function Compare_smooth()
load('ani_fittingALL_pnorm5.mat')
term_choose=68;
aPhys=a_log{term_choose,2};bPhys=b_log{term_choose,2};cPhys=c_log{term_choose,2};
nz=size(aPhys,1);ny=size(aPhys,2);nx=size(aPhys,3);

% ParameterField(aPhys,bPhys,cPhys)
resolution=40;
tic
voxel= voxelField(aPhys,bPhys,cPhys,resolution);
toc
save voxel_afterSmooth40.mat voxel
% tic
% voxel=voxel_ele(aPhys,bPhys,cPhys,10,1,10);
% toc
% sum(voxel,'all')
end

function voxel=voxel_ele(aPhys,bPhys,cPhys,xe,ye,ze)
resolution=40;
h=1.0/resolution;
x2=h/2:h:1-h/2;
y2=h/2:h:1-h/2;
z2=h/2:h:1-h/2;
[x,y,z]=meshgrid(x2+xe-1,y2+ye-1,z2+ze-1);
[Fa,Fb,Fc]=interpField(aPhys,bPhys,cPhys);
a_sim = Fa(x,y,z);b_sim = Fb(x,y,z);c_sim = Fc(x,y,z);
p=cos(2*pi*(x-1/2))+ a_sim.*cos(2*pi*(y-1/2))+ b_sim.*cos(2*pi*(z-1/2))- c_sim;
voxel = p>=0;

a = aPhys(ze,ye,xe);b = bPhys(ze,ye,xe);c = cPhys(ze,ye,xe);
p2=cos(2*pi*(x-1/2))+ a.*cos(2*pi*(y-1/2))+ b.*cos(2*pi*(z-1/2))- c;
voxel2 = p2>=0;

mean(abs(voxel-voxel2),'all')
end

function voxel= voxelField(aPhys,bPhys,cPhys,resolution)
[Fa,Fb,Fc]=interpField(aPhys,bPhys,cPhys);
nz=size(aPhys,1);ny=size(aPhys,2);nx=size(aPhys,3);

h=1.0/resolution;
x2=h/2:h:nx-h/2;
y2=h/2:h:ny-h/2;
z2=h/2:h:nz-h/2;
[x,y,z]=meshgrid(x2,y2,z2);
a_sim = Fa(x,y,z);b_sim = Fb(x,y,z);c_sim = Fc(x,y,z);
p=cos(2*pi*(x-1/2))+ a_sim.*cos(2*pi*(y-1/2))+ b_sim.*cos(2*pi*(z-1/2))- c_sim;

voxel = p>=0;

end


function [Fa,Fb,Fc]=interpField(aPhys,bPhys,cPhys)
nz=size(aPhys,1);ny=size(aPhys,2);nx=size(aPhys,3);
l=0.49;
xx=-1:1:1;
[dx,dy,dz]=meshgrid(xx,xx,xx);
dX=[dx(:),dy(:),dz(:)].*l;
num_p=size(xx,2)^3;

count=1;
a_fun = zeros(nx*ny*nz*num_p,1);
b_fun = zeros(nx*ny*nz*num_p,1);
c_fun = zeros(nx*ny*nz*num_p,1);
in1=zeros(nx*ny*nz*num_p,3);
for i=1:nx
    for j=1:ny
        for k=1:nz           
            for tt=0:num_p-1
                a_fun(count*num_p-tt,1) = aPhys(k,j,i);
                b_fun(count*num_p-tt,1) = bPhys(k,j,i);
                c_fun(count*num_p-tt,1) = cPhys(k,j,i);
                in1(count*num_p-tt,:)=[i-1/2,j-1/2,k-1/2]+dX(tt+1,:);
            end
            count=count+1;
        end
    end
end

Fa=scatteredInterpolant(in1(:,1),in1(:,2),in1(:,3),a_fun,'natural','linear');
Fb=scatteredInterpolant(in1(:,1),in1(:,2),in1(:,3),b_fun,'natural','linear');
Fc=scatteredInterpolant(in1(:,1),in1(:,2),in1(:,3),c_fun,'natural','linear');
% Fa.Method = 'linear';Fb.Method = 'linear';Fc.Method = 'linear';
end

function ParameterField(aPhys,bPhys,cPhys)
nz=size(aPhys,1);ny=size(aPhys,2);nx=size(aPhys,3);
figure()
subplot(311)
imagesc(squeeze(aPhys(:,1,:))); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])
subplot(312)
imagesc(squeeze(bPhys(:,1,:))); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])
subplot(313)
imagesc(squeeze(cPhys(:,1,:))); axis equal; axis tight; axis off;colorbar;caxis([-5,1])

[Fa,Fb,Fc]=interpField(aPhys,bPhys,cPhys);
x2=0:0.1:nx; 
y2=0.5;%y2=0:0.1:1; 
z2=0:0.1:nz;
[x,y,z]=meshgrid(x2,y2,z2);
a_sim = Fa(x,y,z);%b_sim = Fb(x,y,z);c_sim = Fc(x,y,z);

% figure()
% subplot(311)
% imagesc(squeeze(a_sim(1,:,:)).'); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])
% subplot(312)
% imagesc(squeeze(b_sim(1,:,:)).'); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])
% subplot(313)
% imagesc(squeeze(c_sim(1,:,:)).'); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])

x2=0.1;
[x,y,z]=meshgrid(x2,y2,z2);
a_sim2 = Fa(x,y,z);%b_sim = Fb(x,y,z);c_sim = Fc(x,y,z);
sum(abs(a_sim2-a_sim),'all')
% figure()
% subplot(311)
% imagesc(squeeze(a_sim(1,:,:)).'); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])
% subplot(312)
% imagesc(squeeze(b_sim(1,:,:)).'); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])
% subplot(313)
% imagesc(squeeze(c_sim(1,:,:)).'); axis equal; axis tight; axis off;colorbar;caxis([0.5,2])

end