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
Context-free attentional operators: the generalized symmetry transform
International Journal of Computer Vision - Special issue on qualitative vision
Comments on "Symmetry as a Continuous Feature"
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry Detection by Generalized Complex (GC) Moments: A Close-Form Solution
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
Accurate detection of symmetries in 3D shapes
ACM Transactions on Graphics (TOG)
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Towards the standardized exchange of parameterized feature-based CAD models
Computer-Aided Design
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Constructing regularity feature trees for solid models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Detecting symmetry and symmetric constellations of features
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
A new possibility for pattern recognition independently from geometrical measuresetrical measures
ICOSSSE'08 Proceedings of the 7th WSEAS international conference on System science and simulation in engineering
Detecting design intent in approximate CAD models using symmetry
Computer-Aided Design
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
A feature-based method of rapidly detecting global exact symmetries in CAD models
Computer-Aided Design
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Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundary-representation (B-rep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the model to improve its shape, to simplify its analysis, or to constrain it during editing. We give an algorithm to detect local approximate symmetries in a discrete point set derived from a B-rep model: the output comprises the model's potential local symmetries at various automatically detected tolerance levels. Non-trivial symmetries of subsets of the point set are found as unambiguous permutation cycles, i.e. vertices of an approximately regular polygon or an anti-prism, which are sufficiently separate from other points in the point set. The symmetries are detected using a rigorous, tolerance-controlled, incremental approach, which expands symmetry seed sets by one point at a time. Our symmetry cycle detection approach only depends on inter-point distances. The algorithm takes time O(n^4) where n is the number of input points. Results produced by our algorithm are demonstrated using a variety of examples.