Controlling Anisotropy in MassSpring Systems

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Controlling Anisotropyin Mass-Spring Systems

• David Bourguignon and Marie-Paule Cani
• iMAGIS-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 the main venous
system superimposed
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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
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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)

Intersection points
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Forces Calculations
Stretch Axial damped spring forces (each axis)
Shear Angular spring forces (each pair of axes)
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Animation Algorithm
Example taken for a tetrahedral mesh 4 point
masses 3 orthogonal axes of interest
2. Determine local frame deformation
3. Evaluate resulting forces
4. Interpolate to get resulting forces on vertices
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Animation Algorithm
Interpolation scheme for an hexahedral mesh 8
point masses 3 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

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)
Random
Concentric Helicoidal
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Results

• Performance issues benchmarks on an SGI O2 (MIPS
  R5000 CPU 300 MHz, 512 Mb main memory)

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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 the muscle fiber direction in
a human heart
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