[x3d-public] Ray Marching/Sphere Tracing for self intersection

[John Carlson]

I am wondering if Ray Marching and maybe Sphere Tracing might be useful for
self intersecting surfaces, where there are internal surface/ray
intersections.   For example, spherical coordinate equations of the form r
= A + B cos(C*theta) cos(D*phi).   Back in the mid-80’s I tried Newton’s
and Bisection to find external surfaces, but I ran some tests later and
found out that there was no difference in sign for the internal surface/ray
intersection.  Bummer.   Someone who is experienced or has a ray marcher or
sphere ray tracer (or could point me at one)—perhaps we could run some
tests to find internal ray intersections for different configurations of
the equation?  My first guess would be that internal surfaces cannot be
found unless tessellation is done.

It does seem like surfaces in spherical coordinates are likely to suffer
this problem.

Are there spherical coordinate intersection finders?   Do we need to
convert rays to spherical coordinates?

Thanks!

John
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