Introduction
DDL 19.7.12
Five Themes:
- integration of ordinary differential eqn’s
- discontinuities (fracture and collisions)
- rigid bodies
- elastic bodies
- Finite Element Method - FEM
- Discrete Differential Geometry - DDG
- fluids
- navier-stokes
- shallow water equations
Will cover in depth:
- fundamentals of physical simulation
- smooth and discrete theory
- numerical methods
- efficient implementation
Will not cover in depth:
control (flocking, agents)
rigging & interpolation
artistic direction
key-framing
Week 1
介绍一些基本的动力学模型.
Week 2
介绍弹簧的模型.
介绍显示欧拉以及其可能带来的问题.
Week 3
引入隐式欧拉。介绍如何用牛顿法求解这类问题。
Week 4
一些基础的历离散碰撞检测,球和其他物体的检测.
对于碰撞情况的处理方法,Impulse Response & Penalty Method.
Week 5
连续时间碰撞检测。
Week 6
介绍了一些空间加速算法。
hierarchy - 四叉树
amortization
Eulerian Lagrangian
BVH分为自顶向下和自底向上两种构建方法。
Week 7
运动限制,Penalty Method, Lagrange Multipliers & Reduced Coordinates
引入旋转，介绍力矩的概念。 - 一个力在刚体上任意一个点作用是怎么影响重心的速度和旋转速度。
Week 8
对于刚体单个点的碰撞Contact Points建立模型。rigid body contact problem
求解LCP问题。 Linear complementarity problem -> quadratic programming problem
Week 9
介绍Continuum Material。对于这种模型很难用Mass Spring来模拟。
energy associated with the change in shape - change in shape of a triangle - (negative of the gradient) the forces act on each vertex
orthotropic
isotropic
Small Displacement Assumption - not available with large dynamic motion (resist rigid motion)
reduce the polynomial order of energy from quartic to quadratic
Week 10
Liquid / Fluid - material cannot resist a sheer deformation / can not hold their shapes
Liquid has free surface - surface tension
Lagrangian approach - track pieces of material （e.g. smooth particle hydrodynammics SPH)
Eulerian approach - flow through a fixed region of space
Viscosity 粘性 - second derivative
Week 11
Liquid Simulation - 1. Fluid Sover 2. Surface Tracker
Marker-Based Surface Tracking