Using Slice on a Cartesian Grid that was Generated in Cylindrical Coordinates

Hello,

I generate a grid in cylindrical coordinates:

phi_grid = 0:1:360 ;

rho_grid = 5.5:0.1:10;

z_grid = -4:0.1:4;

[Rho_grid,Z_grid,Phi_grid] = meshgrid(rho_grid,z_grid,phi_grid);%creating a grid from those axes

I then convert to spherical & cartesian coordinates for when I need them.

R_grid = (Rho_grid.^2 + Z_grid.^2).^(0.5);% computing a Rad value for each point

Theta_sys3_grid = acosd(Z_grid./R_grid);

x = R_grid.*sind(Theta_sys3_grid).*cosd(Phi_grid);

y = R_grid.*sind(Theta_sys3_grid).*sind(Phi_grid);

z = R_grid.*cosd(Theta_sys3_grid);

I then run code to produce a value at each of these points in the cartesian plane. This code operates on the spherical coordinates. That code is long and complicated, here is replacement

v = x.*exp(-x.^2-y.^2-z.^2);

I now want to make a slice of the this data in the cartesian plane

xslice = linspace(-6,10,20);

yslice = linspace(-6,10,40);

zslice = linspace(-4,4,40);

xslice = xslice';

zslice = zslice';

yslice = yslice';

figure()

slice(x,y,z,v,xslice,yslice,zslice)

And I am returned this error message: "Input grid is not a valid MESHGRID." This is not an issue that one normally has if their grid was created using meshgrid. However, I'm assuming that creating a grid in one coordinate system and then changing the coordinate system can make the data either not monotonic or not plaid, compromising its valuable MESHGRID attributes. What I think I'm looking for, is a way make my new grids monotonic and plaid so I can operate on them with slice and contour slice, or, alternative solutions

Thank you

pH

Answer 1

[Ben Drebing]

One thing to try would be to use your x,y,z, and v to interpolate new data that is a meshgrid. It might run a little slower than you'd like but it would look something like:

 %Create the new meshgrid to slice
 [newX, newY, newZ] = meshgrid(-10:0.5:10, -10:0.5:10, -4:0.5:4);

 %Interpolate
 newV = griddata(x,y,z,v,newX,newY,newZ);

 figure();
 slice(newX, newY, newZ, newV, xslice, yslice, zslice);

Here is the related example in the documentation: https://www.mathworks.com/help/matlab/ref/griddata.html#bvkwypt-2

[Parker Hinton]

that is actually similar to what I ended up doing except with scatteredInterpolant , Thank you for the comment!