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The normal parameterization and its application to collision detection

Römer, Ulrich J. ORCID iD icon 1; Fidlin, Alexander 1; Seemann, Wolfgang 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)


Collision detection is a central task in the simulation of multibody systems. Depending on the description of the geometry, there are many efficient algorithms to address this need. A widespread approach is the common normal concept: potential contact points on opposing surfaces have antiparallel normal vectors. However, this approach leads to implicit equations that require iterative solutions when the geometries are described by implicit functions or the common parameterizations. We introduce the normal parameterization to describe the boundary of a strictly convex object as a function of the orientation of its normal vector. This parameterization depends on a scalar function, the so-called generating potential from which all properties are derived: points on the boundary, continuity/differentiability of the boundary, curvature, offset curves or surfaces. An explicit solution for collisions with a planar counterpart is derived and four iterative algorithms for collision detection between two arbitrary objects with the normal parametrization are compared. The application of this approach for collision detection in multibody models is illustrated in a case study with two ellipsoids and several planes.

Postprint §
DOI: 10.5445/IR/1000118630
Veröffentlicht am 24.04.2021
DOI: 10.1016/j.mechmachtheory.2020.103906
Zitationen: 5
Web of Science
Zitationen: 5
Zitationen: 5
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 09.2020
Sprache Englisch
Identifikator ISSN: 0094-114X
KITopen-ID: 1000118630
Erschienen in Mechanism and machine theory
Verlag Elsevier
Band 151
Seiten Art.-Nr.: 103906
Vorab online veröffentlicht am 23.04.2020
Nachgewiesen in Dimensions
Web of Science
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