NSF Young Investigator: Simulating Global Illumination

合成逼真的图像是计算机图形学面临的一个基本挑战。此任务最困难的方面之一是全局照明的模拟：曲面之间的光线相互反射。本研究将有限元方法应用于整体光照的模拟。该工作分为三个子项目：(1)全局光照的误差度量；(2)光能传递的自适应网格划分；(3)对任意反射率场景的泛化。与其试图衡量“现实主义”--这是一种相当模糊的感知质量--，人们正在开发更简单的定量准确性衡量标准。使用这些误差度量，可以对现有和未来的图像合成算法进行评估和定量排序。在许多光能传递系统中，用于光能传递网格生成的自适应网格只是部分自动化的，并且对各种网格引入的误差知之甚少。最近在简化的二维场景上的实验表明，使用自适应网格和高阶近似可以产生比现有算法更快和/或更准确的解。当光能传递网格跟随解决方案函数中的间断(如阴影边界处的间断)时，会产生更准确、更美观的图片。这些“不连续啮合”技术受到了研究人员的欢迎。在本研究中，使用误差度量作为客观标准来比较和评估用于光能传递的网格。这种对光能传递函数的严格分析提出了新的网格生成技术，从而可以进行更准确的模拟。对具有任意反射比的场景的推广是最后一个子项目，是将这些方法推广到具有真实光散射的场景。真实表面的反射率不是纯粹的漫反射或镜面反射，而是由复杂的双向反射分布函数(BRDF)描述的。最近的工作表明，球谐函数或其他适当的基函数的使用极大地促进了方向相关光函数的近似。正在分析和开发位置和方向函数的这种表示法。最终目标是开发准确、高效的算法来模拟具有任意反射率和透射率的复杂场景中的全局照明。

Synthesizing realistic images is a fundamental challenge for computer graphics. One of the most difficult aspects of this task is the simulation of global illumination: the interreflection of light between surfaces. This research applies finite element methods to the simulation of global illumination. The work is divided into three subprojects: (1) error metrics for global illumination, (2) adaptive meshing for radiosity, and (3) generalization to scenes with arbitrary reflectance. Rather than attempting to measure ``realism'', which is a rather nebulous perceptual quality, simpler, quantitative accuracy measures are being developed. Using these error measures, existing and future image synthesis algorithms can be evaluated and quantitatively ranked. Adaptive meshes for radiosity mesh generation is only partially automated in many radiosity systems, and little is known about the errors introduced by various meshes. Recent experiments on simplified, two-dimensional scenes show that the use of adaptive meshes and higher degree approximations can lead to much faster and/or more accurate solutions than those of existing algorithms. More accurate, better looking pictures result when the radiosity mesh follows discontinuities in the solution function such as those at shadow boundaries. These ``discontinuity meshing'' techniques have been embraced by researchers. In this research, meshes for radiosity are compared and evaluated using error metrics as an objective criterion. This rigorous analysis of radiosity functions suggests new mesh generation techniques allowing more accurate simulations. Generalization to scenes with arbitrary reflectance, the final sub-project, is the generalization of these methods to scenes with realistic light scattering. The reflectance of real surfaces is not purely diffuse or specular, but is described by a complex bidirectional reflectance distribution function (BRDF). Recent work suggests that the use of spherical harmonics or other appropriate basis functions greatly facilitates the approximation of direction-dependent light functions. Such representations for functions of both position and direction are being analyzed and developed. The ultimate goal is the development of accurate, efficient algorithms for simulating global illumination on complex scenes with arbitrary reflectance and transmittance.