graphics - Matlab -plot a vector field -

i have written function in matlab gives me vector @ position (x,y,z).

now looking easiest way make colored map of field on grid , color should related norm of vector.

what easiest way define such grid $x \in [x_0,x_1],y \in [y_0,y_1], z \in [z_0,z_1]$? linspace each component possible, maybe there command gives me grid.

now need evaluate function. problem is, gives me 2 vectors, interested in first one. when first tried thought $[a(i,j,k),~]=function(x(i),y(j),z(k))$ work, did not(my goal was: choose first vector(a) , mark him reference(i,j,k), later on know coordinates vector belongs to).

so highly interested in kind of ideas.

instead of

[a(i,j,k),~]=function(x(i),y(j),z(k)); 

try

[a(i,j,k,:),~]=function(x(i),y(j),z(k)); 

so can fit entire size of 3-coordinate vector. also, if want preallocate space use

 = zeros(nx,ny,nz,3); 

where nx,... dims of coordinate space. @moly explains, use meshgrid generate 3d grid,

 [x y z] = meshgrid(x,y,z); 

and loop or vectorize resolve values of function @ points x(i,j,k),y(i,j,k),z(i,j,k), compute norm , store in 3d array c.

edit

representing cube mesh(x,y,z,c) not possible individual slices of 3d cube can visualized mesh, setting height z equal result of function c. additional work required coloring right.

yet alternative use pcolor or contourf. perhaps easiest way show 4d data beyond creating 3d isosurface.

code:

figure colormap(jet) ii=1:9     subplot(3,3,ii)     pcolor(x(:,:,ii),y(:,:,ii),f(:,:,ii))     axis('equal','square'), title(['z=' num2str(ii)])     caxis([0 1]) end