix+p(1)))&(Xi<uo(ix+p(1)+1)));
end
xp=Xi(found);
[f]=NURBSBasisFunc(ix+p(1),p(1),xp',uo,1);
Sel=length(xp);
for ip=1:(p+1)
indn(nel+(1:Sel))=ix+ip-1;
indp(nel+(1:Sel))=found;
dval(nel+(1:Sel))=f(:,ip,2);
val(nel+(1:Sel))=f(:,ip,1);
nel=nel+Sel;
end
end
phix=sparse(indp,indn,val,npt,Nnx);
dphix=sparse(indp,indn,dval,npt,Nnx);
indp=zeros((p(2)+1)*npt,1);
indn=zeros((p(2)+1)*npt,1);
val=zeros((p(2)+1)*npt,1);
dval=zeros((p(2)+1)*npt,1);
Nny=Nbselems(2)+p(2);
nel=0;
for iy=1:Nbselems(2)
if iy==Nbselems(2)
found=find((Yi>=vo(iy+p(2)))&(Yi<=vo(iy+p(2)+1)));
else
found=find((Yi>=vo(iy+p(2)))&(Yi<vo(iy+p(2)+1)));
end
yp=Yi(found);
[f]=NURBSBasisFunc(iy+p(2),p(2),yp',vo,1);
Sel=length(yp);
for ip=1:(p(2)+1)
indn(nel+(1:Sel))=iy+ip-1;
indp(nel+(1:Sel))=found;
dval(nel+(1:Sel))=f(:,ip,2);
val(nel+(1:Sel))=f(:,ip,1);
nel=nel+Sel;
end
end
phiy=sparse(indp,indn,val,npt,Nny);
dphiy=sparse(indp,indn,dval,npt,Nny);
indp=zeros((p(3)+1)*npt,1);
indn=zeros((p(3)+1)*npt,1);
val=zeros((p(3)+1)*npt,1);
dval=zeros((p(3)+1)*npt,1);
Nnz=Nbselems(3)+p(3);
nel=0;
for iz=1:Nbselems(3)
if iz==Nbselems(3)
found=find((Zi>=wo(iz+p(3)))&(Zi<=wo(iz+p(3)+1)));
else
found=find((Zi>=wo(iz+p(3)))&(Zi<wo(iz+p(3)+1)));
end
zp=Zi(found);
[f]=NURBSBasisFunc(iz+p(3),p(3),zp',wo,1);
Sel=length(zp);
for ip=1:(p(3)+1)
indn(nel+(1:Sel))=iz+ip-1;
indp(nel+(1:Sel))=found;
dval(nel+(1:Sel))=f(:,ip,2);
val(nel+(1:Sel))=f(:,ip,1);
nel=nel+Sel;
end
end
phiz=sparse(indp,indn,val,npt,Nnz);
dphiz=sparse(indp,indn,dval,npt,Nnz);
[indj,indi,indk]=meshgrid(1:Nny,1:Nnx,1:Nnz);
phi=phix(:,indi(:)).*phiy(:,indj(:)).*phiz(:,indk(:));
dphidx=dphix(:,indi(:)).*phiy(:,indj(:)).*phiz(:,indk(:));
dphidy=phix(:,indi(:)).*dphiy(:,indj(:)).*phiz(:,indk(:));
dphidz=phix(:,indi(:)).*phiy(:,indj(:)).*dphiz(:,indk(:));
if strcmp(frame,'physical')
dxdr=dphidx*Px(:);
dydr=dphidx*Py(:);
dzdr=dphidx*Pz(:);
dxds=dphidy*Px(:);
dyds=dphidy*Py(:);
dzds=dphidy*Pz(:);
dxdt=dphidz*Px(:);
dydt=dphidz*Py(:);
dzdt=dphidz*Pz(:);
DetJ =dxdr.*dyds.*dzdt + dxdt .*dydr.*dzds +...
dxds.*dydt.*dzdr - dxdt .*dyds.*dzdr -...
dxdr.*dydt.*dzds - dxds .*dydr.*dzdt;
N_x=diag(sparse((dyds .* dzdt - dydt .* dzds) ./ DetJ))*dphidx+...
diag(sparse(-(dydr .* dzdt - dydt .* dzdr) ./ DetJ))*dphidy+...
diag(sparse((dydr .* dzds - dyds .* dzdr) ./ DetJ))*dphidz;
N_y=diag(sparse(-(dxds .* dzdt - dxdt .* dzds) ./ DetJ))*dphidx+...
diag(sparse((dxdr .* dzdt - dxdt .* dzdr) ./ DetJ))*dphidy+...
diag(sparse(-(dxdr .* dzds - dxds .* dzdr) ./ DetJ))*dphidz;
N_z=diag(sparse((dxds .* dydt - dxdt .* dyds) ./ DetJ))*dphidx+...
diag(sparse(-(dxdr .* dydt - dxdt .* dydr) ./ DetJ))*dphidy+...
diag(sparse((dxdr .* dyds - dxds .* dydr) ./ DetJ))*dphidz;
dphidx=N_x;
dphidy=N_y;
dphidz=N_z;
wgi=wgi.*DetJ;
end
Xi=phi*Px(:);
Yi=phi*Py(:);
Zi=phi*Pz(:);
wgi=diag(sparse(wgi));
end
