Calculate 3D gradient of data corrisponding to a non-uniform grid

Hi all,

In order to obtain a spherical 3D grid, I have generated an evenly-spaced azimuth-elevation-radius ndgrid and subsequently transformed it in cartesian coordinates using sph2cart. In this coordinates system, points are not evenly spaced.

[AZ_grid,EL_grid,R_grid]=ndgrid(AZ_vector,EL_vector,R_vector); % evenly spaced 3D grid
[X_grid,Y_grid,Z_grid]=sph2cart(AZ_grid,EL_grid,R_grid); %non-evenly spaced 3D grid

I have a 3D matrix P of values corresponding to these points in space. Obviously, if X_grid=[NxMxH], also P=[NxMxH].

I have to calculate the gradient of P along every direction. For the spherical case, I think I could write:

[G_AZ,G_EL,G_R]=gradient(P,AZ_spacing,EL_spacing,R_spacing);

as AZ_spacing,EL_spacing,R_spacing are constants.

How can I get the same result in cartesian coordinates (without using scatteredInterpolant or similar as it does not support code generation)? I tried to transform G_AZ,G_EL,G_R using sph2cart (as below), but I'm not sure the results obtained are the correct ones.

[GX,GY,GZ]=sph2cart(G_AZ,G_EL,G_R);

Thanks to anyone who can help me!

Answer 1

[Matt J]

I would just compute the Jacobian matrix of the spherical to cartesian coordinate transformation and multiply the spherical gradients by that.

[Alessandro Favia]

It works! Thank you!!