Fast Ray Tracing of Scale‐Invariant Integral Surfaces

Abstract

Scale‐invariant integral surfaces, which are implicit representations of surfaces, provide a way to define smooth surfaces from skeletons with prescribed radii defined at their vertices. We introduce a new rendering pipeline allowing to visualize such surfaces in real‐time. We rely on the distance to skeleton to define a sampling strategy along the camera rays, dividing each ray into sub‐intervals. The proposed strategy is chosen to capture main field variations. Resulting intervals are processed iteratively, relying on two main ingredients; quadratic interpolation and field mapping, to an approximate squared homothetic distance. The first provides efficient root finding while the second increases the precision of the interpolation, and the combination of both results in an efficient processing routine. Finally, we present a GPU implementation that relies on a dynamic data‐structure in order to efficiently generate the intervals along the ray. This data‐structure also serves as an acceleration structure that allows constant time access to the primitives of interest during the processing of a given ray.