Adaptive Simulation of Soft Bodies in Real-Time

Adaptive Simulation of Soft Bodies in Real-Time

Gilles Debunne Mathieu Desbrun

Marie-Paule Cani Alan Barr

iMAGIS USC Caltech

iMAGIS is a joint project of CNRS - INPG - INRIA - UJF

Grail@USC

iMAGIS-GRAVIR / IMAG

Real time deformable model•Virtual laparoscopic surgery•Real time dynamic simulation•Realistic surface mesh deformation•Force feedback


Contributions•Multi-resolution hierarchical model

•Automatic adaptivity


Overview•Previous work

•Physical model

•Discrete operators

•Adaptive simulation

•Results and video


Previous work

•Finite elements [GTT89][BC96][DCA99][JP99]

•Energy based [TPBF87]

•Mass-spring systems [Hutch96][BW98]

•Particle systems [MP88][DG96]

•Hybrid models [MT92][Gas93][DG95][DDBC99]


Physical model ( I ) : Deformation

• d : displacement field w/r rest position

•Strain tensor = ½ (d + dT)

rest pos.

d = 0


Physical model (II) : Constraint

•Stress tensor , 3x3 symmetric matrix

n

FF = n dA

surface dA


a = g + d + (+) (.d)

Physical model (III) : Hooke’s law• Linear relation between strain and stress

= 2 + tr() I3

• Acceleration of a point

a = g + div

and are the Lamé coefficients


Algorithm

•From the displacement field d

•Compute d and (.d)

•Compute the acceleration a

• Integrate the acceleration


Differential operators

•Computation based on the Gauss theorem

i = x, y or z

Volume integral turned into boundary integral

Volume V Boundary V

/ i X dV =

X . ni dS

n


Definition of associated volume

•The volume associated to a point is its Voronoi region (natural element).

1st ring neighbour


Application•Gauss is applied on the gradient and on the divergence of the displacement field d.

•First order finite elements : linear interpolation

i

j

k

di

dj

dk

di =

1/2A ( (dj-di)ki + (dk-di)ij )


Laplacian d & Grad Div (.d) •Sum over all the surrounding tetrahedrons

•For each participating tetrahedron :

di = - j=1..4 (i . j) dj

(.d) i = - j=1..4 (iT . j) dj

ii


Multi-resolution validation

Dynamic behaviour is preserved


Adapting the resolution


Adaptive simulation : meshes•Several independent meshes of the object


Interface between the meshes


Introducing ghost points

• Information is transmitted through ghost points

FE1

E2

E3

F interpolated from (E1E2E3)

G

H

active ghost


Adaptivity of the simulation• A point is replaced by those of the finer level which

are inside its Voronoi region.


Adaptivity in color

Deformation Level of detail


Conclusion

•Physical model (PDE)

•New discrete operators d and (.d)

•Adaptive simulation


Perspectives

•Cuts in the object

•Plasticity

•Parallelization


Real-time simulation• Imposed constant frame rate

•Computations have to be completed in less time than the frame interval

– Wait if too fast

– Linear time prevents too long computations

0 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 6 7 9 10 118


Cuts in the object

•Weaken then suppress links

•Propagate to higher levels


Local reference frames


Surface rendering•Skin nodes attached to surface points

p = wi pi

p


Time steps•Courant’s criterion

dt < h

•a dt = vnew - vold < max

•Stored in time bin lists.

• Inverse powers of 2 of the frame rate

+20


Computing the Laplacian d•Generalization of 1D equation [DMSB99]

[Fuji95] di = j

dj -di

Lij

2

j Lij

i

jdi

dj

i Lij


Extension to Grad Div (.d)•Measure of volume expansion

(.d) = j nij

(dj -di).nij

Lij

2

j Lij

i

Radial Rotationial

nij


Results


Discretization : Sample Points•Sample points in the material

•Adaptive sampling : hierarchy


Precomputed Particle Neighborhood

•Connectivity is precomputed

•List of potential neighbors

•Limited to a restricted octree


Collision detection•The organ

– triangle mesh– can deform, can be cut

• avoid pre-computations!

•One or more tools– of simple geometry– rigid– passing through a fixed point


Using OpenGL hardware•Using the OpenGL select buffer

Static tool position

orthographic camera

Dynamic tool

perspective camera

+ 2 clipping planes


1

50

100

150

200Performances

•Time– About 0.1 ms

on OpenGL hardware– About 2 ms otherwise

•Acceleration factor

w.r.t. Rapid (OBB Trees)[Gottshalk & al. SIG’96]

SGI Onyx

2 IR

DEC Alpha 4

D60

Pentiu

m (

3Dfx)

Pentiu

m (s

oft)


Collision response•Which points should be moved

•Along which direction


Adaptivity of the simulation• A point is replaced by those of the finer level which

are inside its Voronoi region.

Adaptive Simulation of Soft Bodies in Real-Time

Documents

imagisgravir imagcuts

deformation d

displacement field dcompute

stress s

fastlinear time

rg div s

constraintstress tensor

d dtrest pos