Stabler Neo-Hookean Simulation:
Absolute Eigenvalue Filtering for Projected Newton

Project Page | Paper

Official implementation for the paper:

Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton
Honglin Chen¹, Hsueh-Ti Derek Liu^3,4, David I.W. Levin^2,5, Changxi Zheng¹, Alec Jacobson^2,6

> ¹Columbia University, ²University of Toronto, ³Roblox Research, ⁴University of British Columbia,
    ⁵NVIDIA, ⁶Adobe Research
> SIGGRAPH 2024 (Conference Track)

Installation

To build the code, please run

mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j8

Experiments

To run the code with our absolute eigenvalue projection strategy, please run, e.g.,

sh ../scripts/micky_teaser/abs.sh

We provide several examples in scripts/.

Comparisons

To run the same example with the eigenvalue clamping strategy, run clamp.sh under the same folder (or add --clamp option after the command in abs.sh):

sh ../scripts/micky_teaser/clamp.sh

The default eigenvalue clamping algorithm uses 0 as the clamping threshold. To use a different clamping threshold (e.g., a small positive number), add --epsilon [threshold] option after the command.

Optional arguments

For more options, please see

./example --help

What do we modify in TinyAD to add our absolute eigenvalue projection?

As a research prototype, we choose to make minimal modifications in TinyAD when adding our new projection method. We clone TinyAD to the project folder, and comment out and change lines 71-75 in TinyAD/include/TinyAD/Utils/HessianProjection.hh to:

  if (_eigenvalue_eps < 0) {
      // project to absolute value if the eigenvalue threshold is set to be less than 0
      if (D(i, i) < 0)
      {
          D(i, i) = -D(i, i);
          all_positive = false;
      }
  }
  else {
      // project to epsilon otherwise
      if (D(i, i) < _eigenvalue_eps)
      {
          D(i, i) = _eigenvalue_eps;
          all_positive = false;
      }
  }

Thus we simply use eps < 0 as a flag for absolute eigenvalue projection.

Yet another way to verify our method (which is slightly more complicated)

Our method can also be verified by modifying the code of Hobak [Kim and Eberle 2020].

1. Git clone Hobak in a different folder.

2. Implement our abs eigenvalue projection: Change lines 139-141 in src/Hyperelastic/Volume/SNH.cpp to:

  for (int i = 0; i < 9; i++)
      if (eigenvalues(i) < 0.0)
          eigenvalues(i) = -eigenvalues(i);  

3. Increase the Poisson's ratio to roughly 0.495: Change line 54 in src/Scenes/QUASISTATIC_STRETCH.h to:

  _hyperelastic = new VOLUME::SNH(1.0, 100.0);

3. Create a large initial deformation: Change lines 80-84 in src/Scenes/QUASISTATIC_STRETCH.h to:

  if (_frameNumber < 1)
  {
    _kinematicShapes[0]->translation()[2] -= 0.5;
    return;
  }

Feel free to try an even larger deformation. :)

4. Uncomment line 287 in projects/simulateScene/simulateScene.cpp to choose the quasistatic test:

  scene = new QUASISTATIC_STRETCH();

5. Run make mac or make linux to run the test (see HOBAK's readme).

• Note: HOBAK doesn't include a line search but our method seems to often work fine without one.

When does our absolute eigenvalue projection work best?

Our method stabilizes and accelerates the optimization of stable Neo-Hookean energy when the energy landscape is highly nonconvex. In other words, our absolute eigenvalue projection usually achieves more speedup when the Poisson's ratio is high, the volume change is large and the mesh resolution is high, as each of them will increase the nonconvexity of the stable Neo-Hookean energy (see Sec.6 of our paper). For other cases where the energy landscape is almost convex, our method may slightly damp the convergence (see Sec.8).

Citation

@inproceedings{chen2024abs_eval,
      title={Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton},
      author={Honglin Chen and Hsueh-Ti Derek Liu and David I.W. Levin and Changxi Zheng and Alec Jacobson},
      booktitle = {ACM SIGGRAPH 2024 Conference Proceedings},
      year = {2024}
  }