Has anyone ever tried to raytrace a sphere with complex numbers?
I mean all vectors and points are elements of C^n
Is this question just off the cuff, or have you put some thought into
it? It really doesn't make a lot of sense to me, so it would help if
you would give an application, or otherwise explain what you mean.
The best I can come up with is that the complex numbers represent two
realities which are out of phase with one another. Even the eye
position and the "look" vector can be different in the two realities,
and you wind up with an image in which the pixel values are complex.
However, in this interpretation you can just raytrace the real part and
the complex part separately and combine the results.
I have raytraced using complex numbers to represent the E-field in a
basis for polarization states. I have also raytraced with respect to
partial derivatives of variables in the scene geometry, and with respect
to the wavelength of light.