controlling anisotropy in mass-spring systems
TRANSCRIPT
iMAGIS is a joint project of CNRS - INPG - INRIA - UJF
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Controlling Anisotropyin Mass-Spring Systems
David Bourguignon and Marie-Paule CaniiMAGIS-GRAVIR
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Motivation
•Simulating biological materials– elastic– anisotropic– constant volume deformation
•Efficient model⇒ mass-spring systems(widely used)
A human liver with themain venous systemsuperimposed
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Mass-Spring Systems
•Mesh geometry influences material behavior– homogeneity– isotropy
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Mass-Spring Systems
•Previous solutions– homogeneity
⇒ Voronoi regions [Deussen et al., 1995]
– isotropy/anisotropy⇒ parameter identification:simulated annealing, genetic algorithm[Deussen et al., 1995; Louchet et al., 1995]
⇒ hand-made mesh[Miller, 1988; Ng and Fiume, 1997]
Voronoi regions
v3
v2
v1
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Mass-Spring Systems
•No volume preservation
⇒ correction methods [Lee et al., 1995; Promayon et al., 1996]
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New Deformable Model
•Controlled isotropy/anisotropy⇒ uncoupling springs and mesh geometry
•Volume preservation
•Easy to code, efficient⇒ related to mass-spring systems
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Elastic Volume Element• Mechanical characteristics defined along axes of interest• Forces resulting from local frame deformation• Forces applied to masses (vertices)
I1’
I1 e1
e3
I3
I3’
e2
I2
I2’
I1’
I1 e1
A B
C
α
β
γ Barycenter Intersection points
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Forces Calculations
f1
I1’
I1
e1
f1’
f3
I1’
I1 e1
e3
I3
I3’f1
f1’
f3’
Stretch:Axial damped spring forces (each axis)
Shear:Angular spring forces(each pair of axes)
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F’1
Animation Algorithm
FC = γ F1 + γ’ F’1 + ...
FC
Example taken for atetrahedral mesh:
4 point masses3 orthogonal axes of interest
F1
I1’
I1 e1
2. Determine local frame deformation3. Evaluate resulting forces4. Interpolate to get resulting forces on vertices
xI = α xA + β xB + γ xC
A B
C
α
β
γ
I
1. Interpolate to get intersection points
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Animation Algorithm
xI = ζη xA + (1 – ζ)η xB +
(1 – ζ)(1 – η) xC + ζ(1 – η) xD
ζ
η
A B
CD
I
Interpolation scheme for anhexahedral mesh:
8 point masses3 orthogonal axes of interest
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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
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Results
•Comparison with mass-spring systems:– no more undesired anisotropy– correct behavior in bending
Orthotropic material, same parameters in the 3 directions
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Results
•Control of anisotropy⇒ same tetrahedral mesh⇒ different anisotropic behaviors
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Results
Horizontal Diagonal Hemicircular
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Results
Concentric Helicoidal(top view)
RandomConcentric Helicoidal
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Results
•Performance issues: benchmarks on an SGI O2 (MIPS R5000 CPU 300 MHz, 512 Mb main memory)
Mesh Elements Springs / Element Time (in s)
Mass-Spring System Tetra 804 1.461 0.129
Hexa 125 8.320 0.117
Our Model Tetra 804 ≈10 1.867
Hexa 125 14 0.427
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Conclusion and Future Work
•Same mesh, different behaviors⇒ but different meshes, not the same behavior !
•Soft constraint for volume preservation
•Combination of different volume element types with different orders of interpolation
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Conclusion and Future Work
•Extension to active materials⇒ human heart motion simulation⇒ non-linear springs with time-varying properties
Angular maps of themuscle fiber direction in ahuman heart
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