Energy Embedded Gauss-Seidel Iteration for Soft Body Simulations
Resumo
In this paper, we present our novel energy embedded Gauss-Seidel iteration to simulate soft objects. Our algorithm is inspired by the equality of the kinetic and potential energy changes, and employs the extended Position-Based Dynamics algorithm (XPBD) as the base algorithm. The proposed method does not aim to conserve the total energy of the system, only alters the position constraints based on the kinetic and potential energy balances within the Gauss-Seidel process of the XPBD algorithm. Our algorithm provides an implicit solution for relatively better visual results during the simulation of soft bodies. Since we apply our solution within the Gauss-Seidel iteration, it is not dependent to both simulation step-size and integration methods. We demonstrate the benefits of our method with many position constraints such as geometric deformation constraints, strain based constraints and continuous materials.
Palavras-chave:
Computer Graphics, Animation, Physical Simulation
Referências
M. Müller B. Heidelberger M. Hennix J. Ratcliff "Position based dynamics" Journal of Visual Communication and Image Representation vol. 18 no. 2 pp. 109-2007.
T. Jakobsen "Advanced character physics" Proceedings of the Game Developers Conference pp. 383-2001.
M. Macklin M. Muller N. Chentanez "Xpbd: Position-based simulation of compliant constrained dynamics" Proceedings of the 9th International Conference on Motion in Games ser. MIG’ 16 pp. 49-54 2016.
J. Su R. Sheth R. Fedkiw "Energy conservation for the simulation of deformable bodies" IEEE Transactions on Visualization and Computer Graphics vol. 19 no. 2 pp. 189-feb 2013.
M. Muller N. Chentanez T.-Y. Kim M. Macklin "Strain based dynamics" Eurographics/ACM SIGGRAPH Symposium on Computer Animation 2014.
J. Bender D. Koschier P. Charrier D. Weber "Position-based simulation of continuous materials" Computers & Graphics vol. 44 pp. 1-10 2014.
J.-D. Gascuel M.-P. Gascuel "Displacement constraints for interactive modeling and animation of articulated structures" The Visual Computer vol. 10 no. 4 pp. 191-Apr 1994.
F. Faure "Interactive solid animation using linearized displacement constraints" in Computer Animation and Simulation '98 Vienna:Springer Vienna pp. 61-72 1999.
R. Goldenthal D. Harmon R. Fattal M. Bercovier E. Grinspun "Efficient simulation of inextensible cloth" ACM Trans. Graph. vol. 26 no. 3 pp. 49 2007.
J. Stam "Nucleus: Towards a unified dynamics solver for computer graphics" Computer-Aided Design and Computer Graphics 2009. CAD/Graphics '09. 11th IEEE International Conference on pp. 1-11 2009.
M. Tournier M. Nesme B. Gilles F. Faure "Stable constrained dynamics" ACM Trans. Graph. vol. 34 no. 4 pp. 132:1-132:10 jul 2015.
M. Servin C. Lacoursiere N. Melin "Interactive simulation of elastic deformable materials" proceedings of Sigrad Conference pp. 22-32 2006.
J. Bender M. Muller M. Macklin "A survey on position based dynamics 20EUROGRAPHICS 2017 Tutorials 2017.
M. Muller N. Chentanez "Wrinkle meshes" Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation pp. 85-92 2010.
M. Muller N. Chentanez "Solid simulation with oriented particles" ACM Trans. Graph. vol. 30 no. 4 pp. 92:1-92:10 2011.
T.-Y. Kim N. Chentanez M. Muller-Fischer "Long range attachments - a method to simulate inextensible clothing in computer games" Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation pp. 305-2012.
M. Kelager S. Niebe K. Erleben "A triangle bending constraint model for position-based dynamics" Workshop in Virtual Reality Interactions and Physical Simulation “VRIPHYS” (202010.
M. Muller T.-Y. Kim N. Chentanez "Fast Simulation of Inextensible Hair and Fur" Workshop on Virtual Reality Interaction and Physical Simulation. The Eurographics Association 2012.
M. Macklin M. Muller "Position based fluids" ACM Trans. Graph. vol. 32 no. 4 pp. 104:1-104:12 jul 2013.
F. Marco "Position based facial animation synthesis" Computer Animation and Virtual Worlds vol. 23 no. 3–4 pp. 457-2012.
O. Cetinaslan V. Orvalho "Localized verlet integration framework for facial models" Articulated Motion and Deformable Objects - 9th International Conference AMDO Proceedings ser. Lecture Notes in Computer Science vol. 9pp. 1-15 2016.
