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Controlling Anisotropy in Mass-Spring Systems

Explore an efficient model for simulating biological materials in mass-spring systems, focusing on controlled isotropy/anisotropy by decoupling springs and mesh geometry while ensuring volume preservation. Learn about elastic volume elements, forces calculations, animation algorithms, interpolation schemes, and results in tetrahedral and hexahedral meshes. The study compares isotropic and anisotropic behaviors, addresses performance benchmarks, and outlines future work on extending to active materials like the human heart motion simulation.

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Controlling Anisotropy in Mass-Spring Systems

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  1. Controlling Anisotropyin Mass-Spring Systems David Bourguignon and Marie-Paule Cani iMAGIS-GRAVIR

  2. 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

  3. Mass-Spring Systems • Mesh geometry influences material behavior • homogeneity • isotropy

  4. v2 v1 v3 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

  5. Mass-Spring Systems • No volume preservation • correction methods [Lee et al., 1995; Promayon et al., 1996]

  6. New Deformable Model • Controlled isotropy/anisotropy • uncoupling springs and mesh geometry • Volume preservation • Easy to code, efficient • related to mass-spring systems

  7. I3 Barycenter C e3 g I1’ I2 e2 I1’ I1 e1 I2’ I3’ I1 e1 a A B b Elastic Volume Element • Mechanical characteristics defined along axes of interest • Forces resulting from local frame deformation • Forces applied to masses (vertices) Intersection points

  8. I1’ f1’ f3 f1 I3 e1 f1’ I1 e3 I1’ I1 e1 I3’ f1 f3’ Forces Calculations Stretch: Axial damped spring forces (each axis) Shear: Angular spring forces (each pair of axes)

  9. FC 1. Interpolate to get intersection points C g F’1 I1’ F1 I1 I e1 a A B b xI = a xA + b xB + g xC FC = gF1 + g’ F’1 + ... 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

  10. C D h I z A B xI = zh xA + (1 – z)h xB + (1 – z)(1 – h) xC + z(1 – h) xD Animation Algorithm • Interpolation scheme for an • hexahedral mesh: • 8 point masses • 3 orthogonal axes of interest

  11. With volume forces Mass-spring system Without volume forces Volume preservation • Extra radial forces • Tetra mesh: preserve sum of the barycenter-vertex distances • Hexa mesh: preserve each barycenter-vertex distance Tetrahedral Mesh

  12. Results • Comparison with mass-spring systems: • no more undesired anisotropy • correct behavior in bending Orthotropic material, same parameters in the 3 directions

  13. Results • Control of anisotropy • same tetrahedral mesh • different anisotropic behaviors

  14. Results Horizontal Diagonal Hemicircular

  15. Results Concentric Helicoidal Concentric Helicoidal (top view) Random

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

  17. 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

  18. 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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