Multi-resolution isotropic strain limiting

Question

1. What are the future works in "Multi-resolution isotropic strain limiting" ?

2. What are the contributions in "Multi-resolution isotropic strain limiting" ?

3. What is the simplest way to constrain a point to be inside a sphere?

4. What is the effect of large coefficients on the surface?

Accepted Answer

The authors also provide a bending angle limiting method to resist out-of-plane bending.. In the future, the authors would like to improve the performance of the multi-resolution algorithm by using the constrained Lagrangian method to solve strain and bending angle limiting problems, by finding better solutions to twisting and other deformations that can not be well handled in a multi-resolution fashion, by accelerating the system using parallel processing, and by experimenting with other multi-grid schemes to obtain faster convergence.

Accepted Answer

In this paper the authors describe a fast strain-limiting method that allows stiff, incompliant materials to be simulated efficiently.. The authors demonstrate its use with triangular and tetrahedral linear-basis elements.. For triangulated surfaces in three-dimensional space, the authors also describe a complementary edge-angle-limiting method to limit out-of-plane bending.. To accelerate convergence, the authors propose a novel multi-resolution algorithm that enforces fitted limits at each level of a non-conforming hierarchy.

Accepted Answer

Using strain-component limits for an isotropic material is equivalent to attempting to constrain a point to be inside a sphere using independent limits on the point’s x̂, ŷ, and ẑ coordinates.

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Large coefficients may cause unnaturaljittering on the surface, while small coefficients may cause overdamping artifacts due to the energy loss.

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The multiresolution method reaches an average of 1% residual strain per triangle in 0.510 seconds after 128 iterations at each level (512 iterations total).

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To build a tetrahedral mesh hierarchy, the authors first create a surface mesh hierarchy, use TetGen [Si, 2010] to tessellate the interior with tetrahedra, and then improve the result using Stellar [Klingner and Shewchuk, 2007].

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Standard finiteelement methods (including spring-and-mass systems) model incompliance using large material coefficients that can create severe time integration difficulties.

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limiting parameters for thin shells are not invariant to mesh triangulation because fine-scale out-of-plain buckling appears as compression at coarse scales.

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The multi-resolution limiting approach provides an efficient way to generate stiff behaviors by preventing thin shells and elastic bodies from undergoing large deformations, without using stiff constitutive relations that would prohibit large time steps or lead to instability issues.

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The authors calculate all three vertex updates in the triangle according to three opposing edges using Equation 6, and then remove the center of mass translation of each triangle by a constant offset using Equation 4.

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One problem that a surface embedded in three dimensions does not usually encounter but that can occur for tetrahedra is element inversion.

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The authors can also avoid many of the SVD operations because the singular values of F are square roots of the eigenvalues of FTF, which are the roots of a quadratic or cubic equation.

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Because this method is independent of the underlying coordinate system, the deformation gradient can be computed in any convenient coordinates that need not be the same for different elements.

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The use of simulation-based methods to animate deformable objects has been an active area of graphics research for over twenty years.

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For instance, the tetrahedral dragon mesh cannot satisfy the strain limit [−5%, 5%] without violating the boundary conditions (its bottom is attached to the ground while the roller squeezes its body).

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In a multi-resolution system, the limiting work required at each level is determined by the amount of remaining deformations not covered by higher levels.

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If strain limits are violated in more than one principal di-160:2rection, the element needs to be processed multiple times to push it back into the limit.

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The strain limit for a single triangle or the bending angle limit between two neighboring triangles can be reached instantly in one step using the methods described in Sections 3.1 and 3.1.4.

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This cost is somewhat acceptable for triangles and they do some of the work during a precomputation phase, but extending to tetrahedra would presumably require inverting a 12×12 matrix, which would likely be prohibitively expensive.

Accepted Answer

This process of learning limits for each element and edge in the hierarchy (excluding the fine base mesh) can be time consuming, but the process only needs to be done once for each mesh and setting of its limit parameters.

Multi-resolution isotropic strain limiting

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Most frequently asked questions

1. What are the future works in "Multi-resolution isotropic strain limiting" ?

2. What are the contributions in "Multi-resolution isotropic strain limiting" ?

3. What is the simplest way to constrain a point to be inside a sphere?

4. What is the effect of large coefficients on the surface?

5. How many iterations does the multiresolution method take to reach?

6. How do the authors build a tetrahedral mesh hierarchy?

7. What is the common method used to model incompliance?

8. What is the effect of limiting parameters on thin shells?

9. What is the way to limit the bending angles of thin shells?

10. How do the authors calculate the svd of a triangle?

11. What is the problem that a tetrahedron does not usually encounter?

12. Why do the authors avoid the SVD operations?

13. What is the simplest way to compute the deformation gradient?

14. How many simulations have been used to animate deformable objects?

15. What is the strain limit of a tetrahedral dragon mesh?

16. What is the limiting work required at each level?

17. How many times does the element need to be processed to push it back into the limit?

18. How can The authorreach the strain limit for a single triangle?

19. What is the cost of extending to tetrahedra?

20. How many times does it take to learn limits?

Figures

Citations

Projective dynamics: fusing constraint projections for fast simulation

Fast simulation of mass-spring systems

Quasi-Newton Methods for Real-Time Simulation of Hyperelastic Materials

A Survey on Position-Based Simulation Methods in Computer Graphics

Continuum Foam: A Material Point Method for Shear-Dependent Flows

References

Surface simplification using quadric error metrics

A fast finite element solution for cloth modelling

A simple approach to nonlinear tensile stiffness for accurate cloth simulation

Proceedings of the 14th International Meshing Roundtable

Volume conserving finite element simulations of deformable models

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