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
Comments on "Symmetry as a Continuous Feature"
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Approximate symmetry detection for reverse engineering
Proceedings of the sixth ACM symposium on Solid modeling and applications
Removal of blends from boundary representation models
Proceedings of the seventh ACM symposium on Solid modeling and applications
Constrained fitting in reverse engineering
Computer Aided Geometric Design
Hierarchical Decomposition and Axial Shape Description
IEEE Transactions on Pattern Analysis and Machine Intelligence
3-D Object Recognition with Symmetric Models: Symmetry Extraction and Encoding
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Edge-Based Identification of DP-Features on Free-Form Solids
IEEE Transactions on Pattern Analysis and Machine Intelligence
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Detecting approximate incomplete symmetries in discrete point sets
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Detecting approximate symmetries of discrete point subsets
Computer-Aided Design
Standardized data exchange of CAD models with design intent
Computer-Aided Design
Feature-based reverse modeling strategies
Computer-Aided Design
Towards the standardized exchange of parameterized feature-based CAD models
Computer-Aided Design
Frontal geometry from sketches of engineering objects: is line labelling necessary?
Computer-Aided Design
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Geometric constraints within feature hierarchies
Computer-Aided Design
A generative theory of shape
Constructing regularity feature trees for solid models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
A method for reconstructing sketched polyhedral shapes with rounds and fillets
SG'10 Proceedings of the 10th international conference on Smart graphics
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Towards locally and globally shape-aware reverse 3D modeling
Computer-Aided Design
A feature-based method of rapidly detecting global exact symmetries in CAD models
Computer-Aided Design
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Finding design intent embodied as high-level geometric relations between a CAD model's sub-parts facilitates various tasks such as model editing and analysis. This is especially important for boundary-representation models arising from, e.g., reverse engineering or CAD data transfer. These lack explicit information about design intent, and often the intended geometric relations are only approximately present. A novel solution to this problem is presented based on detecting approximate local incomplete symmetries, in a hierarchical decomposition of the model into simpler, more symmetric sub-parts. Design intent is detected as congruencies, symmetries and symmetric arrangements of the leaf-parts in this decomposition. All elementary 3D symmetry types and common symmetric arrangements are considered. They may be present only locally in subsets of the leaf-parts, and may also be incomplete, i.e. not all elements required for a symmetry need be present. Adaptive tolerance intervals are detected automatically for matching inter-point distances, enabling efficient, robust and consistent detection of approximate symmetries. Doing so avoids finding many spurious relations, reliably resolves ambiguities between relations, and reduces inconsistencies. Experiments show that detected relations reveal significant design intent.