Efficient geometrically exact continuous collision detection

Abstract

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 tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.

Multimaterial mesh-based surface tracking

“…Exact CCD only provably guarantees collision detection; floating point precision hinders true guarantees on response in degenerate scenarios [Brochu et al 2012]. Hence our topological operations are truly safe or canceled, but impulsive response [Bridson et al 2002;Harmon et al 2008] applied after time integration has no theoretical guarantees; we observed no failures.…”

“…We apply exact continuous collision detection (CCD) [Brochu et al 2012], and resolve collisions using the method of Bridson et al [2002] as extended by Harmon et al [2008]. Our enforcement of an intersection-free invariant is crucial: subsequent steps rely on it to ensure that remeshing and topology changes are performed safely and successfully, following the general strategy of Brochu and Bridson [2009].…”

Efficient and robust strain limiting and treatment of simultaneous collisions with semidefinite programming

“…Continuous collision detection (CCD) methods are widely used to detect collisions and intersections in cloth, hair, and thin sheet simulations. Brochu et al [11] proposed a volume-based geometric predictor, and Tang et al [12] proposed a Bernstein sign classification (BSC) based predictor, both of which can provide exact collision results by taking advantage of exact geometric arithmetic. Wang [13] introduced error analysis into a traditional cubic solver for CCD to achieve conservative but acceptable collision results.…”

View-Dependent Adaptive Cloth Simulation with Buckling Compensation

“…Adaptive refinement and simplification techniques have also been proposed for massspring systems [7], articulated bodies [8] and finite element models [9]. Most relevant to our work are techniques for adaptive cloth simulation [10], [11], [12], [13], [14], which use remeshing to resolve detailed wrinkles and folds. The approach of Narain et al [14] has also been extended to efficiently model plastic deformation and sharp creases [15] as well as complex fracture patterns [16].…”