Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Testing approximate symmetry in the plane is NP-hard
MFCS '89 Selected papers of the symposium on Mathematical foundations of computer science
Estimating 3-D rigid body transformations: a comparison of four major algorithms
Machine Vision and Applications - Special issue on performance evaluation
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate symmetry detection for reverse engineering
Proceedings of the sixth ACM symposium on Solid modeling and applications
Symmetry as a Continuous Feature
IEEE Transactions on Pattern Analysis and Machine Intelligence
On finding maximum-cardinality symmetric subsets
Computational Geometry: Theory and Applications - Special issue on Discrete and computational geometry
Approximate Congruence Detection of Model Features for Reverse Engineering
SMI '03 Proceedings of the Shape Modeling International 2003
Testing congruence and symmetry for general 3-dimensional objects
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Detecting design intent in approximate CAD models using symmetry
Computer-Aided Design
A feature-based method of rapidly detecting global exact symmetries in CAD models
Computer-Aided Design
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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.