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Contact and Friction Simulation for Computer Graphics(Siggraph course 2022)
相关的course：SIGGRAPH’20 Course: An Introduction to Physics-Based Animation
Syllabus
Basics：
- contact generation using discrete collision detection
- numerical techniques for solving the associated LCPs and NCPs
advanced topics:
- soft body contact approaches
- penalty and barrier functions
- anisotropic friction modeling
Chapter 1. Introduction to Contact Simulation
there are three main paradigms for contact simulation
constraint based methods(很精确): constrained optimization
penalty based approaches: small abstract springs(也可以不使用弹簧) working between objects to keep them from overlapping. Hence, the springs “penalize” overlap.
- similarities to penalty methods in numerical optimization: barrier methods
impulse-based methods: contact between objects is conceptualized as sequences of micro-collisions
1.1 The Equation of Motion
/[M(t)/dot u(t)=f(q(t),u(t),t)
/]
Notations in this note:
- /(M/): mass matrix
- /(q/): position
- /(u/): velocity
- /(h=/Delta t/): timestep
1.2 Time Integration
Notations:
- /(u^-=u^n/): velocity of the last time step
- /(u^+=u^{n+1}/): velocity of the next time step
1.3 Constraints
two types of constraint equations:
- bilateral: /(/phi(q)=0/), hinges, ball-and-socket, and prismatic joints
- unilateral: /(/phi(q)/ge0/).
/(m/) constraint functions /(/phi(q)/in R^m/) implicitly define a manifold that is embedded in the /(n/)-dimensional space of the simulation degrees of freedom. We can instead formulate the constraint equations in terms of the velocities by computing the gradient of /(
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