lecture14

lecture14 - Advanced Computer Graphics Rigid Body...

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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 physics-based 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 • Newton’s 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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lecture14 - Advanced Computer Graphics Rigid Body...

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