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.

翻译：本文提出宏观面元理论，通过将表面拉伸为体积使其在宏观空间呈现微观面元特性，从而将微观面元理论从微观空间拓展至宏观空间。由此我们建立了采用经典指数参与介质的宏观微观面元表达形式。同时，我们观察到传统微观面元模型在定义上等价于高斯过程，但忽略了沿宏观表面几何法线的相关性。我们扩展了微观面元理论，使宏观面元能够处理该问题并以统计方式表征高斯过程隐式表面。因此，我们的方法将高斯过程隐式表面转化为经典指数介质，无需具体实现即可渲染表面、体积及其过渡状态。相较于基于具体实现的方法，本方法在提升渲染性能的同时实现了高效绘制，并在理论上建立了微观面元模型与高斯过程之间的桥梁。此外，该方法易于实现且对艺术创作者友好。