Choosing nodes in parametric curve interpolation
Computer-Aided Design
Parameter optimization in approximating curves and surfaces to measurement data
Computer Aided Geometric Design
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd 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
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Family of projected descent methods for optimization problems with simple bounds
Journal of Optimization Theory and Applications
Advanced surface fitting techniques
Computer Aided Geometric Design
Newton's Method for Large Bound-Constrained Optimization Problems
SIAM Journal on Optimization
Journal of Global Optimization
IEEE Transactions on Visualization and Computer Graphics
Total least squares fitting of Bézier and B-spline curves to ordered data
Computer Aided Geometric Design
Meshless Parameterization and B-Spline Surface Approximation
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Reconstruction of B-Spline Surfaces from Scattered Data Points
CGI '00 Proceedings of the International Conference on Computer Graphics
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
On the design of optimisers for surface reconstruction
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Monotone piecewise rational cubic interpolation
International Journal of Computer Mathematics
Automatic knot adjustment using an artificial immune system for B-spline curve approximation
Information Sciences: an International Journal
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
Information Sciences: an International Journal
Computing optimized curves with NURBS using evolutionary intelligence
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
A triangulation-based hole patching method using differential evolution
Computer-Aided Design
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Curve or surface reconstruction is a challenging problem in the fields of engineering design, virtual reality, film making and data visualization. Non-uniform rational B-spline (NURBS) fitting has been applied to curve and surface reconstruction for many years because it is a flexible method and can be used to build many complex mathematical models, unlike certain other methods. To apply NURBS fitting, there are two major difficult sub-problems that must be solved: (1) the determination of a knot vector and (2) the computation of weights and the parameterization of data points. These two problems are quite challenging and determine the effectiveness of the overall NURBS fit. In this study, we propose a new method, which is a combination of a hybrid optimization algorithm and an iterative scheme (with the acronym HOAAI), to address these difficulties. The novelties of our proposed method are the following: (1) it introduces a projected optimization algorithm for optimizing the weights and the parameterization of the data points, (2) it provides an iterative scheme to determine the knot vectors, which is based on the calculated point parameterization, and (3) it proposes the boundary-determined parameterization and the partition-based parameterization for unorganized points. We conduct numerical experiments to measure the performance of the proposed HOAAI with six test problems, including a complicated curve, twisted and singular surfaces, unorganized data points and, most importantly, real measured data points from the Mashan Pumped Storage Power Station in China. The simulation results show that the proposed HOAAI is very fast, effective and robust against noise. Furthermore, a comparison with other approaches indicates that the HOAAI is competitive in terms of both accuracy and runtime costs.