Accelerating Sphere Tracing

Abstract

This paper presents two performance improvements on sphere tracing. First, a sphere tracing variant designed to take optimal step sizes near planar surfaces is proposed. We demonstrate how relaxation is used to make this method applicable to sphere tracing arbitrary geometries and compare its performance to classical (by Hart) and relaxed (Keinert et al.) sphere tracing in rendering various scenes. The method is also general in the sense that it can be applied in any scenario that requires the computation of ray-surface intersections. Our second contribution is a multi-resolution rendering strategy that can be used with any sphere tracing variant. By starting from a lower resolution and gradually increasing it, render times can be reduced.