Review

Particle Dynamics
(see transparencies in class)
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M. C. Lin
Disclaimer
 The
following slides reuse materials
from SIGGRAPH 2001 Course Notes
on Physically-based Modeling
(copyright  2001 by Andrew Witkin
at Pixar).
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A Newtonian Particle
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Second Order Equations
As discussed in the last lecture,
we can transform a second
order equation into a couple of
first order equations.
   as shown here.
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Phase (State) Space
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Particle Structure
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Solver Interface
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Particle Systems
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Overall Setup
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Derivatives Evaluation Loop
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Particle Systems with Forces
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Solving Particle System Dynamics
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Type of Forces
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Gravity
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Force Fields

Magnetic Fields
– the direction of the velocity, the direction of the magnetic field,
and the resulting force are all perpendicular to each other.
The charge of the particle determines the direction of the
resulting force.

Vortex (an approximation)
– rotate around an axis of rotation Q = magnitude/Rtightness
– need to specify center, magnitude, tightness
– R is the distance from center of rotation

Tornado
– try a translation along the vortex axis that is also
dependent on R, e.g. if Y is the axis of rotation, then
T (0,
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1
R2
,0)
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Viscous Drag
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Spring Forces
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Collision and Response
After applying forces, check for
collisions or penetration
 If one has occurred, move particle to
surface
 Apply resulting contact force (such
as a bounce or dampened spring
forces)

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Bouncing off the Wall
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Normal & Tangential Forces
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Collision Detection
Collision!
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Collision Response
(kr is the coefficient of restitution, 0  kr  1)
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Condition for Contact
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Contact Forces
Fc = - FN = - (N•F)F
Friction: Ff = -kf (-N•F) vt
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