A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Curves and surfaces in computer aided geometric design
Curves and surfaces in computer aided geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Fair surface reconstruction from point clouds
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Advanced surface fitting techniques
Computer Aided Geometric Design
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Interpolation by geometric algorithm
Computer-Aided Design
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Weighted progressive iteration approximation and convergence analysis
Computer Aided Geometric Design
The convergence of the geometric interpolation algorithm
Computer-Aided Design
Generating B-spline curves with points, normals and curvature constraints: a constructive approach
The Visual Computer: International Journal of Computer Graphics
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors
IEEE Transactions on Visualization and Computer Graphics
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Recently, the use of B-spline curves/surfaces to fit point clouds by iteratively repositioning the B-spline's control points on the basis of geometrical rules has gained in popularity because of its simplicity, scalability, and generality. We distinguish between two types of fitting, interpolation and approximation. Interpolation generates a B-spline surface that passes through the data points, whereas approximation generates a B-spline surface that passes near the data points, minimizing the deviation of the surface from the data points. For surface interpolation, the data points are assumed to be in grids, whereas for surface approximation the data points are assumed to be randomly distributed. In this paper, an iterative geometric interpolation method, as well as an approximation method, which is based on the framework of the iterative geometric interpolation algorithm, is discussed. These two iterative methods are compared with standard fitting methods using some complex examples, and the advantages and shortcomings of our algorithms are discussed. Furthermore, we introduce two methods to accelerate the iterative geometric interpolation algorithm, as well as a method to impose geometric constraints, such as reflectional symmetry, on the iterative geometric interpolation process, and a novel fairing method for non-uniform complex data points. Complex examples are provided to demonstrate the effectiveness of the proposed algorithms.