- Author:
- David Baraff
This thesis examines the problems and difficulties in the forward dynamic simulation of rigid bodies subject to non-penetration constraints. By adopting a simple but well-defined model of rigid body dynamics, we are able to focus on and gain insight into some of the inherent difficulties of rigid body simulation. Additionally, computationally practical solutions to some of the problems encountered in this thesis are presented.
Enforcing non-penetration constraints is essentially a two step process. The first step of the simulation involves the detection of potential contacts between bodies. This thesis presents collision detection algorithms for the dynamic simulation of bodies that are composed of both polyhedra and convex closed curved surfaces. The collision detection algorithms exploit temporal coherence to achieve fast running times and are a practical solution to the problem of collision detection during simulation.
The second step of the simulation involves the computation of the contact forces between bodies that maintain the non-penetration constraint. This thesis considers first the problem of computing contact forces between a pair of bodies that contact at a point without friction. A mathematical formulation for the contact force between the bodies is presented, and then modified to yield a formulation that is computationally practical for use in a simulator. After considering the dynamics of single point contacts, systems with multiple contacts are considered both in terms of computational complexity measures and practical solution methods. The methods used in this thesis to compute constraint forces are also theoretically and practically compared with a popular method for preventing inter-penetration called the "penalty method".
After considering frictionless systems, this thesis considers systems of bodies that behave according to the classical Coulomb model of friction (which includes both sliding and dry friction). This leads us to consider systems in which there are no solutions to the classical constraint force equations, as well as systems which admit multiple solutions for the constraint force equations and whose subsequent behavior is thus indeterminate. Both computational and practical complexity results for simulating such systems are discussed.
Cited By
Baraff D and Witkin A Large Steps in Cloth Simulation Seminal Graphics Papers: Pushing the Boundaries, Volume 2, (767-778)- Köster T, Perumalla K and Uhrmacher A Efficient Simulation of Nested Hollow Sphere Intersections Proceedings of the 2017 ACM SIGSIM Conference on Principles of Advanced Discrete Simulation, (173-183)
- Capannini G and Larsson T Adaptive collision culling for large-scale simulations by a parallel sweep and prune algorithm Proceedings of the 16th Eurographics Symposium on Parallel Graphics and Visualization, (1-10)
- Capannini G and Larsson T Efficient collision culling by a succinct bi-dimensional sweep and Prune algorithm Proceedings of the 32nd Spring Conference on Computer Graphics, (25-32)
- Maggiorini D, Ripamonti L and Sauro F (2018). Unifying rigid and soft bodies representation, International Journal of Computer Games Technology, 2014, (6-6), Online publication date: 1-Jan-2014.
- Liu F, Harada T, Lee Y and Kim Y (2010). Real-time collision culling of a million bodies on graphics processing units, ACM Transactions on Graphics, 29:6, (1-8), Online publication date: 1-Dec-2010.
- Liu F, Harada T, Lee Y and Kim Y Real-time collision culling of a million bodies on graphics processing units ACM SIGGRAPH Asia 2010 papers, (1-8)
- Parker E and O'Brien J Real-time deformation and fracture in a game environment Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (165-175)
- Otaduy M, Igarashi T and LaViola J Interaction ACM SIGGRAPH 2009 Courses, (1-66)
- Woulfe M and Manzke M A framework for benchmarking interactive collision detection Proceedings of the 25th Spring Conference on Computer Graphics, (205-212)
- Boeing A and Bräunl T Evaluation of real-time physics simulation systems Proceedings of the 5th international conference on Computer graphics and interactive techniques in Australia and Southeast Asia, (281-288)
- Hadap S, Cani M, Lin M, Kim T, Bertails F, Marschner S, Ward K and Kačić-Alesić Z Strands and hair ACM SIGGRAPH 2007 courses, (1-150)
- Glencross M, Chalmers A, Lin M, Otaduy M and Gutierrez D Exploiting perception in high-fidelity virtual environments (Additional presentations from the 24th course are available on the citation page) ACM SIGGRAPH 2006 Courses, (1-es)
- Hadap S Oriented strands Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, (91-100)
- Rodrigues T, Pires R and Dias J D4MD Proceedings of the 2005 ACM SIGCHI International Conference on Advances in computer entertainment technology, (330-333)
- Govindaraju N, Knott D, Jain N, Kabul I, Tamstorf R, Gayle R, Lin M and Manocha D Interactive collision detection between deformable models using chromatic decomposition ACM SIGGRAPH 2005 Papers, (991-999)
- Otaduy M and Lin M Introduction to haptic rendering ACM SIGGRAPH 2005 Courses, (3-es)
- Govindaraju N, Knott D, Jain N, Kabul I, Tamstorf R, Gayle R, Lin M and Manocha D (2005). Interactive collision detection between deformable models using chromatic decomposition, ACM Transactions on Graphics, 24:3, (991-999), Online publication date: 1-Jul-2005.
- Acosta L, Toledo J, Sigut M, Marichal G, Mendez J and Torres S Studying the stability of a four rotor helicopter prototype using the lifting operators Proceedings of the 4th WSEAS International Conference on Systems Theory and Scientific Computation, (1-6)
- Kim Y, Otaduy M, Lin M and Manocha D Fast penetration depth computation for physically-based animation Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, (23-31)
- Hoff K, Zaferakis A, Lin M and Manocha D Fast and simple 2D geometric proximity queries using graphics hardware Proceedings of the 2001 symposium on Interactive 3D graphics, (145-148)
- Mirtich B Timewarp rigid body simulation Proceedings of the 27th annual conference on Computer graphics and interactive techniques, (193-200)
- Baraff D and Witkin A Large steps in cloth simulation Proceedings of the 25th annual conference on Computer graphics and interactive techniques, (43-54)
- Cani-Gascuel M and Desbrun M (1997). Animation of Deformable Models Using Implicit Surfaces, IEEE Transactions on Visualization and Computer Graphics, 3:1, (39-50), Online publication date: 1-Jan-1997.
- Ponamgi M, Manocha D and Lin M (1997). Incremental Algorithms for Collision Detection Between Polygonal Models, IEEE Transactions on Visualization and Computer Graphics, 3:1, (51-64), Online publication date: 1-Jan-1997.
- Ponamgi M, Manocha D and Lin M Incremental algorithms for collision detection between solid models Proceedings of the third ACM symposium on Solid modeling and applications, (293-304)
- Gascuel M An implicit formulation for precise contact modeling between flexible solids Proceedings of the 20th annual conference on Computer graphics and interactive techniques, (313-320)
- Baraff D and Witkin A Dynamic simulation of non-penetrating flexible bodies Proceedings of the 19th annual conference on Computer graphics and interactive techniques, (303-308)
- Baraff D and Witkin A (1992). Dynamic simulation of non-penetrating flexible bodies, ACM SIGGRAPH Computer Graphics, 26:2, (303-308), Online publication date: 1-Jul-1992.
Index Terms
- Dynamic simulation of nonpenetrating rigid bodies
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