物体碰撞与摩擦的方法总结
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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 \(
标签：phi,based,methods,constraint,物体,碰撞,penalty,contact,摩擦 来源： https://www.cnblogs.com/Heskey0/p/16629712.html