kDet: Parallel Constant Time Collision Detection for Polygonal Objects

We define a novel geometric predicate and a class of objects that enables us to prove a linear bound on the number of intersecting polygon pairs for colliding 3D objects in that class. Our predicate is relevant both in theory and in practice: it is easy to check and it needs to consider only the geo...

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Veröffentlicht in:Computer graphics forum Jg. 36; H. 2; S. 131 - 141
Hauptverfasser: Weller, René, Debowski, Nicole, Zachmann, Gabriel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.05.2017
Schlagworte:
3-D graphics
Algorithms
Categories and Subject Descriptors (according to ACM CCS)
Complexity
Computer graphics
Data structures
Deformation
Formability
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
Object recognition
Parallel processing
Polygons
Run time (computers)
Topological manifolds
Triangles
ISSN:0167-7055, 1467-8659
Online-Zugang:Volltext
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Zusammenfassung:We define a novel geometric predicate and a class of objects that enables us to prove a linear bound on the number of intersecting polygon pairs for colliding 3D objects in that class. Our predicate is relevant both in theory and in practice: it is easy to check and it needs to consider only the geometric properties of the individual objects – it does not depend on the configuration of a given pair of objects. In addition, it characterizes a practically relevant class of objects: we checked our predicate on a large database of real‐world 3D objects and the results show that it holds for all but the most pathological ones. Our proof is constructive in that it is the basis for a novel collision detection algorithm that realizes this linear complexity also in practice. Additionally, we present a parallelization of this algorithm with a worst‐case running time that is independent of the number of polygons. Our algorithm is very well suited not only for rigid but also for deformable and even topology‐changing objects, because it does not require any complex data structures or pre‐processing. We have implemented our algorithm on the GPU and the results show that it is able to find in real‐time all colliding polygons for pairs of deformable objects consisting of more than 200k triangles, including self‐collisions.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13113