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 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...

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 ...

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.

Wang-Ball (WB) curve is one of the generalized cubic Ball basis which was first put forward in CONSURF system by Ball. Wang extended it to arbitrary odd and even degrees. An algorithmic approach to degree reduction of interval Wang-Ball curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed WB curves) associated with the original interval WB curve are obtained. Th...

This paper presents a multi-degree reduction approximation algorithm for a usable type of curves in Computer Aided Geometric Design, generalized Ball curves of Wang-Said type in L2-norm, which has many advantages such as explicit expression, endpoint constrains, best approximation and error prediction. The basic idea is by deriving and using the conversion formulas between the WSGB basis and th...

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...