Analytical methods for dynamic simulation of non-penetrating rigid bodies
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
How to simulate billiards and similar systems
Journal of Computational Physics
Impulse-based simulation of rigid bodies
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Rigid-Body Dynamics with Friction and Impact
SIAM Review
Realistic animation of rigid bodies
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Robust treatment of collisions, contact and friction for cloth animation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Nonconvex rigid bodies with stacking
ACM SIGGRAPH 2003 Papers
Convex Optimization
Fast frictional dynamics for rigid bodies
ACM SIGGRAPH 2005 Papers
ACM SIGGRAPH 2005 Papers
Particle-based simulation of granular materials
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Mathematical Programming: Series A and B
Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3-D Technology) (The Morgan Kaufmann Series in Interactive 3D Technology)
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Velocity-based shock propagation for multibody dynamics animation
ACM Transactions on Graphics (TOG)
Robust treatment of simultaneous collisions
ACM SIGGRAPH 2008 papers
Staggered projections for frictional contact in multibody systems
ACM SIGGRAPH Asia 2008 papers
Free-flowing granular materials with two-way solid coupling
ACM SIGGRAPH Asia 2010 papers
SPH granular flow with friction and cohesion
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Numerical methods for linear complementarity problems in physics-based animation
ACM SIGGRAPH 2013 Courses
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Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.