Fast and exact continuous collision detection with Bernstein sign classification

Abstract

We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bézier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. Our algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits.

A fast algebraic non-penetration filter for continuous collision detection

“…Moreover, the proposed filter is complementary to many prior broad culling algorithms for continuous collision detection such as dynamic BVHs [6], continuous normal cones [15], representative-triangles [13], etc. For error-sensitive applications, some complementary error-defending or exact algorithms [20,21] can be applied further.…”

“…An exact algorithm was presented in [19] to eliminates 99% elementary tests, but its computational cost is very high. Two recent work [20,21] handled exact CCD problem using error analysis and Bernstein sign classification. In [11], a sequence of simple feature-level filtering tests based on local conservative advancement are used to accelerate continuous collision detection for deforming triangles.…”

“…These filter are complementary to many broad stage culling algorithms for continuous collision detection such as dynamic BVHs [6], continuous normal cones [15], representative-triangles [13], error-defending algorithms [20], exact algorithm based on Bernstein sign classification [21], etc. [20] and [21] are used to handle numerical errors and rounding errors. They can be used in a succeeding stage.…”

A Simple Filtering Algorithm for Continuous Collision Detection Using Taylor Models

“…All variants of the algorithm can reduce the false positive ratios of elementary collision detection. Moreover, the proposed filtering algorithm is complementary to many prior broad culling algorithms for continuous collision detection such as dynamic BVHs [13], continuous normal cones [5], representative-triangles [10], exact continuous collision de- Table II. tection [11], [17], [18], etc.…”

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.…”