A Geometric Method for Accelerated Sphere Tracing of Implicit Surfaces

Sphere tracing is a common raytracing technique used for rendering implicit surfaces defined by a signed distance function (SDF). However, these distance functions are often expensive to compute, prohibiting several real-time applications despite recent efforts to accelerate it. This paper presents a method to precompute a slightly augmented distance field that hugely accelerates rendering. This novel method called quadric tracing supports two configurations: (i) accelerating raytracing without losing precision, so the original SDF is still needed; (ii) entirely replacing the SDF and tracing an interpolated surface. Quadric tracing can offer 20% to 100% speedup in rendering static scenes and thereby amortizing the slowdown caused by the complexity of the geometry.