How could raytracing algorithms be generalized to higher dimensions, "surface tracing" or "volume tracing"? For instance, instead of computing ray-surface intersection, what if we wanted surface-volume intersections?
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Suppose you have a function 𝑓: ℝⁿ ↦ ℝ. Then define a level hypersurface 𝑓(𝒓) = c. Say I want to adaptively approximate points of that surface in ℝⁿ up to a certain precision. Except the points aren't constrained to rays, but some pre-defined surface or volume element.
For concreteness let’s assume we’re intersecting with a plane. I would start with a random point on the plane and evaluate f, if the value is c then you add the point to your collection. It it isn’t, calculate the derivatives and do gradient descent.