C. Deul J. Bender "Physically-based character skinning" Virtual Reality Interactions and Physical Simulations (VRIPhys) nov 2013.
N. A. Rumman M. Fratarcangeli "Position-based skinning for soft articulated characters" Computer Graphics Forum vol. 34 no. 6 pp. 240-2015.
N. Umetani R. Schmidt J. Stam "Position-based elastic rods" Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation ser. SCA '14 pp. 21-30 2014.
C. Deul T. Kugelstadt M. Weiler J. Bender "Direct position-based solver for stiff rods" Computer Graphics Forum vol. 37 no. 6 pp. 313-2018.
A. Stern M. Desbrun "Discrete geometric mechanics for variational time integrators" in SIGGRAPH '06: ACM SIGGRAPH 2006 Courses New York:ACM Press pp. 75-80 2006.
E. Hairer C. Lubich "Long-time energy conservation of numerical methods for oscillatory differential equations" SIAM Journal on Numerical Analysis vol. 38 no. 2 pp. 414-2000.
A. Lew J. E. Marsden M. Ortiz M. West "Variational time integrators" International Journal for Numerical Methods in Engineering vol. 60 no. 1 pp. 153-2004.
K.-J. Bathe "Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme" Comput. Struct. vol. 85 no. 7–8 pp. 437-2007.
D. Dinev T. Liu L. Kavan "Stabilizing integrators for real-time physics" ACM Trans. Graph. vol. 37 no. 1 pp. 9:1-9:19 jan 2018.
O. Cetinaslan "Localized constraint based deformation framework for triangle meshes" Entertainment Computing vol. 26 pp. 78-87 2018.
E. Sifakis J. Barbic "Fem simulation of 3d deformable solids: A practitioner's guide to theory discretization and model reduction" ACM SIGGRAPH 2012 Courses ser. SIGGRAPH '12 pp. 20:1-20:50 2012.
S. Bouaziz S. Martin T. Liu L. Kavan M. Pauly "Projective dynamics: Fusing constraint projections for fast simulation" ACM Trans. Graph. vol. 33 no. 4 pp. 154:1-154:11 jul 2014.
M. Muller N. Chentanez T.-Y. Kim M. Macklin "Air meshes for robust collision handling" ACM Trans. Graph. vol. 34 no. 4 pp. 133:1-133:9 jul 2015.
M. Fratarcangeli V. Tibaldo F. Pellacini "Vivace: A practical gauss-seidel method for stable soft body dynamics" ACM Trans. Graph. vol. 35 no. 6 pp. 214:1-214:9 Nov. 2016.
T. Jakobsen "Advanced character physics" Proceedings of the Game Developers Conference pp. 383-2001.
M. Macklin M. Muller N. Chentanez "Xpbd: Position-based simulation of compliant constrained dynamics" Proceedings of the 9th International Conference on Motion in Games ser. MIG’ 16 pp. 49-54 2016.
J. Su R. Sheth R. Fedkiw "Energy conservation for the simulation of deformable bodies" IEEE Transactions on Visualization and Computer Graphics vol. 19 no. 2 pp. 189-feb 2013.
M. Muller N. Chentanez T.-Y. Kim M. Macklin "Strain based dynamics" Eurographics/ACM SIGGRAPH Symposium on Computer Animation 2014.
J. Bender D. Koschier P. Charrier D. Weber "Position-based simulation of continuous materials" Computers & Graphics vol. 44 pp. 1-10 2014.
J.-D. Gascuel M.-P. Gascuel "Displacement constraints for interactive modeling and animation of articulated structures" The Visual Computer vol. 10 no. 4 pp. 191-Apr 1994.
F. Faure "Interactive solid animation using linearized displacement constraints" in Computer Animation and Simulation '98 Vienna:Springer Vienna pp. 61-72 1999.
R. Goldenthal D. Harmon R. Fattal M. Bercovier E. Grinspun "Efficient simulation of inextensible cloth" ACM Trans. Graph. vol. 26 no. 3 pp. 49 2007.
J. Stam "Nucleus: Towards a unified dynamics solver for computer graphics" Computer-Aided Design and Computer Graphics 2009. CAD/Graphics '09. 11th IEEE International Conference on pp. 1-11 2009.
M. Tournier M. Nesme B. Gilles F. Faure "Stable constrained dynamics" ACM Trans. Graph. vol. 34 no. 4 pp. 132:1-132:10 jul 2015.
