Geometric Numerical Integration of Inequality Constrained Nonsmooth Hamiltonian Systems

Danny Kaufman, Dinesh Pai We consider the geometric numerical integration of Hamiltonian systems subject to both equality and “hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric methods for these cases has […]

Interpenetration Free Simulation of Thin Shell Rigid Bodies

R. Elliot English, Michael Lentine, Ron Fedkiw We propose a new algorithm for rigid body simulation that guarantees each body is in an interpenetration free state, both increasing the accuracy and robustness of the simulation as well as alleviating the need for ad hoc methods to separate bodies for subsequent simulation and rendering. We cleanly separate collision […]

Speculative Parallel Asynchronous Contact Mechanics

Samantha Ainsley, Etienne Vouga, Eitan Grinspun, Rasmus Tamstorf We extend the Asynchronous Contact Mechanics algorithm [Harmon et al. 2009] and improve its performance by two orders of magnitude, using only optimizations that do not compromise ACM’s three guarantees of safety, progress, and correctness. The key to this speedup is replacing ACM’s timid, forward-looking mechanism for detecting collisions—locating and […]

Energy-Based Self-Collision Culling for Arbitrary Mesh Deformations

Changxi Zheng, Doug James In this paper, we accelerate self-collision detection (SCD) for a deforming triangle mesh by exploiting the idea that a mesh cannot self collide unless it deforms enough. Unlike prior work on subspace self-collision culling which is restricted to low-rank deformation subspaces, our energy-based approach supports arbitrary mesh deformations while still being […]

Adaptive Image-Based Intersection Volume

Bin Wang, Francois Faure, Dinesh Pai A method for image-based contact detection and modeling, with guaranteed precision on the intersection volume, is presented. Unlike previous image-based methods, our method optimizes a non-uniform ray sampling resolution and allows precise control of the volume error. By cumulatively projecting all mesh edges into a generalized 2D texture, we […]

Reflections on Simultaneous Impact

Breannan Smith, Danny Kaufman, Etienne Vouga, Rasmus Tamstorf, Eitan Grinspun 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 […]

Interactive Editing of Deformable Simulations

Jernej Barbic, Funshing Sin, Eitan Grinspun We present an interactive animation editor for complex deformable object animations. Given an existing animation, the artist directly manipulates the deformable body at any time frame, and the surrounding animation immediately adjusts in response. The automatic adjustments are designed to respect physics, preserve detail in both the input motion […]

PolyDepth: Real-Time Penetration Depth Computation using Iterative Contact-Space Projection

Changsoo Je, Min Tang, Youngeun Lee, Minkyoung Lee, Young J. Kim We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid […]

Efficient Geometrically Exact Continuous Collision Detection

Tyson Brochu, Essex Edwards, Robert Bridson Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation […]

Continuous Penalty Forces

Min Tang, Dinesh Manocha, Miguel Otaduy, Ruofeng Tong We present a simple algorithm to compute continuous penalty forces to determine collision response between rigid and deformable models bounded by triangle meshes. Our algorithm provides a well-behaved solution in contrast to the traditional stability and robustness problems of penalty methods, induced by force discontinuities. We trace […]