Hyperbolic Polynomial Uniform B-Spline with Shape Parameter

2005 ◽  
Vol 16 (4) ◽  
pp. 625 ◽  
Author(s):  
Wen-Tao WANG
Keyword(s):  
Shape Parameter ◽  
Hyperbolic Polynomial ◽  
B Spline

Hyperbolic polynomial uniform B-spline curves and surfaces with shape parameter

2010 ◽  
Vol 72 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Liu Xumin ◽  
Xu Weixiang ◽  
Guan Yong ◽  
Shang Yuanyuan
Keyword(s):  
Shape Parameter ◽  
Hyperbolic Polynomial ◽  
B Spline ◽  
Curves And Surfaces ◽  
Spline Curves

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.

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.

scholarly journals Shape Designing Using Quadratic Trigonometric B-Spline Curves

2019 ◽  
Vol 3 (2) ◽  
pp. 36-49
Author(s):  
Amna Abdul Sittar ◽  
Abdul Majeed ◽  
Abd Rahni Mt Piah
Keyword(s):  
Shape Parameter ◽  
Control Points ◽  
B Spline ◽  
Spline Curves ◽  
Computer Aided ◽  
And Control

The B-spline curves, particularly trigonometric B-spline curves, have attained remarkable significance in the field of Computer Aided Geometric Designing (CAGD). Different researchers have developed different interpolants for shape designing using Ball, Bezier and ordinary B-spline. In this paper, quadratic trigonometric B-spline (piecewise) curve has been developed using a new basis for shape designing. The proposed method has one shape parameter which can be used to control and change the shape of objects. Different objects like flower, alphabet and vase have been designed using the proposed method. The effects of shape parameter and control points have been discussed also.

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.

scholarly journals Cubic B-Spline Curves with Shape Parameter and Their Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Houjun Hang ◽  
Xing Yao ◽  
Qingqing Li ◽  
Michel Artiles
Keyword(s):  
Basis Function ◽  
Shape Parameter ◽  
Engineering Application ◽  
Shape Design ◽  
Control Points ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Smooth Connection

The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application.

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