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Controlling Anisotropy in Mass-Spring Systems - HAL

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Controlling Anisotropy
in Mass-Spring Systems
David Bourguignon and Marie-Paule Cani
iMAGIS-GRAVIR
iMAGIS is a joint project of CNRS - INPG - INRIA - UJF
iMAGIS-GRAVIR / IMAG
Motivation
• Simulating biological materials
– elastic
– anisotropic
– constant volume deformation
• Efficient model
пѓћ mass-spring systems
(widely used)
A human liver with the
main venous system
superimposed
iMAGIS-GRAVIR / IMAG
Mass-Spring Systems
• Mesh geometry influences material behavior
– homogeneity
– isotropy
iMAGIS-GRAVIR / IMAG
Mass-Spring Systems
• Previous solutions
v2
– homogeneity
пѓћ Voronoi regions [Deussen et al., 1995]
– isotropy/anisotropy
пѓћ parameter identification:
simulated annealing, genetic algorithm
[Deussen et al., 1995; Louchet et al., 1995]
v3
v1
Voronoi regions
пѓћ hand-made mesh
[Miller, 1988; Ng and Fiume, 1997]
iMAGIS-GRAVIR / IMAG
Mass-Spring Systems
• No volume preservation
пѓћ correction methods [Lee et al., 1995; Promayon et al., 1996]
iMAGIS-GRAVIR / IMAG
New Deformable Model
• Controlled isotropy/anisotropy
пѓћ uncoupling springs and mesh geometry
• Volume preservation
• Easy to code, efficient
пѓћ related to mass-spring systems
iMAGIS-GRAVIR / IMAG
Elastic Volume Element
• Mechanical characteristics defined along axes of interest
• Forces resulting from local frame deformation
• Forces applied to masses (vertices)
C
g
Barycenter
Intersection points
I3
I1’
e3
I2
I1
I1
e1
e2
e1
I2’
I3’
a
A
I1’
b
B
iMAGIS-GRAVIR / IMAG
Forces Calculations
Stretch:
Axial damped spring forces
(each axis)
Shear:
Angular spring forces
(each pair of axes)
f
I1’
I3
3
e3
f1’
I1’
f1’
f1
I1
e1
I1
e1
I3’
f1
f3’
iMAGIS-GRAVIR / IMAG
Animation Algorithm
FC
Example
1.
Interpolate
takentofor
getaintersection points
tetrahedral mesh:
2.4Determine
local frame deformation
point masses
orthogonal
axes offorces
interest
3.3Evaluate
resulting
4. Interpolate to get resulting
F1
forces on vertices
C
g
I1’
I1 I
F’1
e1
a
A
b
B
F = g F + g’ F’ + ...
xIC= a xA1+ b xB 1+ g xC
iMAGIS-GRAVIR / IMAG
Animation Algorithm
Interpolation scheme for an
hexahedral mesh:
8 point masses
3 orthogonal axes of interest
C
D
h I
z
A
B
xI = zh xA + (1 – z)h xB +
(1 – z)(1 – h) xC + z(1 – h) xD
iMAGIS-GRAVIR / IMAG
Volume preservation
• Extra radial forces
• Tetra mesh: preserve sum of the barycenter-vertex distances
• Hexa mesh: preserve each barycenter-vertex distance
With volume forces
Mass-spring system
Without volume forces
Tetrahedral Mesh
iMAGIS-GRAVIR / IMAG
Results
• Comparison with mass-spring systems:
– no more undesired anisotropy
– correct behavior in bending
Orthotropic material, same parameters in the 3 directions
iMAGIS-GRAVIR / IMAG
Results
• Control of anisotropy
пѓћ same tetrahedral mesh
пѓћ different anisotropic behaviors
iMAGIS-GRAVIR / IMAG
Results
Horizontal
Diagonal
Hemicircular
iMAGIS-GRAVIR / IMAG
Results
Concentric Helicoidal
Concentric Helicoidal
(top view)
Random
iMAGIS-GRAVIR / IMAG
Results
• Performance issues: benchmarks on an SGI O2
(MIPS R5000 CPU 300 MHz, 512 Mb main memory)
M esh
M ass-S p rin g S y stem
O u r M o d el
E lem en ts S p rin g s / E lem en t T im e (in s)
T etra
804
1 .4 6 1
0 .1 2 9
H ex a
125
8 .3 2 0
0 .1 1 7
T etra
804
п‚»10
1 .8 6 7
H ex a
125
14
0 .4 2 7
iMAGIS-GRAVIR / IMAG
Conclusion and Future Work
• Same mesh, different behaviors
пѓћ but different meshes, not the same behavior !
• Soft constraint for volume preservation
• Combination of different volume element types
with different orders of interpolation
iMAGIS-GRAVIR / IMAG
Conclusion and Future Work
• Extension to active materials
пѓћ human heart motion simulation
пѓћ non-linear springs with time-varying properties
Angular maps of the
muscle fiber direction in a
human heart
iMAGIS-GRAVIR / IMAG
iMAGIS-GRAVIR / IMAG
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