Monte Carlo geometry processing: a grid-free approach to PDE-based methods on volumetric domains
Monte Carlo geometry processing: a grid-free approach to PDE-based methods on volumetric domains
复制标题
蒙特卡罗几何处理：体积域上基于偏微分方程的无网格方法
DOI：
10.1145/3386569.3392374
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发表时间：
2020
影响因子：
6.2
通讯作者：
Crane, Keenan
中科院分区：
文献类型：
--
作者：
Sawhney, Rohan;Crane, Keenan
近年来，几何模型的复杂性急剧增加，但仍远未达到自然界中发现的复杂性，例如，考虑引起物理或生物行为的详细微观结构（图 1）。基于偏微分方程的方法为处理和分析此类数据提供了强大的工具，但尚未达到算法“正常工作”的程度：即使是基本任务仍然需要仔细的预处理或参数调整，而强大的算法可能会在时间或内存方面表现出较差的扩展性。蒙特卡罗方法为几何处理提供了新的机会，与传统的有限元方法 (FEM) 发生了巨大的突破。特别是，通过避免网格生成的艰巨挑战，它们提供了一个高度可扩展、可并行且数值稳健的框架，并显着扩展了可在基于偏微分方程的算法中使用的几何类型。真实感渲染在 20 世纪 90 年代经历了类似的发展：有限元光能传递 [Goral 等人。 1984] 让位于光传输方程的蒙特卡罗积分 [Kajiya 1986]，其原因由 Wann Jensen [2001，第 1 章] 很好地总结。尽管这种转变部分是出于对更复杂照明的渴望，但它也使得处理极其复杂的几何场景成为可能——现代渲染器可以处理数万亿个有效多边形[Georgiev et al. 2017]。 2018]
The complexity of geometric models has increased dramatically in recent years, but is still far from matching the complexity found in nature—consider, for instance, detailed microstructures that give rise to physical or biological behavior (Fig. 1). PDE-based methods provide powerful tools for processing and analyzing such data, but have not yet reached a point where algorithms “just work”: even basic tasks still entail careful preprocessing or parameter tuning, and robust algorithms can exhibit poor scaling in time or memory. Monte Carlo methods provide new opportunities for geometry processing, making a sharp break with traditional finite element methods (FEM). In particular, by avoiding the daunting challenge of mesh generation they offer a framework that is highly scalable, parallelizable, and numerically robust, and significantly expands the kind of geometry that can be used in PDE-based algorithms. Photorealistic rendering experienced an analogous development around the 1990s: finite element radiosity [Goral et al. 1984] gave way to Monte Carlo integration of the light transport equation [Kajiya 1986], for reasons that are nicely summarized by Wann Jensen [2001, Chapter 1]. Although this shift was motivated in part by a desire for more complex illumination, it has also made it possible to work with scenes of extreme geometric complexity—modern renderers handle trillions of effective polygons [Georgiev et al. 2018]