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

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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


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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

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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?

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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
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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

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Electronic Visualization Laboratory University of Illinois at Chicago

An example showing collisions and contacts:

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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
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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)

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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

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Electronic Visualization Laboratory University of Illinois at Chicago

An example showing the comparison:

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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

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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

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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
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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:

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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

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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)
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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
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Electronic Visualization Laboratory University of Illinois at Chicago

There are many kinds of basic joints:

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Electronic Visualization Laboratory University of Illinois at Chicago

An example of joints combination:

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Electronic Visualization Laboratory University of Illinois at Chicago

An evidence of efficiency of closed loops:

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Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops:

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Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops:

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Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops:

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Electronic Visualization Laboratory University of Illinois at Chicago

Another evidence of efficiency of closed loops:

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Electronic Visualization Laboratory University of Illinois at Chicago

First simulation involving large stacks:

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Electronic Visualization Laboratory University of Illinois at Chicago

Second simulation involving large stacks:

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Electronic Visualization Laboratory University of Illinois at Chicago

  • 1. Theory behind
  • 2. Core idea
  • 3. Examples
  • 4. Conclusions
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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

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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/