Exterior Calculus in Graphics: Course Notes for a SIGGRAPH 2023 Course
Exterior Calculus in Graphics: Course Notes for a SIGGRAPH 2023 Course
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DOI：
10.1145/3587423.3595525
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发表时间：
2023-07
期刊：
影响因子：
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通讯作者：
Stephanie Wang;M. Nabizadeh;Albert Chern
中科院分区：
文献类型：
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作者：
Stephanie Wang;M. Nabizadeh;Albert Chern
在计算机图形学研究中，对更先进的多变量演算的需求迅速增加，例如物理模拟、几何合成和可微渲染。计算机图形学的研究人员经常不得不求助于图形学研究之外的参考资料，以研究诸如雷诺传输定理或应力和应变张量之间的几何关系等恒等式。本课程将全面介绍外部微积分，以几何直观的方式涵盖许多这些高级主题。本课程的目标是任何了解本科水平的多变量微积分和线性代数的人，并且没有任何先决条件。与现有的参考文献相反，它们只服务于纯数学或工程界，我们使用及时和相关的图形示例来说明外部微积分的理论。我们还提供了几个高级主题的解释，包括连续介质力学，流体动力学和几何优化。本课程分为两个主要部分：一个关于核心外部微积分概念和恒等式的讲座，以及图形应用的简短示例，以及一系列关于使用外部微积分的图形主题的小型讲座。
The demand for a more advanced multivariable calculus has rapidly increased in computer graphics research, such as physical simulation, geometry synthesis, and differentiable rendering. Researchers in computer graphics often have to turn to references outside of graphics research to study identities such as the Reynolds Transport Theorem or the geometric relationship between stress and strain tensors. This course presents a comprehensive introduction to exterior calculus, which covers many of these advanced topics in a geometrically intuitive manner. The course targets anyone who knows undergraduate-level multivariable calculus and linear algebra and assumes no more prerequisites. Contrary to the existing references, which only serve the pure math or engineering communities, we use timely and relevant graphics examples to illustrate the theory of exterior calculus. We also provide accessible explanations to several advanced topics, including continuum mechanics, fluid dynamics, and geometric optimizations. The course is organized into two main sections: a lecture on the core exterior calculus notions and identities with short examples of graphics applications, and a series of mini-lectures on graphics topics using exterior calculus.