用新型球谐函数实现极化光实时渲染，解决旋转不变性难题。
Spin-Weighted Spherical Harmonics for Polarized Light Transport
- 基于自旋加权球谐理论构建极化球谐函数（PSH），保持斯托克斯矢量在角度域的连续性。
- 提出频域极化渲染方程与球卷积，实现近似逐元素乘积的高效计算。
- 首次实现极化环境光下的实时极化光传输，适合虚拟现实与光学仿真场景。
极化渲染的目标是模拟具有极化依赖特性的材料与光的相互作用。然而，将极化引入渲染面临巨大挑战，显著增加计算开销。主要难点在于高效建模和计算与极化光相关的复杂反射现象。特别是，频域分析对高效环境光照和复杂光相互作用存储至关重要，但目前仍缺乏有效方法。为利用频域技术高效模拟和重现极化光交互，我们解决了斯托克斯矢量在角度域中连续性保持的问题。传统球谐函数无法有效处理斯托克斯矢量的连续性与旋转不变性。为此，我们基于自旋加权球谐理论提出极化球谐函数（PSH），提供斯托克斯矢量场的旋转不变表示。进一步，我们建立了基于PSH的极化渲染方程与频域球卷积形式。首先在角度域定义了斯托克斯矢量场上的球卷积，其在频域中近似为逐元素乘积，实现极化光传输的高效计算。该频域框架推动了首个在极化环境光照下实现实时极化渲染的技术——预计算极化辐射传输（precomputed polarized radiance transfer）。结果表明，本方法能有效且准确地模拟复杂反射中的极化光交互。
原文摘要 · Abstract (English)
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.
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