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Unformatted text preview: Advanced Computer Graphics Rigid Body Simulation Professor Brogan Upcoming Assignments Who wants a midterm instead of an assignment? Final will be take home Cloth/water/parallel particle sim presentations Volunteers? Papers selected by Thursday Physical Simulation References Text book (4.3 and Appendix B) Physics for Game Developers (Bourg) Chris Hecker Game Developer articles http://www.d6.com/users/checker/dynamics.htm Equations of Motion The physicsbased equations that define how objects move Gravity Turbulence Contact forces with objects Friction Joint constraints Equations of Motion Current State Position and velocity Accelerations Forces Velocities Equations of Motion Integrate Integrate Integrate Equations of Motion Linear motions: Example: Constant acceleration of 5 m/s 2 = = dt t a t v dt t v t r ) ( ) ( ) ( ) ( + + = + = = + = = + = + = = = 2 2 5 5 ) ( ) ( 5 ) ( ) ( 5 ) ( 5 5 ) ( r t v t dt v t dt t v t r v t t v C v C v C t dt dt a t v Linear Momentum Mass times velocity = linear momentum, p Newtons Second Law a m v m dt v m d dt p d p F = = = = = ) ( v m p = Ceasing to identify vectors Rigid Bodies Imagine a rigid body as a set of point masses Total momentum, p T, is sum of momentums of all points: Center of Mass (CM) is a single point. Vector to CM is linear combination of vectors to all points in rigid body weighted by their masses, divided by total mass of body = i i i T v m p M r m r i i i CM = Total Momentum Rewrite total momentum in terms of CM Total linear momentum equals total mass times the velocity of the center of mass...
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This note was uploaded on 01/23/2012 for the course CS 551 taught by Professor Staff during the Fall '10 term at Syracuse.
 Fall '10
 Staff
 Computer Graphics

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