物体碰撞与摩擦的方法总结
2022/8/27 6:23:08
本文主要是介绍物体碰撞与摩擦的方法总结,对大家解决编程问题具有一定的参考价值,需要的程序猿们随着小编来一起学习吧!
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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
SIGGRAPH'22 Course: Contact and Friction Simulation for Computer Graphics (siggraphcontact.github.io)
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
流形优化方法求解约束问题
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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