UNC Chapel Hill M. C. Lin

Review

Particle Dynamics

(see transparencies in class)

UNC Chapel Hill 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).

UNC Chapel Hill M. C. Lin

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 = 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

)0,1

,0(2R

T

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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

Friction: Ff = -kf (-N•F) vt

Fc = - FN = - (N•F)F