Physics-based Animation of Solids and Fluids
Course ID 15763
Description This seminar-based course delves into the heart of physics-based animations of solids and fluids, a key component in fields ranging from visual effects and VR to digital fashion. Central to this is solving partial differential equations (PDEs) using numerical methods, with applications extending to computational mechanics, robotic training, and 3D content creation. Combining lectures with student presentations, we will explore the simulation of various physical entities, such as rigid bodies, deformable bodies (open-source online book available, including Python and CUDA examples), shells, rods, liquids, and smoke, all the way from the discretization of the governing PDEs to the efficient implementation and evaluation of the numerical solvers. Students will acquire a thorough understanding of both classic and state-of-the-art methods of solids and fluids simulation in computer graphics. They will also gain insights into the existing challenges in enhancing and applying these methods within the broader field.
Key Topics
Time integration;
The mass-spring system;
The finite element method;
Boundary conditions and frictional self-contact;
Isotropic and anisotropic elasticity;
Barrier-type and inversion-robust elasticity;
Weak form derivation;
Shells, rods, rigid bodies, and reduced-order models;
Eulerian, SPH, and FLIP methods for fluid simulation;
Unconstrained optimization methods;
Constrained optimization methods.
Required Background Knowledge
programming, linear algebra, vector calculus, computer graphics, numerical methods
Course Relevance
junior, senior, MS, PhD in all relevant fields
Course Goals
Students will acquire a thorough understanding of both classic and state-of-the-art methods of solids and fluids simulation in computer graphics. They will also gain insights into the existing challenges in enhancing and applying these methods within the broader field.
Learning Resources
https://phys-sim-book.github.io/
https://www.physicsbasedanimation.com/
Assessment Structure
Final Project: 70% (50% checkpoints & presentations + 20% final report)
In-Class Paper Presentation: 20%
Class Participation: 10% (attendance and discussion)
(NOTE: this may subject to change)
Extra Time Commitment
n/a
Course Link
https://www.cs.cmu.edu/~15763-s25/