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.

翻译：我们提出了宏面元理论，将微面元理论从微观空间扩展到宏观空间。这通过将曲面转化为保留微面元特征的体表示来实现。因此，我们利用经典的指数参与介质构建了一个宏观微面元模型。同时，我们发现传统微面元模型在定义上等价于高斯过程，但忽略了宏观曲面几何法线方向上的相关性。我们扩展了微面元理论以解决这一局限。我们的公式以统计方式表示高斯过程隐式曲面，并将其称为高斯过程统计曲面。最终，我们的方法将高斯过程统计曲面转化为经典的指数介质，无需生成具体实现即可渲染曲面、体积以及介于两者之间的混合形态。这实现了高效渲染，相较于基于实现的方法提升了性能，同时在理论上架起了微面元模型与高斯过程之间的桥梁。此外，我们的方法易于实现。