Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
The NURBS book
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Self-organizing maps
Conformal mapping for the parameterization of surfaces to fit range data
GMCAD '96 Proceedings of the fifth IFIP TC5/WG5.2 international workshop on geometric modeling in computer aided design on Product modeling for computer integrated design and manufacture
Global reparametrization for curve approximation
Computer Aided Geometric Design
Automatic Mesh Generation: Applications to Finite Element Methods
Automatic Mesh Generation: Applications to Finite Element Methods
Adaptive Parameterization for Reconstruction of 3D Freeform Objects from Laser-Scanned Data
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Approximating Digital 3D Shapes by Rational Gaussian Surfaces
IEEE Transactions on Visualization and Computer Graphics
Extending Neural Networks for B-Spline Surface Reconstruction
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Interpolating scattered data using 2D self-organizing feature maps
Graphical Models
Functional networks for B-spline surface reconstruction
Future Generation Computer Systems - Special issue: Computer graphics and geometric modeling
Differentials-based segmentation and parameterization for point-sampled surfaces
Journal of Computer Science and Technology
Particle Swarm Optimization for Bézier Surface Reconstruction
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Automatic Order of Data Points in RE Using Neural Networks
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Automatic sequence of 3D point data for surface fitting using neural networks
Computers and Industrial Engineering
Functional networks for B-spline surface reconstruction
Future Generation Computer Systems
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Information Sciences: an International Journal
Quasi-interpolants based multilevel b-spline surface reconstruction from scattered data
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Information Sciences: an International Journal
The calculation of parametric NURBS surface interval values using neural networks
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Surface creation on unstructured point sets using neural networks
Computer-Aided Design
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Reverse engineering ordinarily uses laser scanners since they can sample 3D data quickly and accurately relative to other systems. These laser scanner systems, however, yield an enormous amount of irregular and scattered digitized point data that requires intensive reconstruction processing. Reconstruction of freeform objects consists of two main stages: 1) parameterization and 2) surface fitting. Selection of an appropriate parameterization is essential for topology reconstruction as well as surface fitness. Current parameterization methods have topological problems that lead to undesired surface fitting results, such as noisy self-intersecting surfaces. Such problems are particularly common with concave shapes whose parametric grid is self-intersecting, resulting in a fitted surface that considerably twists and changes its original shape. In such cases, other parameterization approaches should be used in order to guarantee non-self-intersecting behavior. The parameterization method described in this paper is based on two stages: 1) 2D initial parameterization and 2) 3D adaptive parameterization. Two methods were developed for the first stage: Partial Differential Equation (PDE) parameterization and neural network Self Organizing Maps (SOM) parameterization. PDE parameterization yields a parametric grid without self-intersections. Neural network SOM parameterization creates a grid where all the sampled points, not only the boundary points, affect the grid, leading to a uniform and smooth surface. In the second stage, a 3D base surface was created and then adaptively modified. To this end, the Gradient Descent Algorithm (GDA) and Random Surface Error Correction (RSEC), both of which are iterative surface fitting methods, were developed and implemented. The feasibility of the developed parameterization methods and fitting algorithms is demonstrated on several examples using sculptured free objects.