Detecting approximate incomplete symmetries in discrete point sets

Li, Ming, Langbein, Frank Curd ORCID: https://orcid.org/0000-0002-3379-0323 and Martin, Ralph Robert 2007. Detecting approximate incomplete symmetries in discrete point sets. Presented at: ACM Symposium on Solid and Physical Modeling, Beijing, China, 4-6 June 2007. Proceedings, SPM 2007 : ACM Symposium on Solid and Physical Modeling : Beijing, China, June 04-06, 2007. New York, USA: Association for Computing Machinery, pp. 335-340. 10.1145/1236246.1236294

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Abstract

Motivated by the need to detect design intent in approximate boundary representation models, we give an algorithm to detect incomplete symmetries of discrete points, giving the models' potential local symmetries at various automatically detected tolerances. Here, incomplete symmetry is defined as a set of incomplete cycles which are constructed by, e.g., a set of consecutive vertices of an approximately regular polygon, induced by a single isometry. All seven 3D elementary isometries are considered for symmetry detection. Incomplete cycles are first found using a tolerance-controlled point expansion approach. Subsequently, these cycles are clustered for incomplete symmetry detection. The resulting clusters have welldefined, unambiguous approximate symmetries suitable for design intent detection, as demonstrated experimentally.

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	approximate incomplete symmetry ; design intent ; reverse engineering
Publisher:	Association for Computing Machinery
ISBN:	9781595936660; 1595936661
Last Modified:	17 Oct 2022 09:41
URI:	https://orca.cardiff.ac.uk/id/eprint/5222

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