Macrofacet Theory for Gaussian Process Statistical Surfaces

TL;DR

This paper introduces macrofacet theory to extend microfacet models to macro-surfaces using Gaussian processes, enabling efficient rendering of complex surfaces without realizations.

Contribution

It formulates Gaussian process statistical surfaces through macrofacet theory, bridging microfacet models and Gaussian processes for improved rendering efficiency.

Findings

Transforms surfaces into volumetric representations preserving microfacet features.

Represents Gaussian process surfaces in a statistical manner for rendering.

Enables efficient rendering without surface realizations.

Abstract

We present macrofacet theory to extend microfacet theory from the micro-space to the macro-space. This is achieved by transforming surfaces into volumetric representations that preserve microfacet characteristics. Therefore, we formulate a macroscopic microfacet model using a classic exponential participating medium. Meanwhile, we observe that traditional microfacet models are equivalent to Gaussian processes by definition but ignore the correlation along the geometric normal of the macro-surface. We extend microfacet theory to address this limitation. Our formulation represents Gaussian process implicit surfaces in a statistical manner, which we refer to as Gaussian process statistical surfaces. As a result, our approach converts Gaussian process statistical surfaces into classic exponential media to render surfaces, volumes and in-betweens without realizations. This enables efficient rendering and improves performance compared to realization-based approaches, while theoretically bridging microfacet models and Gaussian processes. Moreover, our approach is easy to implement.