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.

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.

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.

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.

PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS

2012 ◽  
Vol 12 (04) ◽  
pp. 1250028
Author(s):  
MRIDULA DUBE ◽  
REENU SHARMA
Keyword(s):  
Trigonometric Polynomial ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curve ◽  
Control Polygon ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Polynomial Curve ◽  
Trigonometric Spline ◽  
The Given

Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

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.

scholarly journals Local Convexity-PreservingC2Rational Cubic Spline for Convex Data

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Jamaludin Md. Ali
Keyword(s):  
Shape Parameter ◽  
Cubic Spline ◽  
Convex Curve ◽  
Shape Feature ◽  
Local Convexity ◽  
Shape Parameters ◽  
Numerical Examples ◽  
2D Data ◽  
Industrial Demand ◽  
Made In

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data usingC2rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.

An additional branch free algebraic B-spline curve fitting method

2010 ◽  
Vol 26 (6-8) ◽  
pp. 801-811 ◽  
Author(s):  
Mingxiao Hu ◽  
Jieqing Feng ◽  
Jianmin Zheng
Keyword(s):  
Curve Fitting ◽  
B Spline ◽  
Spline Curve ◽  
Fitting Method ◽  
Additional Branch ◽  
Curve Fitting Method
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