Efficient Light Transport Algorithms for Computer Graphics

在过去的几年里，已经提出了许多逼真的图像合成算法，但遗憾的是，它们往往效率很低，通常需要数小时或数天的计算。因此，这些算法提供的视觉提示(着色、阴影、透明度、反射等)仍然没有被需要可视化的应用程序常规使用。该项目致力于开发基于表示环境中光传输的积分方程式的高效图像合成算法。它使用最近开发的技术在线性时间内解决N体问题。初步结果表明，积分方程式所对应的相互作用矩阵可以近似为线性块数。由于这种近似具有线性空间的复杂性，因此可以探索以前过于耗时和内存而无法考虑的求解技术。它还研究了可见性问题，采样和网格问题，以及在求解光传输方程的背景下的懒惰评估策略。最后，这些想法将得到实施和检验。所有这项研究的长期目标是开发健壮和实用的算法，这些算法可以整合到未来的3D图形工作站中。

Many realistic image synthesis algorithms have been proposed in the last few years, but unfortunately they tend to be very inefficient, often requiring hours or days of calculations. As a result, the visual cues provided by these algorithms (shading, shadows, transparency, reflections, etc.) still have not been used routinely by applications requiring visualization. This project is concerned with development of efficient image synthesis algorithms based on the integral equation representing light transport in the environment. It used techniques recently developed to solve the N-body problem in linear time. Preliminary results indicate that the interaction matrix corresponding to the integral equation with a linear number of blocks can be approximated. Since this approximation has linear-space complexity, it makes it possible to explore solution techniques that have been previously too time and memory intensive to consider. It also studies visibility problems, sampling and meshing problems, and lazy evaluation strategies within the context of solving the light transport equation. Finally, these ideas will be implemented and tested. The long range goal of all this research is to develop robust and practical algorithms that can be incorporated into 3D graphics workstations of the future.