Rachel Weinstein, Joseph Teran and Ron Fedkiw presented by Marco - PowerPoint PPT Presentation

Rachel Weinstein, Joseph Teran and Ron Fedkiw presented by Marco Bernasconi (mberna7@uic.edu) University of Illinois at Chicago – Politecnico di Milano Electronic Visualization Laboratory University of Illinois at Chicago

A couple of questions: • Why did I choose this paper? • What does “contact” vs “collision” mean? • What are the theoretical bases of articulated rigid bodies? • What is an “impulse”? • What was “the previous work of Guendelman” about? Electronic Visualization Laboratory University of Illinois at Chicago

1. Theory behind: • Collisions and contacts • Time stepping • Articulated rigid body math 2. Core idea 3. Examples 4. Conclusions Electronic Visualization Laboratory University of Illinois at Chicago

Collisions Contacts • Bodies bounce off each • Bodies rest one stuck to other (elasticity factor) the other • Motion of bodies • Bodies slide (with or changes discontinuously without friction) one upon within a discrete time the other step • “Before” and “After” states need to be computed Electronic Visualization Laboratory University of Illinois at Chicago

An example showing collisions and contacts: Electronic Visualization Laboratory University of Illinois at Chicago

Simulation loop Traditional approach Guendelman approach • Update position and • Process collision velocity • Update velocity • Process collision • Process contact • Process contact • Update position Electronic Visualization Laboratory University of Illinois at Chicago

Traditional approach: problem Example: block sliding down inclined plane • Initially sliding down • Update position and velocity interpenetrating plane • Process collision velocity reflected • No contact to process • Next iteration SOLUTION: velocity threshold object bounces (Mirthic & Canny 1995) Electronic Visualization Laboratory University of Illinois at Chicago

Guendelman approach Example: block sliding down inclined plane • No collisions to process • Update velocity block gains downward velocity • Process contact stops normal motion • Update position slides down with no bounce Electronic Visualization Laboratory University of Illinois at Chicago

An example showing the comparison: Electronic Visualization Laboratory University of Illinois at Chicago

Maximal coord. Generalized coord. ( x 0 , y 0 , z 0 , 0 , f 0 , 0 ) + ( x 0 , y 0 , z 0 , 0 , f 0 , 0 ) + ( 1 , f 1 ) + ( x 1 , y 1 , z 1 , 1 , f 1 , 1 ) + ( x 2 , y 2 , z 2 , 2 , f 2 , 2 ) = ( 2 ) = 18 state variables 9 state variables Electronic Visualization Laboratory University of Illinois at Chicago

The equations for rigid body evolution are: d x v v x • = position, = velocity dt d q 1 q q • = orientation, = angular velocity dt 2 d v F F = net force, m = mass • dt m d L d ( I ) L = angular momentum • = net torque dt dt Electronic Visualization Laboratory University of Illinois at Chicago

1. Theory behind 2. Core idea: • Time integration and impulse theory • Prestabilization • Algorithm 3. Examples 4. Conclusions Electronic Visualization Laboratory University of Illinois at Chicago

These equations are time integrated according to: n 1 n n 1 n n n ˆ q q ( t ) q x x t v Impulses are found and applied iteratively: Electronic Visualization Laboratory University of Illinois at Chicago

Goal: apply impulses to the rigid bodies BEFORE the integration step with the intention of achieving the target joint state after that integration step. Position constraint equations: j new n 1 new n v v I ( r j ) m Electronic Visualization Laboratory University of Illinois at Chicago

The algorithm is applied as follows: • Process collisions (and velocity poststabilization) • Integrate velocities (and velocity poststabilization) • Resolve contacts and articulation prestabilization • Update position (and velocity poststabilization) Electronic Visualization Laboratory University of Illinois at Chicago

1. Theory behind 2. Core idea 3. Examples • Black box definition of joints and constraints • Closed loops • Stacks of articulated rigid bodies 4. Conclusions Electronic Visualization Laboratory University of Illinois at Chicago

There are many kinds of basic joints: Electronic Visualization Laboratory University of Illinois at Chicago

An example of joints combination: Electronic Visualization Laboratory University of Illinois at Chicago

An evidence of efficiency of closed loops: Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops: Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops: Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops: Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops: Electronic Visualization Laboratory University of Illinois at Chicago

First simulation involving large stacks: Electronic Visualization Laboratory University of Illinois at Chicago

Second simulation involving large stacks: Electronic Visualization Laboratory University of Illinois at Chicago

1. Theory behind 2. Core idea 3. Examples 4. Conclusions Electronic Visualization Laboratory University of Illinois at Chicago

• Any black box method for joint constraints • Linearity both in the number of bodies AND in the number of constraints • No special treatments of closed loops • Advantage of pre vs post stabilization Electronic Visualization Laboratory University of Illinois at Chicago

References: http://graphics.stanford.edu/~rachellw/ http://www.graphics.stanford.edu/~fedkiw/ http://graphics.stanford.edu/~jteran/ E-mail: mberna7@uic.edu Electronic Visualization Laboratory University of Illinois at Chicago