Shape control of curve design by weighted rational spline

1999 ◽  
Vol 6 (3) ◽  
pp. 537-547
Author(s):  
Qi Duan ◽  
Botang Li ◽  
K. Djidjeli ◽  
W. G. Price ◽  
E. H. Twizell
Keyword(s):  
Shape Control ◽  
Curve Design ◽  
Rational Spline

A method of shape control of curve design

2000 ◽  
Author(s):  
Qi Duan ◽  
T.S. Chen ◽  
K. Djidjeli ◽  
W.G. Price ◽  
E.H. Twizell
Keyword(s):  
Shape Control ◽  
Curve Design

α Extension of the Cubic Ball Curve

2012 ◽  
Vol 235 ◽  
pp. 85-89
Author(s):  
Cheng Wei Wang
Keyword(s):  
Shape Control ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Shape Design ◽  
Shape Preserving ◽  
Curve Design ◽  
Extension Curve ◽  
Cad Cam ◽  
Control Capability ◽  
Better Than

Ball curve； curve design； shape parameter Abstract. Ball curve is found similar to Bézier curve，also it has a good property of shape preserving，and in some respects，it has better properties than the Bézier curve. Therefore, In the shape design，Ball curve is paid more and more attention, it has a wide application. By introducing the concept of weights in NURBS curve into a blending technique, the paper extends the representation of the cubic Ball curve. The generalized cubic Ball curve is denoted as α extension cubic Ball curve, whose shape-control capability is shown to be much better than that of Ball curve. The representation and properties of the extension curve are studied. The curve is easy and intuitive to reshape by varying the parameters; so it is useful in some applications of CAD/CAM.

scholarly journals Shape Modification forλ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Gang Hu ◽  
Xiaomin Ji ◽  
Xinqiang Qin ◽  
Suxia Zhang
Keyword(s):  
Constrained Optimization ◽  
Shape Control ◽  
Control Parameter ◽  
Tangent Vector ◽  
Control Points ◽  
Shape Modification ◽  
Shape Preserving ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curve Design

Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance on adjusting their shapes by changing shape control parameter. Specially, in the case where the shape control parameter equals zero, theλ-Bézier curves degenerate to the classical Bézier curves. In this paper, the shape modification ofλ-Bézier curves by constrained optimization of position and tangent vector is investigated. The definition and properties ofλ-Bézier curves are given in detail, and the shape modification is implemented by optimizing perturbations of control points. At the same time, the explicit formulas of modifying control points and shape parameter are obtained by Lagrange multiplier method. Using this algorithm,λ-Bézier curves are modified to satisfy the specified constraints of position and tangent vector, meanwhile the shape-preserving property is still retained. In order to illustrate its ability on adjusting the shape ofλ-Bézier curves, some curve design applications are discussed, which show that the proposed method is effective and easy to implement.

Constrained plasma shape control in ITER

2009 ◽  
Author(s):  
Massimiliano Mattei ◽  
Domenico Famularo ◽  
Carmelo Vincenzo Labate
Keyword(s):  
Shape Control

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

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