Macrofacet Theory for Gaussian Process Statistical Surfaces

We present macrofacet theory, taking microfacet theory from micro-space to macro-space by stretching a surface to a volume to make it have microfacet characteristic in marco-space. In this way, we have a macroscopic microfacet formulation that uses a classic exponential participating medium. Meanwhile, we observe that traditional microfacet models are equivalent to Gaussian processes in definition but ignore the correlation along the geometric normal of macro-surface. We extend microfacet theory so that macrofacet can handle this problem and represent Gaussian process implicit surfaces in a statistical way. As a result, our approach converts Gaussian process implicit surfaces into classic exponential media to render surfaces, volumes and in-betweens without realization. These enable efficient rendering with performance improvement compared to realization-based approaches, while bridging microfacet models and Gaussian processes theoretically. Moreover, our approach is easy to implement and friendly for artists.