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Cloth Simulation

An Brief Introduction to Its History and Method

Wenxuan Wu

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Outline

  • Motivation and Application
  • Cloth Simulation Models
    • Geometric-based Model
    • Physical-based Model
  • Numerical Solvers
  • Collision Detection
  • Optimization

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Motivation

  • Clothes for Gaming
    • Precision vs Real-time
  • Clothes for Design
  • Clothes for Shopping
  • Clothes for Virtual Avatar

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Motivation

  • Clothes for Gaming
    • Precision vs Real-time
  • Clothes for Design
  • Clothes for Shopping
  • Clothes for Virtual Avatar

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Motivation

  • Clothes for Gaming
    • PC vs Mobile
    • Real-time
  • Clothes for Design
  • Clothes for Shopping
  • Clothes for Virtual Avatar

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Motivation

  • Clothes for Gaming
    • PC vs Mobile
    • Real-time
  • Clothes for Design
  • Clothes for Shopping
  • Clothes for Virtual Avatar

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Geometric Model

  • Represent folds and creases by geometrical equations.
  • Aim at modeling the appearance of the cloth
  • Not focus on the physical aspects of cloth

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Jerry Weil (1986)

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  • Surface Approximation Stage
    • Approximate the y position of cloth vertices between two constrained points using curve

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Jerry Weil (1986)

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  • Iterative Relaxation Stage
    • Assume the distances of a point with its four neighbor is 1
    • Set all exterior points y = - infinity
    • Iteratively update all points position based on constraint vectors

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Physical-Based Model

  • Represent cloth as grids
  • Vertices are points with finite mass
  • Forces and energies of points are calculated from the relations with other points

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Provot (1995)

  • Spring-Mass System
    • Internal Forces and External Forces
    • Integration: Simple Euler method
    • Dynamic Inverse Constraints

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Stretching Model ( 1 / 3 )

  • Stretching
    • Strong Resistance
  • Bending
    • Weak Resistance
  • Shearing
  • Nonlinear Characteristics
    • Friction, Deformation, etc

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Bending Model ( 2 / 3 )

  • Stretching
    • Strong Resistance
  • Bending
    • Weak Resistance
  • Shearing
  • Nonlinear Characteristics
    • Friction, Deformation, etc

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Shearing Model ( 3 / 3 )

  • Stretching
    • Strong Resistance
  • Bending
    • Weak Resistance
  • Shearing
  • Nonlinear Characteristics
    • Friction, Deformation, etc

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Nonlinear Model (Anisotropy) *

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Discrete Spring-mass Grid

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Müller et al. (2007)

  • Position-based Method
    • Adding constraints to each particle.
    • Use current velocity and position to predict new
    • Solve constraint and calculate current state

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Numerical Solvers

  • Linear Methods
    • Euler, Midpoint, Runge-Kutta
    • Verlet Integration
  • Nonlinear Methods
    • Newton-Raphson
    • Gradient Descent
    • Projective Dynamics

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Numerical Solvers

  • Linear Methods
    • Euler, Midpoint, Runge-Kutta
    • Verlet Integration
  • Nonlinear Methods
    • Newton-Raphson
    • Gradient Descent
    • Projective Dynamics

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Linear Solvers (Verlet Integration)

  • Verlet Integration does not need to consider about velocity when calculate, so is faster

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Linear Solvers (Verlet Integration)

  • Verlet Integration use positions to calculate position, alleviating error propagation.

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Linear Solvers Demo Time

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Nonlinear Solvers

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Feel Similar?

  • Position Based Model can also be solved by optimization

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Nonlinear Solvers

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Gradient Descent (1/3)

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  • Pros
    • GPU friendly
    • Very simple
  • Cons
    • 1st-order convergence rate
    • No simulator uses this as it is

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Newton-Raphson (2/3)

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  • Pros
    • 2rd-order convergence rate
  • Cons
    • How to solve A'f ? High cost!
    • It can fail to converge if x is far from the solution

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Newton-Raphson (2/3)

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Projective Dynamics (3/3)

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  • Pros
    • Fast on CPUs, fast convergence in the first few iterations.
  • Cons
    • Not GPU-friendly, still 1st-order convergence rate.

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Nonlinear Solver (Summary)

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Collision Detection

  • Broad Phase Collision Detection
    • Spatial Hashing
    • BVH
  • Narrow phase Collision Detection
    • Point to face distance
    • And other tricks

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Fun Demo

https://matthias-research.github.io/pages/tenMinutePhysics/15-selfCollision.html

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Grid Spatial Hashing

  • We hash the point into a cell and append it to that cell’s list.
  • Then hash table maps to cells, cells maps to points.
  • For collision detection, just iterate the neighbor of the cell as well as itself.

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More tricks

  • Continuous collision detection
  • Substepping
  • Enforce maximal velocity
    • The larger the sub-steps, the larger the limiting velocity!
  • Introduce contact constraints

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Collision Response

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References

SIGGRAPH Courses & Papers

  • SIGGRAPH 2003 Course: Clothing Simulation and Animation
  • SIGGRAPH 2005 Course: Advanced Topics in Clothing Simulation and Animation

🔷 Course Notes & Lecture Slides

  • 2021 USTC Summer Seminar – Real-Time Cloth Simulation on GPU, by Huaming Wang�🔗 Watch on Bilibili
  • Games 104 Lecture 11 – Modern Game Engine: Cloth Simulation, by Xi Wang�🔗 Watch on Bilibili

🔷 Online Tutorials

🔷 Student Presentation Notes

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