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
201-2366 Main Mall
Vancouver, V6T 1Z4, Canada
AGEIA PhysX
Tec
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
Constraint force!
Single implicit constraint!
Multip
Constrained rigid body
Collision detection!
Contact point!
Colliding contact!
Resting contact!
Friction
Collision detection
Determine whether the collision occurs within
a numerical tolerance!
Determine all pairs of bounding boxes that
overlap!
Fu
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
deformation
Measurement of deformation
Measurement of elastic
Differential Equations
Overview of differential equation
Initial value problem
Explicit numeric methods
Implicit numeric methods
Modular implementation
Physics-based simulation
An algorithm that produces a sequence of
states over time under the laws
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 and positioning
Useful points
Can edit properties of an o
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 DOFs
48 rotational DOFs
Each joint can have up to 3 DOFs
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 Andrew Witkin and David Baraff. This chapter may be freely d
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/AY2014/
cs4496_spring
Slides and assignments are online
N
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 least 10 frames per second
a period of blackness betw
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 spatial extent!
Particles are the easiest objects to s
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 David Baraff. This chapter may be freely
duplicated and
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!
Constrained system!
collision and contact
Problems
Perfo
Motion capture
Applications!
Systems!
Motion capture pipeline!
Biomechanical analysis
Applications
Computer animation
Biomechanics
Robotics
Cinema
Video games
Anthropology
What is captured?
Humans
Animals
Objects
Celebrities
What is captured?
Face
Who
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 Baraff. This chapter may be freely
duplicated and distr
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 derivatives!
T
f f
gradient operator!f = x , y
f x
f y
d