Reconstruction of B-spline surfaces from scattered data points

This paper looks in the effectiveness of bicubic B-spline surface fitting and radial basis function, specifically the thin plate spline surface fitting in constructing the surface from the set of scattered data three dimensions (3D) points. Modification of the B-spline approximation algorithm is used to determine the unknown B-spline control points, followed by the construction of the bicubic B-spline surface patch, which can be joined together to form the final surface. The non-interpolation scheme of thin plate spline is also used to fit the data points in this study. The sample of scattered data points is chosen from a specific region in the point set model by using k-nearest neighbour search method. Observation is further carried out to observe the effect of noise in the bicubic B-spline surface fitting and the thin plate spline surface fitting. From the visual aspect, non-interpolation scheme of thin plate spline fits the surface better than bicubic B-spline in the presence of noises.

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Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme

Journal of Science and Technology Issue on Information and Communications Technology ◽

10.31130/jst.2017.41 ◽

2017 ◽

Vol 3 (1) ◽

pp. 82

Author(s):

Nga Le-Thi-Thu ◽

Khoi Nguyen-Tan ◽

Thuy Nguyen-Thanh

Keyword(s):

Free Form ◽

Subdivision Scheme ◽

B Spline ◽

Geometric Fitting ◽

Arbitrary Topology ◽

Spline Surface ◽

Spline Surfaces ◽

Low Degree ◽

Data Points ◽

Free Form Surfaces

Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adjusted locally by a simple geometric fitting algorithm to increase the accuracy of the obtained B-spline. The reconstructed B-spline having the low degree along with arbitrary topology is interpolative to most of the given data points after some fitting steps without solving any linear system. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Results show that this approach is simple, fast, flexible and can be successfully applied to a variety of surface shapes.

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Parallel Hierarchical Genetic Algorithm for Scattered Data Fitting through B-Splines

Applied Sciences ◽

10.3390/app9112336 ◽

2019 ◽

Vol 9 (11) ◽

pp. 2336 ◽

Cited By ~ 1

Author(s):

Jose Edgar Lara-Ramirez ◽

Carlos Hugo Garcia-Capulin ◽

Maria de Jesus Estudillo-Ayala ◽

Juan Gabriel Avina-Cervantes ◽

Raul Enrique Sanchez-Yanez ◽

...

Keyword(s):

Genetic Algorithm ◽

Curve Fitting ◽

Fitness Function ◽

Scattered Data ◽

Model Parameters ◽

B Spline ◽

B Splines ◽

Scattered Data Fitting ◽

Data Points ◽

Hierarchical Genetic Algorithm

Curve fitting to unorganized data points is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of scattered and noisy data points, the goal is to construct a curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Although many papers have addressed the problem, this remains very challenging. In this paper we propose to solve the curve fitting problem to noisy scattered data using a parallel hierarchical genetic algorithm and B-splines. We use a novel hierarchical structure to represent both the model structure and the model parameters. The best B-spline model is searched using bi-objective fitness function. As a result, our method determines the number and locations of the knots, and the B-spline coefficients simultaneously and automatically. In addition, to accelerate the estimation of B-spline parameters the algorithm is implemented with two levels of parallelism, taking advantages of the new hardware platforms. Finally, to validate our approach, we fitted curves from scattered noisy points and results were compared through numerical simulations with several methods, which are widely used in fitting tasks. Results show a better performance on the reference methods.

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