Precomputing Interactive Dynamic Deformable Scenes

Doug L.Jams and Kayvon Fatahailian

报告人：宋超

Physically Based Modeling and Interactive Simulation

Approach

a. Analysis Method: to get analysis solution of the physics equation

b. numerical method : FEA,caculus of differences,etc

c. data driven

▪ Challenge: a. the difficulty of getting the analysis solution

b. no-linear question widely exiting

c. how to acquire the data?

d. how to use the data?

About data-driven An important strategy How to identify and control complex

systems Former works ▪ Nelles 2000----Nural Network

▪ Reissell and Pai 2001 ----ARX models

▪ Atkeson et.al.1997---Locally weighted Learning (Lazy learningl)

▪ D.Jams and K. Fatahalian

Impulse response functions (IRFs)

Precomputing Interactive Dynamic Deformable Scenes

Contribution ▪ black box offline simulators

▪ Dimensional Model Reduction

Excellence ▪ Robust

▪ Real-time

▪ Handle nonlinear deformation

▪ Illumination

▪ can be synthesized on programmable graphics hardware

Using Scope ▪ particular system ▪ very particular interaction conditions

Precomputing Interactive Dynamic Deformable Scenes

Procedure

▪ Fore treatment (including mesh ,creating

the mechanics model)

▪ Dimensional Model Reduction

▪ Analyze the interaction condition

▪ Pre –calculate and create IBFs

▪ Implement

About Fore-treatment and acquire deterministic iteractor

Get geometric mesh Determine the system DOF Determine the pre-computing

• According the interaction based on probability.

Dimensional Model Reduction(1) Deterministic static space model Dynamics: Appearance

State nodes: Time step edge: Orbits: a temporal sequence of nodes,connected

by time step edge Discrete phase portrait(P): the collection of all

pre-computed orbits

),( )()()1( ttt xfx

)()()1( ,( ttt xfx )()()1( ,( ttt xfx

)( )()( tt xgy

)(tx),,( )()()1( ttt xxe

Dimensional Model Reduction(2)

Model Reduction Detail

N state nodes,v vertices

N displacement field

that is (each u has 3 vector components)

vikiu ,...1

Nvvv

N

Nu

uuu

uuu

uuuA

21

122

11

21 ],,,[

Dimensional Model Reduction(3)

Model Reduction Detail

▲ a small number of vibration modes can be sufficient to approximate observed dynamics.

(SVD)

Re-parameterization of the phase portrait

the state vector:

Dimensional Model Reduction(3)

Reduced state vector coordination ▲displacement

▲velocity

Precomputation Process Data-driven modeling complication

insufficient data;high-demensional state space; divergence of nearby orbits;self-collisions.etc

Impulse Response Function

IRFs Index: IRFs:

FIx ,,

Impulse Response Functions(2)

An important special case : FI

Impulse Palettes

Impulse palette based on IRFs:

Impulsively sampling the phase portrait

▲sample time

▲no redundancy

▲orbits terminate

Simulate Implement

Blending Impulse Responses

Approximate the IRF at

That is

x

Example(1)

Dinosaur on moving car dashboard

Plant in moving pot

Cloth on moving door

Example(2) The pre-computing time

Example

Example(3)

Thank you!