A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...

a disk wang-bézier type generalized ball curve is a wang-bézier type generalized ball curve whose control points are disks in a plane. it can be viewed as a parametric curve with error tolerances. in this paper, we discuss the problem of degree reduction of disk wang-bézier type generalized ball curve, that is, bounding disk wang-bézier type generalized ball curves with lower degree disk wang-b...

A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...

In this paper, we research on constructing an explicit parametric curve to be taken as the limitation curve of Progressive Iteration Approximation (PIA) which can interpolate some scattered data points by using normalized totally positive (NTP) basis. We prove that when the data points and corresponding parameter list are given, the limitation curve has the unique explicit expression. There is ...

In 2000, Wu presented two new types of generalized Ball curves, one of which is called an NB1 curve located between the Wang–Ball curve and the Said–Ball curve. In this article, the authors aim to discuss properties of NB1 curves and surfaces, including the recursive algorithms, conversion algorithms between NB1 and Bézier curves and surfaces, etc. In addition the authors compare the computatio...

Theoretical study shows that Said-Bézier generalized Ball curves (SBGB curves) are distinctly superior to Bézier curves in evaluation, degree elevation and reduction. However in practical engineering, there is no effective algorithm for explicit multi-degree reduction of SBGB curves with endpoints constraints in the world. It is going against designing and applying generalized Ball curves. In o...

We study the curve smoothing problem in the context of Bézier curves of constant length. Specifically, we present a degree-independent simulated annealing based technique to smooth a lengthconstrained Bézier curve with arbitrary, user-specified geometric constraints. Smoothing is accomplished in two stages. First, a generalized degree-independent technique is used to generate several Bézier cur...

This paper presents a simple method for approximating a rational Bézier curve with Bézier curve sequence, whose control points are those of degree-elevated rational Bézier curves. It is proved that the derivatives with any given degree of the Bézier curve sequence constructed this way would uniformly converge to the corresponding derivatives of the original rational Bézier curve. © 2008 Publish...

Generalized Bernstein-like functions (gB-like functions) with different shape parameters are used in this work. Parametric and geometric conditions generalized form developed. Some numerical examples of the parametric continuity (PC) (GC) constraints Bézier-like curves curves) analyzed graphical representation. symmetric rotation surfaces constructed by gB-like curves. Vase Capsule Taurus model...

A rational quadratic trigonometric Bézier curve with two shape parameters, which is analogous to cubic Bézier curve, is presented in this paper. The shape of the curve can be adjusted as desired, by simply altering the value of shape parameters, without changing the control polygon. The rational quadratic trigonometric Bézier curve can be made close to the rational cubic Bézier curve or closer ...