M. Li, F. C. Langbein, R. R. Martin
In: Proc. ACM Symp. Solid and Physical Modeling,
pp. 335-340, ACM Siggraph 2007.
ISBN 1595936660.
[DOI: 10.1145/1236246.1236294] [Preprint] [CiteSeer]
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 well-defined, unambiguous approximate symmetries suitable for design intent detection, as demonstrated experimentally.
@INPROCEEDINGS{Li2007,
author = {Ming Li and Frank C. Langbein and Ralph R. Martin},
title = {Detecting Approximate Incomplete Symmetries in
Discrete Point Sets},
booktitle = {Proc. ACM Symposium Solid and Physical Modeling},
year = 2007,
pages = {335-340},
address = {New York, NY, USA},
publisher = {ACM Siggraph},
isbn = 1595936660,
doi = {10.1145/1236246.1236294},
url = {http://www.langbein.org/research/solids/did/li2007/},
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 well-defined, unambiguous
approximate symmetries suitable for design intent
detection, as demonstrated experimentally.},
}
Detecting Approximate Incomplete Symmetries in Discrete Point Sets,http://www.langbein.org/research/solids/did/li2007 by Frank C Langbein [ 6/December/2008, 19:26].
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