scholarly journals Irregular Symmetrical Object Designed By Using Lambda Miu B-Spline Degree Four

2021 ◽  
Vol 2084 (1) ◽  
pp. 012018
Author(s):  
Nursyazni Binti Mohamad Sukri ◽  
Puteri Ainna Husna Binti Megat Mohd ◽  
Siti Musliha Binti Nor-Al-Din ◽  
Noor Khairiah Binti Razali
Keyword(s):  
Shape Parameter ◽  
B Spline ◽  
3 Dimensional ◽  
B Splines ◽  
Spline Curve ◽  
Geometry Design ◽  
Actual Volume ◽  
Symmetrical Object ◽  
Sweep Surface ◽  
Improved Methods

Abstract In Computer Aided Geometry Design (CAGD), B-splines curves are piecewise polynomial parametric curves that play an important role. CAGD involves the interpolation and approximation curves and surfaces. CAGD has been widely used which brings good impact of computers to industries in manufacturing. There are many improved methods in the B-spline curve such as extended cubic B-spline, trigonometric B-spline, quasi trigonometric B-spline, and λμ-B-spline. Each of the methods has its behaviour and advantage. In this paper, λμ-B-spline was used to be implemented in generating irregular symmetrical objects. λμ-B-spline has a shape parameter that can change the global shape by manipulating the value of the shape parameter. The bottle has been chosen as an irregular symmetrical object. The 2-dimensional symmetrical curves of Bottle design were formed by using λμ-B-spline degree 4. The curves designed are dependent on the shape parameter which can be adjusted. Then, the curves generated were revolved using the Sweep Surface method to form 3-dimensional objects. Every object has its volume and this research focused on the numerical method which was Simpson’s 3/8 to compute the volume. The volumes obtained were compared to the actual volume to determine the best shape parameter used. The results show that the λμ-B-spline curve with a shape parameter of 1 is the best shape parameter in designing symmetrical irregular objects with the desired volume.

The Quadratic Trigonometric B-Spline Curve with a Shape Parameter

2012 ◽  
Vol 468-471 ◽  
pp. 2463-2466 ◽  
Author(s):  
Jun Cheng Li ◽  
Guo Hua Chen ◽  
Lian Yang
Keyword(s):  
Shape Parameter ◽  
B Spline ◽  
Spline Curve ◽  
Control Polygon

A quadratic trigonometric B-spline curve analogous to the standard quadratic uniform B-spline curve, with a shape parameter, is presented in this work. The shape of the proposed curve can be adjusted by altering the value of the shape parameter while the control polygon is kept unchanged. With the shape parameter, the quadratic trigonometric B-spline curve can be closer to given polygon than the standard quadratic uniform B-spline curve. The proposed curve can be used to accurately represent the ellipse.

T-B Spline Curves with a Shape Parameter

2012 ◽  
Vol 241-244 ◽  
pp. 2144-2148
Author(s):  
Li Juan Chen ◽  
Ming Zhu Li
Keyword(s):  
Shape Parameter ◽  
Simple Structure ◽  
Control Points ◽  
Curve Segment ◽  
Closed Curves ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves

A T-B spline curves with a shape parameter λ is presented in this paper, which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the curves are C^2 continuous, but when the shape parameter λ equals to 0 , the curves are C^3 continuous. Moreover, this spline curve can be used to construct open and closed curves and can express ellipses conveniently.

Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization

2014 ◽  
Vol 903 ◽  
pp. 338-343
Author(s):  
Ali Munira ◽  
Nur Najmiyah Jaafar ◽  
Abdul Aziz Fazilah ◽  
Z. Nooraizedfiza
Keyword(s):  
Image Processing ◽  
Literature Review ◽  
Computer Aided Design ◽  
B Spline ◽  
B Splines ◽  
Curves And Surfaces ◽  
Geometry Design ◽  
Nurbs Curves ◽  
Computer Aided ◽  
Aided Design

This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have been conducted in optimizing the parameters in order to construct the intended curves and surfaces are highlighted in this paper.

