How can I generate a rotationally invariant surface from a profile?

I have a vector, e.g. V = [1 2 3 4 3 2 1], that represents a profile through the center of a rotationally invariant surface. I'm trying to generate a matrix representing the surface.

Alternatively, if there's a spherical cap but all I have is a profile from one edge, through the center, how can I generate the spherical cap from the profile?

Thanks in advance for any help!

Answer 1

[Matt J]

Something like this, maybe

      radius=length(V)-1;

      [X,Y]=ndgrid(linspace(0,radius,100););

      R=sqrt(X.^2+Y.^2);

      surfaceSamples=interp1(0:radius,V,R(:));
        surfaceSamples=reshape(surfaceSamples,size(X));

      surf(X,Y,surfaceSamples);

[Mike]

Wow Matt! Thanks!

It solves it except that the code produces just one quadrant of the entire surface. I can try to tweak the code but something tells me you'd do it in 1/1000th the time it'd take me.

[Matt J]

This line controls the region sampled. Going from -radius to radius should include all quadrants.

     [X,Y]=ndgrid(linspace(-radius,radius,100););

[Mike]

Much appreciated Matt!