Solid interpolation from surfaces

I have an external set of 4D data with dimensions (k,l,m,n), from which I have first created a cell array {m,n}(k,l), then I have used a matrix to sum the different matrices on the single column in m and interpolated, creating n surfaces. Using interp2 and defining the desired point on one of the n surfaces, I can obtain the desired value for the fixed n value of the surface.

This is the code relative to it:

[Xq,Zq]=meshgrid(linspace(palpha_n,palpha_x,dxsurf*palpha_dx),linspace(pRe_n,pRe_x,dxsurf*pRe_dx));

alpha=20;

Re=4e6;

Ma=0.12;

pol_r=cell(1,size(pol_surf,2));

for iMa=1:size(pol_surf,2)

j=1;

for iRe=1:size(pol_surf,1)

for ialpha=1:size([pol_surf{iRe,iMa}],1)

pol_r{iMa}(j,:)=num2cell(pol_surf{iRe,iMa}(ialpha,:));

j=j+1;

end

end

figure

scatter3(cell2mat(pol_r{iMa}(:,1)),cell2mat(pol_r{iMa}(:,2)),cell2mat(pol_r{iMa}(:,8)),'filled','Color',[iMa./size(pol_surf,2) iMa./size(pol_surf,2) iMa./size(pol_surf,2)]);

FCl=scatteredInterpolant(cell2mat(pol_r{iMa}(:,1)),cell2mat(pol_r{iMa}(:,8)),cell2mat(pol_r{iMa}(:,2)));

Clq(:,:,iMa)=FCl(Xq,Zq);

Cl_interp(:,iMa)=mesh(Xq,Clq(:,:,iMa),log10(Zq));

Cl(:,iMa)=interp2(Xq,Zq,Clq(:,:,iMa),alpha,Re);

end

I would like now to interpolate the n surfaces into a solid, in order to replicate the same interpolation process on the higher dimension and keeping the information relative to the surface, but I have no idea how to tackle the problem.

Any suggestions?

Answer 1

[Gojo]

Hey @Filippo Sanangelantoni,

I understand that you have created n surfaces from the 4D data and now you want to interpolate these surfaces into a solid.

You can use the “interp3” function for interpolating the 3D data in a mesh-grid format.

You can also refer to “griddedInterpolant” function which can perform interpolation on N-D gridded data set.

For more information please refer to:

https://www.mathworks.com/help/releases/R2020b/matlab/ref/interp3.html

https://www.mathworks.com/help/releases/R2020b/matlab/ref/griddedinterpolant.html

Hope this helps!!