Kernel-Reflection Sequences

Abstract

Complex geometries, like those of plants, rocks, terrain, or even clouds are challenging to model in a way that allows for real-time rendering but does not make concessions in terms of visible detail. In this paper we propose a procedural modeling approach, called KRS, or kernel-reflection sequences, inspired by iterated function systems. The model is composed of kernel geometries defined by signed distance functions, and reflection transformations that multiply them. We show that a global distance function can be evaluated over this structure without recursion, allowing for the implementation of real-time sphere tracing on parallel hardware. We also show how the algorithm readily delivers continuous level-of-detail and minification filtering. We propose several techniques to enhance modeling freedom and avoid conspicuous symmetries. Most importantly, we extend sphere tracing to conformally transformed geometries. We also propose a GPU load balancing scheme for best utilization of computing power. To prove that the model can be used to realize various natural phenomena in uncompromising detail and extents, without obvious clues of symmetry, we render aquatic and terrestrial surface formations and vegetation in real-time.