Reexamination of the Schlick Approximation with Graphics Hardware in the Early 2020s

Abstract

In the field of game graphics, Fresnel's equation is often used to calculate surface reflections. Furthermore, the approximation devised by Schlick is often used when applying Fresnel's equation. However, in the course of studying polarization in real-time ray tracing, we discovered a phenomenon where the approximation by Schlick renders slower than the case where the Fresnel formula is not approximated. In this study, we re-examined the Schlick approximation on modern graphics hardware, and found that in real-time rendering and real-time ray tracing on GPUs in 2023, if we use the Schlick approximation, which is implemented in a simplistic manner based on speed alone, we should replace it with the Fresnel formula proposed in this paper. The proposed Fresnel formula can be used to achieve the unpolarized Fresnel effect without loss of quality at almost equivalent application execution speeds.