Exterior Calculus in Graphics

SIGGRAPH 2023 Course



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.

Presenters / Authors

Stef Stephanie Wang

Sina Mohammad Sina Nabizadeh

Albert Albert Chern

Presentation info

Our presentation at SIGGRAPH ‘23 will take place on Sunday Auguest 6th 2023, 2pm-5pm PDT at Room 411.


This work was funded by NSF CAREER Award 2239062 and UC San Diego Center for Visual Computing. Additional support was provided by the WiGRAPH Rising Stars Program, SideFX Software, and Activision Blizzard.


Lecture Notes (Version 1.00)


author = {Wang, Stephanie and Nabizadeh, Mohammad Sina and Chern, Albert},
title = {Exterior Calculus in Graphics},
booktitle = {ACM SIGGRAPH 2023 courses},
series = {SIGGRAPH '23},
location = {Los Angeles, CA, USA},
year = {2023},
publisher = {ACM},
address = {New York, NY, USA},