F LUID S IMULATION
SIGGRAPH 2006 Course Notes
Robert Bridson1
University of British Columbia
Matthias Muller-Fischer2
AGEIA Inc.
Eran Guendelman3
Stanford University
Computer Science Department
201-23
Constrained dynamics
Simple particle system
In principle, you can make just
about anything out of spring
systems!
In practice, you can make just
about anything as long as its jello
Hard constraints
Deformable Bodies
Deformation
x
p(x)
Given a rest shape x and its deformed configuration p(x), how
large is the internal restoring force f(p)?
To answer this question, we need a way to measure
deforma
Differential Equations
Overview of differential equation
Initial value problem
Explicit numeric methods
Implicit numeric methods
Modular implementation
Physics-based simulation
An algorithm that
Maya Tutorial
Put together from material at: http:/download.autodesk.com/us/maya/Maya_2014_GettingStarted/index.html
Getting your bearings
Adding objects
Scale, rotate and translate objects
Viewing an
3D orientation
Rotation matrix!
Fixed angle and Euler angle!
Axis angle!
Quaternion!
Exponential map
Joints and rotations
Rotational DOFs are widely used in character animation
3 translational DO
Physically Based Modeling: Principles and Practice Differential Equation Basics
Andrew Witkin and David Baraff Robotics Institute Carnegie Mellon University
Please note: This document is 1997 by Andre
Computer Animation
Karen Liu
associate professor at School of
Interactive Computing
Mukul Sati
graduate student at School of Interactive
Computing
Administrations
http:/www.cc.gatech.edu/classes/AY20
Keyframe animation
Process of keyframing
Keyframe interpolation
Hermite and Bezier curves
Splines
Speed control
Oldest keyframe animation
Two conditions to make moving images in 19th
century
at
Particle dynamics
Particle overview!
Particle system!
Forces!
Constraints!
Second order motion analysis
Particle system
Particles are objects that have mass, position,
and velocity, but without
An Introduction to Physically Based Modeling:
Rigid Body Simulation IUnconstrained Rigid Body
Dynamics
David Baraff
Robotics Institute
Carnegie Mellon University
Please note: This document is 1997 by
Rigid body dynamics
Rigid body simulation
Once we consider an object
with spatial extent, particle
system simulation is no
longer sufcient
Rigid body simulation
Unconstrained system!
no contact!
Co
An Introduction to Physically Based Modeling:
Rigid Body Simulation IINonpenetration
Constraints
David Baraff
Robotics Institute
Carnegie Mellon University
Please note: This document is 1997 by David
Fluid dynamics
Fields
Domain!
! R2
Scalar eld!
f !: R
Vector eld
f : R2
Types of derivatives
Derivatives measure how something changes
due to its parameters!
f
Temporal derivatives!
t
Spatial d