14.1 Physically Based Simulation II Mass-Spring Systems Hao Li - - PowerPoint PPT Presentation

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14.1 Physically Based Simulation II Mass-Spring Systems Hao Li - - PowerPoint PPT Presentation

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Fall 2015 CSCI 420: Computer Graphics 14.1 Physically Based Simulation II Mass-Spring Systems Hao Li http://cs420.hao-li.com 1 Mass-Spring Systems The 101 of Physics Simulation What do we want to simulate? Deformable Objects Design

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CSCI 420: Computer Graphics

Hao Li

http://cs420.hao-li.com

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Fall 2015

14.1 Physically Based Simulation II

Mass-Spring Systems

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Mass-Spring Systems

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  • The 101 of Physics Simulation
  • What do we want to simulate? Deformable Objects
  • Design a model. Mass points + springs.
  • Write differential equations. Newton’s 2nd Law (Hooke)
  • Discretize equations. Integration methods for ODEs
  • Add interaction. Collision detection + response
  • Simulate!
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Mass-Spring Systems

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  • Simulation of cloth based on deformable surfaces

(Polygonal mesh)

  • Realistic simulation of cloth with different fabrics such as

wool, cotton, or silk for garment design

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Facial Animation

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  • Simulation of facial expressions based on deformable

surfaces/volumes/muscles

  • Animation of face models from speech and mimic

parameters

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Medical Simulation

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  • Simulation of deformable soft tissue
  • Surgical planning
  • Medical training
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Overview

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  • Model and Physics
  • Implementation Hints
  • Time-Discretization
  • Collision Response
  • (Simulation Loop)
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Mass-Point System

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  • Discretization of an object into mass points (gas, fluid,

elastic object, inelastic object)

  • System with multiple mass centers (Planetary System)
  • Interaction between points i and j≠i based on internal

forces

  • All other forces at point i are external forces
  • Overall force
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Mass-Point System

  • Discretization of an object into mass points
  • Representation of forces between masses by springs
  • Computation of dynamics
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Mass-Points

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Physically-based Equations

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Elastic Forces: Springs

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Elastic Energies

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Forces at a Mass Point

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Dissipative Forces

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System Equations

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System Equations

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Overview

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  • Model and Physics
  • Implementation Hints
  • Time-Discretization
  • Collision Response
  • (Simulation Loop)
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Elastic Spring

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Mass Point

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Force Computation

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Overview

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  • Model and Physics
  • Implementation Hints
  • Time-Discretization
  • Collision Response
  • (Simulation Loop)
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System Equations

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Solution

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Problem

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Numerical Integration Methods

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Numerical Integration Methods

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Explicit Integration

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Explicit Integration

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Explicit Integration

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Error Accumulation

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Problems

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Improving Accuracy - Leap Frog

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Improving Accuracy - Runge Kutta

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2nd order (midpoint method)

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Midpoint vs Euler

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Implementation

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Avoiding Instability

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Topology and Stability

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Volumetric Models - Tet Meshes

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Topology Ambiguity Problem

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Cloth Forces

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Cloth Springs

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Cloth Springs

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Cloth Springs

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http://cs420.hao-li.com

Thanks!

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