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Controlling Anisotropy in Mass-Spring Systems

Controlling Anisotropy in Mass-Spring Systems. David Bourguignon and Marie-Paule Cani i MAGIS-GRAVIR. Motivation. Simulating biological materials elastic anisotropic constant volume deformation Efficient model mass-spring systems (widely used). A human liver with the

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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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