A research-oriented elastic body simulator

• Position-based dynamics (PBD) [Müller+07]
• Extended position-based dynamics (XPBD) [Macklin+16]
• Small-steps XPBD [Macklin+19]
• Projective dynamics [Bouaziz+14]
• Quasi-Newton dynamics [Liu+17]
• ...

• Gauss-Seidel update
• Jacobi update

• Area conservation constraint [Müller+14]
• Bending constraint [Müller+07]
• Continuum-tetrahedron constraint [Bender+14]
• Continuum-triangle constraint [Bender+14]
• Distance constraint [Müller+07]
• Environmental collision constraint
• Example-based shape matching constraint [Koyama+12]
• Fixed point constraint
• Isometric bending constraint [Bergou+06; Bender+14]
• Long range attachments constraint [Kim+12]
• Shape matching constraint [Müller+05]
• Tetrahedron strain constraint [Müller+14]
• Triangle strain constraint [Müller+14]
• Volume conservation constraint [Müller+14]
• ...

• Alembic export of simulated cloth meshes
• Simple aerodynamics for clothes [Wilson+14]

• Alembic https://github.com/alembic/alembic [BSD 3-Clause]
  • OpenEXR https://github.com/openexr/openexr [BSD 3-Clause]
• Eigen http://eigen.tuxfamily.org/ [MPL2]
• tinyobjloader https://github.com/syoyo/tinyobjloader [MIT]

• bigger https://github.com/yuki-koyama/bigger [MIT]
  • bigg https://github.com/JoshuaBrookover/bigg [Unlicense]
    • bgfx.cmake https://github.com/JoshuaBrookover/bgfx.cmake [CC0]
      • bgfx https://github.com/bkaradzic/bgfx [BSD 2-Clause]
      • bimg https://github.com/bkaradzic/bimg [BSD 2-Clause]
      • bx https://github.com/bkaradzic/bx [BSD 2-Clause]
    • Dear ImGui https://github.com/ocornut/imgui [MIT]
    • GLFW https://github.com/glfw/glfw [Zlib]
    • GLM https://github.com/g-truc/glm [MIT]
  • random-util https://github.com/yuki-koyama/rand-util [MIT]
  • string-util https://github.com/yuki-koyama/string-util [MIT]
  • tinyobjloader https://github.com/syoyo/tinyobjloader [MIT]
• timer https://github.com/yuki-koyama/timer [MIT]

• googletest https://github.com/google/googletest [BSD 3-Clause]

macOS:

brew install eigen openexr

Ubuntu 16.04:

apt install libeigen3-dev openexr

git clone https://github.com/yuki-koyama/elasty.git --recursive
mkdir build
cd build
cmake ../elasty
make

The constraint stiffnesses in PBD [Müller+07] are dependent on the number of iterations for constraint solving. As the number of iterations increases, the constraints become infinitely stiff regardless of the stiffness parameters. This issue makes the parameter tuning difficult.

XPBD [Macklin+16] resolves this issue. As the number of iterations increases, the constraint stiffnesses converge to some (non-infinitely-stiff) states in accordance with the compliance parameters. This property makes the parameter tuning easier and more consistent.

These simulated results were generated by examples/pbd-xpbd-comparison/main.cpp.

This library supports wind effects for cloth simulation. This library calculates aerodynamic "drag" and "lift" forces based on the model used in Disney's Frozen [Wilson+14].

This simulated result was generated by examples/aerodynamics/main.cpp.

MIT License

Issue reports and pull requests are highly welcomed.

• [Bender+14] Jan Bender, Dan Koschier, Patrick Charrier, and Daniel Weber. 2014. Position-based simulation of continuous materials. Comput. Graph. 44 (2014), 1-10. DOI: http://doi.org/10.1016/j.cag.2014.07.004
• [Bender+17] Jan Bender, Matthias Müller, and Miles Macklin. 2017. A survey on position based dynamics, 2017. In Proc. Eurographics '17 Tutorials, Article 6, 31 pages. DOI: https://doi.org/10.2312/egt.20171034
• [Bergou+06] Miklos Bergou, Max Wardetzky, David Harmon, Denis Zorin, and Eitan Grinspun. 2006. A quadratic bending model for inextensible surfaces. In Proc. SGP '06, 227--230. DOI: https://doi.org/10.2312/SGP/SGP06/227-230
• [Bouaziz+14] Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective dynamics: fusing constraint projections for fast simulation. ACM Trans. Graph. 33, 4 (2014), 154:1--154:11. DOI: https://doi.org/10.1145/2601097.2601116
• [Kim+12] Tae-Yong Kim, Nuttapong Chentanez, and Matthias Müller-Fischer. 2012. Long range attachments: a method to simulate inextensible clothing in computer games. In Proc. SCA '12, 305--310. DOI: https://doi.org/10.2312/SCA/SCA12/305-310
• [Koyama+12] Yuki Koyama, Kenshi Takayama, Nobuyuki Umetani, and Takeo Igarashi. 2012. Real-time example-based elastic deformation. In Proc. SCA '12, 19-24. DOI: https://doi.org/10.2312/SCA/SCA12/019-024
• [Liu+17] Tiantian Liu, Sofien Bouaziz, and Ladislav Kavan. 2017. Quasi-Newton methods for real-time simulation of hyperelastic materials. ACM Trans. Graph. 36, 3 (2017), 23:1--23:16. DOI: https://doi.org/10.1145/2990496
• [Macklin+16] Miles Macklin, Matthias Müller, and Nuttapong Chentanez. 2016. XPBD: position-based simulation of compliant constrained dynamics. In Proc. MIG '16, 49-54. DOI: https://doi.org/10.1145/2994258.2994272
• [Macklin+19] Miles Macklin, Kier Storey, Michelle Lu, Pierre Terdiman, Nuttapong Chentanez, Stefan Jeschke, and Matthias Müller. 2019. Small steps in physics simulation. In Proc. SCA '19, 2:1–2:7. DOI: https://doi.org/10.1145/3309486.3340247
• [Müller+05] Matthias Müller, Bruno Heidelberger, Matthias Teschner, and Markus Gross. 2005. Meshless deformations based on shape matching. ACM Trans. Graph. 24, 3 (2005), 471-478. DOI: https://doi.org/10.1145/1073204.1073216
• [Müller+07] Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratcliff. 2007. Position based dynamics. J. Vis. Comun. Image Represent. 18, 2 (2007), 109-118. DOI: https://doi.org/10.1016/j.jvcir.2007.01.005
• [Umetani+14] Nobuyuki Umetani, Ryan Schmidt, and Jos Stam. 2014. Position-based elastic rods. In Proc. SCA '14, 21-30. DOI: https://doi.org/10.2312/sca.20141119
• [Wilson+14] Keith Wilson, Aleka McAdams, Hubert Leo, and Maryann Simmons. 2014. Simulating wind effects on cloth and hair in Disney’s Frozen. In ACM SIGGRAPH 2014 Talks, 48:1. DOI: https://doi.org/10.1145/2614106.2614120
• (TODO)