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

Electronic Visualization Laboratory University of Illinois at Chicago

presented by

Marco Bernasconi (mberna7@uic.edu) University of Illinois at Chicago – Politecnico di Milano

Rachel Weinstein, Joseph Teran and Ron Fedkiw

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
• ther (elasticity factor)
• Motion of bodies

changes discontinuously within a discrete time step

• “Before” and “After”

states need to be computed

• Bodies rest one stuck to

the other

• Bodies slide (with or

without friction) one upon the other

Electronic Visualization Laboratory University of Illinois at Chicago

An example showing collisions and contacts:

Electronic Visualization Laboratory University of Illinois at Chicago

Traditional approach Guendelman approach Simulation loop

• Update position and

velocity

• Process collision
• Process contact
• Process collision
• Update velocity
• 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
• bject bounces

SOLUTION: velocity threshold (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 (x0, y0, z0,

0, f 0, 0)

Maximal coord. Generalized coord.

(x1, y1, z1,

1, f 1, 1)

(x2, y2, z2,

2, f 2, 2)

+ + =

18 state variables

(x0, y0, z0,

0, f 0, 0) +

(

1, f 1) +

(

2) =

9 state variables

Electronic Visualization Laboratory University of Illinois at Chicago

The equations for rigid body evolution are:

v dt x d

• = position, = velocity

x v q dt q d 2 1

• = orientation, = angular velocity

q

• = net force, m = mass

m F dt v d F dt I d dt L d ) (

• = angular momentum

= net torque

L

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 n n

v t x x

1

n n n

q t q q ) ( ˆ

1

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:

m j v v

n new

) (

1

j r I

n new

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
• f closed loops
• Advantage of

pre vs post stabilization

Electronic Visualization Laboratory University of Illinois at Chicago

E-mail: mberna7@uic.edu

References:

http://graphics.stanford.edu/~rachellw/ http://www.graphics.stanford.edu/~fedkiw/ http://graphics.stanford.edu/~jteran/