Two Kinds of Trigonometric Spline Curves with Shape Parameter

2009 ◽  
Author(s):  
LanLan Yan ◽  
JiongFeng Liang ◽  
GuoGen Wu
Keyword(s):  
Shape Parameter ◽  
Spline Curves ◽  
Trigonometric Spline

Cubic TP B-Spline Curves with a Shape Parameter

2013 ◽  
Vol 11 ◽  
pp. 59-72 ◽  
Author(s):  
Mridula Dube ◽  
Reenu Sharma
Keyword(s):  
Tensor Product ◽  
Shape Parameter ◽  
Control Points ◽  
Shape Parameters ◽  
Special Shape ◽  
B Spline ◽  
Control Polygon ◽  
Spline Curves ◽  
Trigonometric Spline ◽  
The Given

In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

A subdivision algorithm for trigonometric spline curves

2002 ◽  
Vol 19 (1) ◽  
pp. 71-88 ◽  
Author(s):  
M.K. Jena ◽  
P. Shunmugaraj ◽  
P.C. Das
Keyword(s):  
Spline Curves ◽  
Trigonometric Spline ◽  
Subdivision Algorithm

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.

Shape-Preserving Positive Trigonometric Spline Curves

2016 ◽  
Vol 42 (2) ◽  
pp. 763-775
Author(s):  
Malik Zawwar Hussain ◽  
Farsia Hussain ◽  
Muhammad Sarfraz
Keyword(s):  
Shape Preserving ◽  
Spline Curves ◽  
Trigonometric Spline

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 Trigonometric Nonuniform Spline Curves and Surfaces

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Lanlan Yan
Keyword(s):  
Shape Parameter ◽  
Basis Functions ◽  
Surfaces Of Revolution ◽  
Local Shape ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Totally Positive ◽  
Positive Property ◽  
Spline Basis ◽  
Representation Scheme

A class of cubic trigonometric nonuniform spline basis functions with a local shape parameter is constructed. Their totally positive property is proved. The associated spline curves inherit most properties of usual polynomialB-spline curves and enjoy some other advantageous properties for engineering design. They haveC2continuity at single knots. For equidistant knots, they haveC3continuity andC5continuity for particular choice of shape parameter. They can express freeform curves as well as ellipses. The associated spline surfaces can exactly represent the surfaces of revolution. Thus the curve and surface representation scheme unifies the representation of freeform shape and some analytical shapes, which is popular in engineering.

Sign in / Sign up

Export Citation Format

Share Document