标题： 自旋加权球谐函数用于偏振光传输 显示英文标题

标题： Spin-Weighted Spherical Harmonics for Polarized Light Transport

摘要： 极化渲染的目标是模拟光与具有极化依赖行为的材料之间的相互作用。 然而，将极化整合到渲染中具有挑战性，并显著增加了计算成本。 主要困难在于高效建模和计算与偏振光相关的复杂反射现象。 具体而言，对于高效环境光照和复杂光相互作用的存储至关重要的频域分析尚不存在。 为了使用频域技术高效模拟和再现偏振光相互作用，我们解决了在角度域中由斯托克斯矢量表示的偏振光传输连续性问题。 传统的球谐函数方法无法有效处理斯托克斯矢量的连续性和旋转不变性。 为克服这一问题，我们基于自旋加权球谐函数理论开发了一种新方法，称为极化球谐函数（PSH）。 我们的方法提供了斯托克斯矢量场的旋转不变表示。 此外，我们引入了基于PSH的极化渲染方程和球面卷积的频域公式。 我们首先在角度域中定义斯托克斯矢量场上的球面卷积，它还提供了偏振光传输的高效计算，在频域中几乎相当于逐元素乘积。 我们的频域公式，包括球面卷积，导致了在偏振环境照明下首个实时极化渲染技术的开发，称为预计算极化辐射传输，该技术使用我们的极化球谐函数。 结果表明，我们的方法能够有效地、准确地模拟和再现复杂反射现象中的偏振光相互作用。 显示英文摘要

摘要： The objective of polarization rendering is to simulate the interaction of light with materials exhibiting polarization-dependent behavior. However, integrating polarization into rendering is challenging and increases computational costs significantly. The primary difficulty lies in efficiently modeling and computing the complex reflection phenomena associated with polarized light. Specifically, frequency-domain analysis, essential for efficient environment lighting and storage of complex light interactions, is lacking. To efficiently simulate and reproduce polarized light interactions using frequency-domain techniques, we address the challenge of maintaining continuity in polarized light transport represented by Stokes vectors within angular domains. The conventional spherical harmonics method cannot effectively handle continuity and rotation invariance for Stokes vectors. To overcome this, we develop a new method called polarized spherical harmonics (PSH) based on the spin-weighted spherical harmonics theory. Our method provides a rotation-invariant representation of Stokes vector fields. Furthermore, we introduce frequency domain formulations of polarized rendering equations and spherical convolution based on PSH. We first define spherical convolution on Stokes vector fields in the angular domain, and it also provides efficient computation of polarized light transport, nearly on an entry-wise product in the frequency domain. Our frequency domain formulation, including spherical convolution, led to the development of the first real-time polarization rendering technique under polarized environmental illumination, named precomputed polarized radiance transfer, using our polarized spherical harmonics. Results demonstrate that our method can effectively and accurately simulate and reproduce polarized light interactions in complex reflection phenomena.