Collaborative Research: Theory and Algorithms for High Quality Real-Time Rendering and Lighting/Material Design in Computer Graphics

计算机图形学通常用于视频游戏、电子商务或科学可视化中的交互式可视化和渲染。这些应用通常需要实时结果，包括多次光反射（全局照明），材料变化和空间变化的局部照明。计算机图形学也越来越多地用于动画、娱乐、汽车设计和建筑等不同行业的原型或设计照明和材料特性。电影场景的灯光设计师希望通过最终照明和具有最终材料属性的物体（无论是油漆，天鹅绒还是玻璃）来预先想象场景。建筑师想要可视化建筑材料在其自然环境中的反射特性。在许多应用中，如果照明或材料设计师可以交互式地指定这些属性，则可以获得更大的真实感和可信度。在这项研究中，我们正在为高质量的实时渲染和照明/材料设计开发理论基础和下一代实用算法。我们的研究包括重要的理论和实践组成部分。我们正在开发一个新的理论框架来分析局部目标区域的维数和局部低维逼近。我们还分析了设计材料的理论和实际算法，同时渲染最终场景的全全局照明。由于BRDF中的外观不是线性的，我们的公式涉及一个多线性张量表示来处理多个反弹。对于具有局部照明的场景的交互式渲染，以及对于一般照明设计，我们正在开发一种方法，在给定完整入射光场的情况下重新照亮场景。最后，基于预计算的方法的缺点之一是预计算时间长，特别是在考虑全局照明效果时。我们正在为一种新的光子映射方法开发理论和算法，这种方法可以大大加快这一过程。

Computer graphics is commonly used for interactive visualization and rendering in video games, electronic commerce or scientific visualization. These applications often demand real-time results, including multiple bounces of light (global illumination), material changes and spatially-varying local lighting. Computer graphics is also increasingly used to prototype or design illumination and material properties, for industries as diverse as animation, entertainment, automobile design, and architecture. A lighting designer on a movie set wants to pre-visualize the scene lit by the final illumination and with objects having their final material properties -- be they paint, velvet or glass. An architect wants to visualize the reflectance properties of building materials in their natural setting. In many applications, much greater realism and faithfulness can be obtained if the lighting or material designer could interactively specify these properties. In this research, we are developing the theoretical foundations and next generation practical algorithms for high quality real-time rendering and lighting/material design.Our research involves both significant theoretical and practical components. We are developing a new theoretical framework for analyzing the dimensionality of local object regions and locally-low dimensional approximation. We also analyze the theory and practical algorithms for designing materials, while rendering the final scene with full global illumination. Because appearance is not linear in the BRDF, our formulation involves a multi-linear tensor representation to handle multiple bounces. For interactive rendering of scenes with local lighting, and for general lighting design, we are developing an approach that relights a scene given a full incident light field. Finally, one of the banes of precomputation-based approaches is the long time for precomputation, especially once global illumination effects are taken into account. We are developing the theory and algorithms for a new photon-mapping approach that substantially accelerates the process.