scholarly journals Parameterization Method on B-Spline Curve

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
H. Haron ◽  
A. Rehman ◽  
D. I. S. Adi ◽  
S. P. Lim ◽  
T. Saba
Keyword(s):  
Computer Model ◽  
Basis Function ◽  
Real Object ◽  
Reconstruction Process ◽  
B Spline ◽  
Parameterization Method ◽  
Spline Basis ◽  
Data Points ◽  
Data Point ◽  
2D And 3D

The use of computer graphics in many areas allows a real object to be transformed into a three-dimensional computer model (3D) by developing tools to improve the visualization of two-dimensional (2D) and 3D data from series of data point. The tools involved the representation of 2D and 3D primitive entities and parameterization method using B-spline interpolation. However, there is no parameterization method which can handle all types of data points such as collinear data points and large distance of two consecutive data points. Therefore, this paper presents a new parameterization method that is able to solve those drawbacks by visualizing the 2D primitive entity of scanned data point of a real object and construct 3D computer model. The new method has improved a hybrid method by introducing exponential parameterization method in the beginning of the reconstruction process, followed by computing B-spline basis function to find maximum value of the function. The improvement includes solving a linear system of the B-spline basis function using numerical method. Improper selection of the parameterization method may lead to the singularity matrix of the system linear equations. The experimental result on different datasets show that the proposed method performs better in constructing the collinear and two consecutive data points compared to few parameterization methods.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

PB-Spline Hybrid Surface Fitting Technique

2009 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Large Scale ◽  
Free Form ◽  
Rectangular Array ◽  
B Spline ◽  
Large Scale Data ◽  
Spline Surface ◽  
Spline Basis ◽  
Data Points ◽  
Free Form Surfaces ◽  
Scale Data

This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization of tensor product splines, are adopted. The basic idea of this paper is to fit large scale data with a tensorial B-spline surface and to refine the surface until a specified tolerance is met. Since some isolated domains exceeding tolerance may result, detail features on these domains are modeled by a tensorial B-spline basis with a finer resolution, superimposed by employing the PB-spline approach. The present method leads to an efficient model of free form surfaces, since both large scale data and local geometrical details can be efficiently fitted. Two application examples are presented. The first one concerns the fitting of a set of data points sampled from an interior car trim with a central geometrical detail. The second one refers to the modification of the tensorial B-spline surface representation of a mould in order to create a local adjustment. Considerations regarding strengths and limits of the approach then follow.

Creating smooth SI. B-spline basis function representations of insulin sensitivity

2018 ◽  
Vol 44 ◽  
pp. 270-278
Author(s):  
Kent W. Stewart ◽  
Christopher G. Pretty ◽  
Geoffrey M. Shaw ◽  
J. Geoffrey Chase
Keyword(s):  
Insulin Sensitivity ◽  
Basis Function ◽  
B Spline ◽  
Spline Basis

A COMPARISON STUDY BETWEEN B-SPLINE SURFACE FITTING AND RADIAL BASIS FUNCTION SURFACE FITTING ON SCATTERED POINTS

2016 ◽  
Vol 78 (6-5) ◽  
Author(s):  
Liew Khang Jie ◽  
Ahmad Ramli ◽  
Ahmad Abd. Majid
Keyword(s):  
Radial Basis Function ◽  
Thin Plate ◽  
Basis Function ◽  
Scattered Data ◽  
Surface Fitting ◽  
Thin Plate Spline ◽  
Interpolation Scheme ◽  
B Spline ◽  
Spline Surface ◽  
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.  

A Novel Adaptive GA-based B-spline Curve Interpolation Method

2019 ◽  
Vol 13 (3) ◽  
pp. 289-304
Author(s):  
Maozhen Shao ◽  
Liangchen Hu ◽  
Huahao Shou ◽  
Jie Shen
Keyword(s):  
Genetic Algorithm ◽  
Traditional Method ◽  
Interpolation Method ◽  
Tangent Vector ◽  
Adaptive Genetic Algorithm ◽  
B Spline ◽  
Spline Curve ◽  
Curve Interpolation ◽  
Data Points ◽  
Data Point

Background: Curve interpolation is very important in engineering such as computer aided design, image analysis and NC machining. Many patents on curve interpolation have been invented. Objective: Since different knot vector configuration and data point parameterization can generate different shapes of an interpolated B-spline curve, the goal of this paper is to propose a novel adaptive genetic algorithm (GA) based interpolation method of B-spline curve. Method: Relying on geometric features owned by the data points and the idea of genetic algorithm which liberalizes the knots of B-spline curve and the data point parameters, a new interpolation method of B-spline curve is proposed. In addition, the constraint of a tangent vector is also added to ensure that the obtained B-spline curve can approximately satisfy the tangential constraint while ensuring strict interpolation. Results: Compared with the traditional method, this method realizes the adaptive knot vector selection and data point parameterization. Therefore, the interpolation result was better than the traditional method to some extent, and the obtained curve was more natural. Conclusion: The proposed method is effective for the curve reconstruction of any scanned data point set under tangent constraints. Meanwhile, this paper put forward a kind of tangent calculation method of discrete data points, where users can also set the tangent of each data point in order to get more perfect interpolation results.

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