Star-contours for efficient hierarchical self-collision detection

Abstract

Collision detection is a problem that has often been addressed efficiently with the use of hierarchical culling data structures. In the subproblem of self-collision detection for triangle meshes, however, such hierarchical data structures lose much of their power, because triangles adjacent to each other cannot be distinguished from actually colliding ones unless individually tested. Shape regularity of surface patches, described in terms of orientation and contour conditions, was proposed long ago as a culling criterion for hierarchical self-collision detection. However, to date, algorithms based on shape regularity had to trade conservativeness for efficiency, because there was no known algorithm for efficiently performing 2D contour self-intersection tests.In this paper, we introduce a star-contour criterion that is amenable to hierarchical computations. Together with a thorough analysis of the tree traversal process in hierarchical self-collision detection, it has led us to novel hierarchical data structures and algorithms for efficient yet conservative self-collision detection. We demonstrate the application of our algorithm to several example animations, and we show that it consistently outperforms other approaches.

Energy-based self-collision culling for arbitrary mesh deformations

“…In contrast, our certificates can efficiently cull self-collision tests even in areas of non-smooth geometry (like [Barbič and James 2010]), and, furthermore, we can cull patches with nonsmooth deformations. Curvature-based culling also requires a potentially expensive "contour test" for correctness, but recently it was shown how this could be performed efficiently using "Star Contours" [Schvartzman et al 2010]. In comparisons provided later ( §8), we observe larger speedups using ESCC on the same examples.…”

“…Numerous results and statistics are shown in Table 1 for a range of animated mesh examples, including ones made by us and from prior works [Briceño et al 2003;James and Twigg 2005;Barbič and James 2010;Schvartzman et al 2010;Curtis et al 2008]. Please see the supplemental video for animations and detailed performance information.…”

“…For example, methods based on chromatic decompositions [Govindaraju et al 2005a] and representative triangles [Curtis et al 2008] can effectively reduce the number of redundant low-level triangle overlap tests. Curvature tests [Volino and Magnenat-Thalmann 1994;Schvartzman et al 2010] and normal bounds [Provot 1997;Grinspun and Schröder 2001;Tang et al 2009;Schvartzman et al 2009] can also cull overlap tests in potentially large regions, however, unlike ESCC, these methods can only cull effectively in regions with smooth geometry and smooth deformations. In contrast, our certificates can efficiently cull self-collision tests even in areas of non-smooth geometry (like [Barbič and James 2010]), and, furthermore, we can cull patches with nonsmooth deformations.…”

“…The lowest speedups are for examples with significant interpenetration or dynamic close-proximity scenarios as indicated by the culling difficulty measure defined as the ratio of the number of inter-node overlap tests between disconnected leaf nodes to the total number of leaf nodes. Examples from prior work are indicated using † for [Schvartzman et al 2010], ‡ for [Barbič and James 2010], for [Briceño et al 2003;James and Twigg 2005], and • for [Curtis et al 2008].…”

“…We evaluated ESCC on challenging datasets from "Star Contours" [Schvartzman et al 2010]. In comparison, we always observe larger speedups than "Star Contours" method; the speedups compared as (StarContours|ESCC) are: bunny lowres (1.8x|5.5x), bunny highres (2.2x|4.2x), bunnynoisy (1.1x|3.3x), bunny spiky (0.83x|2.0x), cloth (1.5x|4.5x) horse (1.05x|1.4x), and cat (1.2x|4.1x).…”