M. Servin C. Lacoursiere N. Melin "Interactive simulation of elastic deformable materials" proceedings of Sigrad Conference pp. 22-32 2006.
J. Bender M. Muller M. Macklin "A survey on position based dynamics 20EUROGRAPHICS 2017 Tutorials 2017.
M. Muller N. Chentanez "Wrinkle meshes" Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation pp. 85-92 2010.
M. Muller N. Chentanez "Solid simulation with oriented particles" ACM Trans. Graph. vol. 30 no. 4 pp. 92:1-92:10 2011.
T.-Y. Kim N. Chentanez M. Muller-Fischer "Long range attachments - a method to simulate inextensible clothing in computer games" Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation pp. 305-2012.
M. Kelager S. Niebe K. Erleben "A triangle bending constraint model for position-based dynamics" Workshop in Virtual Reality Interactions and Physical Simulation “VRIPHYS” (202010.
M. Muller T.-Y. Kim N. Chentanez "Fast Simulation of Inextensible Hair and Fur" Workshop on Virtual Reality Interaction and Physical Simulation. The Eurographics Association 2012.
M. Macklin M. Muller "Position based fluids" ACM Trans. Graph. vol. 32 no. 4 pp. 104:1-104:12 jul 2013.
F. Marco "Position based facial animation synthesis" Computer Animation and Virtual Worlds vol. 23 no. 3–4 pp. 457-2012.
O. Cetinaslan V. Orvalho "Localized verlet integration framework for facial models" Articulated Motion and Deformable Objects - 9th International Conference AMDO Proceedings ser. Lecture Notes in Computer Science vol. 9pp. 1-15 2016.
C. Deul J. Bender "Physically-based character skinning" Virtual Reality Interactions and Physical Simulations (VRIPhys) nov 2013.
N. A. Rumman M. Fratarcangeli "Position-based skinning for soft articulated characters" Computer Graphics Forum vol. 34 no. 6 pp. 240-2015.
N. Umetani R. Schmidt J. Stam "Position-based elastic rods" Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation ser. SCA '14 pp. 21-30 2014.
C. Deul T. Kugelstadt M. Weiler J. Bender "Direct position-based solver for stiff rods" Computer Graphics Forum vol. 37 no. 6 pp. 313-2018.
A. Stern M. Desbrun "Discrete geometric mechanics for variational time integrators" in SIGGRAPH '06: ACM SIGGRAPH 2006 Courses New York:ACM Press pp. 75-80 2006.
E. Hairer C. Lubich "Long-time energy conservation of numerical methods for oscillatory differential equations" SIAM Journal on Numerical Analysis vol. 38 no. 2 pp. 414-2000.
A. Lew J. E. Marsden M. Ortiz M. West "Variational time integrators" International Journal for Numerical Methods in Engineering vol. 60 no. 1 pp. 153-2004.
K.-J. Bathe "Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme" Comput. Struct. vol. 85 no. 7–8 pp. 437-2007.
D. Dinev T. Liu L. Kavan "Stabilizing integrators for real-time physics" ACM Trans. Graph. vol. 37 no. 1 pp. 9:1-9:19 jan 2018.
O. Cetinaslan "Localized constraint based deformation framework for triangle meshes" Entertainment Computing vol. 26 pp. 78-87 2018.
E. Sifakis J. Barbic "Fem simulation of 3d deformable solids: A practitioner's guide to theory discretization and model reduction" ACM SIGGRAPH 2012 Courses ser. SIGGRAPH '12 pp. 20:1-20:50 2012.
S. Bouaziz S. Martin T. Liu L. Kavan M. Pauly "Projective dynamics: Fusing constraint projections for fast simulation" ACM Trans. Graph. vol. 33 no. 4 pp. 154:1-154:11 jul 2014.
M. Muller N. Chentanez T.-Y. Kim M. Macklin "Air meshes for robust collision handling" ACM Trans. Graph. vol. 34 no. 4 pp. 133:1-133:9 jul 2015.
M. Fratarcangeli V. Tibaldo F. Pellacini "Vivace: A practical gauss-seidel method for stable soft body dynamics" ACM Trans. Graph. vol. 35 no. 6 pp. 214:1-214:9 Nov. 2016.
Publicado
28/10/2019
Como Citar
CETINASLAN, Ozan; CHAVES, Rafael.
Energy Embedded Gauss-Seidel Iteration for Soft Body Simulations. In: CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI), 32. , 2019, Rio de Janeiro.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2019
.
DOI: https://doi.org/10.5753/sibgrapi.2019.9805.