scholarly journals Cubic Curve Fitting Method in Reconstruction of Chinese Calligraphy Outline

2021 ◽  
Vol 2084 (1) ◽  
pp. 012020
Author(s):  
Noor Khairiah Binti Razali ◽  
Nur Nabilah Binti Che Draman ◽  
Siti Musliha Binti Nor-Al-Din ◽  
Nursyazni Binti Mohamad Sukri
Keyword(s):  
Shape Parameter ◽  
Chinese Calligraphy ◽  
B Spline ◽  
3 Dimensional ◽  
Control Polygon ◽  
Cubic Curve ◽  
Fitting Method ◽  
Trigonometric Spline ◽  
Curve Fitting Method ◽  
Time Required

Abstract Curve plays a significant role in CAGD and brings the good impact of computers to manufacturing industries in designing 2 and 3-dimensional shapes and objects. Reconstruction of Chinese calligraphy outline based on the actual character is presented in this paper. Chinese calligraphy is the stylized artistic writings of Chinese characters. It is believed that this writing may help to express the feelings and ideas of the writers, which are difficult to be described. The shapes, smooth lines, and perfect curves are among the important qualities which are particularly emphasized in selecting good Chinese calligraphy. The Cubic B-Spline, Cubic Trigonometric Spline, and Cubic Trigonometric Bezier were used to generate the curves. The factors that have influenced the effects of the curves modifications were examined based on the changes of control polygon and the values of shape parameter. The fastest approach was then chosen by measuring the processing time required to construct the complete design. Results show the Cubic Trigonometric Bezier curve produced the closest curves to the control polygon, accurate to the actual character with λ = 1 and CPU time taken is 2.032 seconds. This is followed by Cubic Trigonometric Spline and Cubic B-Spline.

scholarly journals Two Extensions of the Quadratic Nonuniform B-Spline Curve with Local Shape Parameter Series

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xiang Kong ◽  
Jun Chen
Keyword(s):  
Line Segment ◽  
Shape Parameter ◽  
Linear Functions ◽  
Local Shape ◽  
B Spline ◽  
Numerical Examples ◽  
Spline Curve ◽  
Control Polygon ◽  
Tangent Direction ◽  
Special Case

Two extensions of the quadratic nonuniform B-spline curve with local shape parameter series, called the W3D3C1P2 spline curve and the W3D4C2P1 spline curve, are introduced in the paper. The new extensions not only inherit most excellent properties of the quadratic nonuniform B-spline curve but also can move locally toward or against the fixed control polygon by varying the shape parameter series. They are C1 and C2 continuous separately. Furthermore, the W3D3C1P2 spline curve includes the quadratic nonuniform B-spline curve as a special case. Two applications, the interpolation of the position and the corresponding tangent direction and the interpolation of a line segment, are discussed without solving a system of linear functions. Several numerical examples indicated that the new extensions are valid and can easily be applied.

A Fast Algorithm to Compute B-Splines and its Application in Curve Fitting

2008 ◽  
Vol 392-394 ◽  
pp. 743-749 ◽  
Author(s):  
Hai Yang Sun ◽  
M. Chai ◽  
Da Peng Fan
Keyword(s):  
Parallel Computing ◽  
Curve Fitting ◽  
Fast Algorithm ◽  
Spline Function ◽  
New Method ◽  
Spline Method ◽  
Computing Architecture ◽  
B Spline ◽  
B Splines ◽  
Spline Curve

B-spline method plays an important role in data interpolating, fitting and smoothing. Through analyzing the computed path of the de Boor-Cox algorithm, a new method for calculating B-spline function is given based on the vector extending operation. The proposed method has a parallel computing architecture and is suitable to realize by computers. Compared with the de Boor-Cox algorithm, the proposed method can improve computing efficiency by (2k+1) times in the task of calculating all nonzero values of k-degree B-spine functions. As an application in B-spline curve fitting, it shows that the proposed algorithm can reduce the computing efforts obviously.

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

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