Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights
Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights
复制标题
用于使用许多多边形区域光进行实时渲染的解析球谐梯度
DOI：
--
复制
发表时间：
2020
影响因子：
6.2
通讯作者：
R. Ramamoorthi
中科院分区：
文献类型：
--
作者：
Lifan Wu;Guangyan Cai;Shuang Zhao;R. Ramamoorthi
最近的工作已经开发了球谐（SH）系数的解析公式，从均匀的多边形光，使近场区域光被包括在预计算辐射传输（PRT）系统，并在离线渲染。然而，该方法是低效的，因为系数需要在每个顶点或阴影点处重新计算，对于每个光，即使SH系数在空间中平滑地变化。复杂性与灯光数量成线性比例，这使得多灯光渲染变得困难。在本文中，我们开发了一个新的解析公式的球谐系数的空间梯度均匀多边形区域光。其结果是一个显着的推广，涉及雷诺输运定理，以减少问题的边界积分，我们推导出一个新的解析公式，显示如何减少一个关键项的SH系数的早期复发。实现只需要轻微增加现有的代码SH系数。研究结果也对最近的可微渲染的努力产生了影响。我们表明，SH梯度，使非常稀疏的空间采样，其次是准确的Hermite插值。这使得PRT能够以最小的开销和实时帧速率扩展到数百个区域灯。此外，SH梯度公式是一个新的数学结果，可能使许多其他图形应用程序。
Recent work has developed analytic formulae for spherical harmonic (SH) coefficients from uniform polygonal lights, enabling near-field area lights to be included in Precomputed Radiance Transfer (PRT) systems, and in offline rendering. However, the method is inefficient since coefficients need to be recomputed at each vertex or shading point, for each light, even though the SH coefficients vary smoothly in space. The complexity scales linearly with the number of lights, making many-light rendering difficult. In this paper, we develop a novel analytic formula for the spatial gradients of the spherical harmonic coefficients for uniform polygonal area lights. The result is a significant generalization, involving the Reynolds transport theorem to reduce the problem to a boundary integral for which we derive a new analytic formula, showing how to reduce a key term to an earlier recurrence for SH coefficients. The implementation requires only minor additions to existing code for SH coefficients. The results also hold implications for recent efforts on differentiable rendering. We show that SH gradients enable very sparse spatial sampling, followed by accurate Hermite interpolation. This enables scaling PRT to hundreds of area lights with minimal overhead and real-time frame rates. Moreover, the SH gradient formula is a new mathematical result that potentially enables many other graphics applications.