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
A simple and efficient algorithm for determining the symmetries of polyhedra
CVGIP: Graphical Models and Image Processing
Data structures, algorithms, and performance
Data structures, algorithms, and performance
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Finding approximate shape regularities in reverse engineered solid models bounded by simple surfaces
Proceedings of the sixth ACM symposium on Solid modeling and applications
Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Finding approximate shape regularities in reverse engineered solid models bounded by simple surfaces
Proceedings of the sixth ACM symposium on Solid modeling and applications
Topological and geometric beautification of reverse engineered geometric models
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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
Reverse engineering of a symmetric object
Computers and Industrial Engineering
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
Symmetry-Aware Mesh Processing
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Feature-based reverse modeling strategies
Computer-Aided Design
Technical Section: An optimisation-based reconstruction engine for 3D modelling by sketching
Computers and Graphics
Detecting design intent in approximate CAD models using symmetry
Computer-Aided Design
Constructing regularity feature trees for solid models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Hi-index | 0.00 |
The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. B-rep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable B-rep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n 3.5 log4 n), and a justification is given that on common engineering objects it takes about O(n2 log4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.