Fresnel term approximations for metals

Abstract

Colored reflections are governed by the Fresnel term, which can be expressed from the refraction index of the material. This function, especially for metals where the refraction index becomes a complex number, is rather computation intensive. This paper presents an accurate simplification, which can also cope with complex refraction indices. In order to establish the approximation, Schlick’s formula is rescaled and the residual error is compensated by a simple rational approximation. The resulting formula can present realistic metals and is simple enough to be implemented on the vertex or pixel shader, and used in games.