Slicing a 3D vector field (defined in spherical basis and converted to cartesian basis) to view only the xz-plane of the vector field

Suppose we have a vector field defined over a spherical grid

Example code (simpler vector field than the one I'm actually dealing with) directly below just a general problem statement (actual code later)

I'd like to isolate planes instead of writing an entirely new script.

% Defining spherical grid, extract vectors, and transpose
c4 = 180*(pi^(-1));
n = 25;
rmin = 0.001;
rmax = 400;
phi = linspace(-pi,pi - ((n)^(-1))*2*pi,n);
theta = linspace(-0.5*pi,0.5*pi - ((n)^(-1))*2*pi,n);
r = linspace(rmin,rmax,n);


[Phi,Theta,R] = meshgrid(phi,theta,r);
SPM = [Phi(:),Theta(:),R(:)];                     %Spherical Points from Mesh
SPMT = SPM';                  %Spherical Points from Mesh Transpose

SPMD = c4*SPM;          %Now in degrees
SPMDT = SPMD';          % Now in degrees

%first have to convert the entire position grid to cartesian

[X,Y,Z] = sph2cart(Phi,Theta,R);

CPFM = [X(:),Y(:),Z(:)]; %Cartesian Points from mesh 

CPFMT = CPFM'; %Cartesian Points from mesh transposed

% Suppose we have a vector field



for i1 = 1:size(SPMT,2)
    Fr(1,i1) = SPMT(3,i1);
end

Faz = zeros(size(Fr));
Fel = zeros(size(Fr));

Fspherical = vertcat(Faz,Fel,Fr);

% Convert to this spherical basis to cartesian

for i2 = 1:size(Fspherical,2)
    FCartesian(:,i2) = sph2cartvec(Fspherical(:,i2),SPMDT(1,i2),SPMDT(2,i2));
end

% quiver3 plot

quiver3(CPFMT(1,:),CPFMT(2,:),CPFMT(3,:),Fspherical(1,:),Fspherical(2,:),Fspherical(3,:))

The actual vector field I'm working with is the Poynting vector field of a radiating electric dipole and the script is really long and would be much more difficult to decipher. So instead I contrived the simper vector field above. Hopefully any advice I get will transfer over to my script.

Thanks in Advanced.

Answer 1

[darova]

Use griddata to create 3D matrix

Use slice to create a crossection