The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said–Ball and the Wang–Ball basis, respectively. In this paper, we analyze some shape preserving and stability properties of these bases. We prove that the Wang–Ball basis is strictly monotonicity preserving for all m. However, it is not geometrical...

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 ...

A disk Bézier curve is a Bézier 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 Bézier curves, that is, bounding disk Bézier curves with lower degree disk Bézier curves. We propose an efficient method to solve this problem. The algorithm starts by finding an optimal a...

Abstract Bézier splines are widely available in various systems with the curves and surface designs. In general, the Bézier spline can be specified with the Bézier curve segments and a Bézier curve segment can be fitted to any number of control points. The number of control points determines the degree of the Bézier polynomial. This paper presents a method which determines control points for Bé...

In this paper, a G(1), C(1), C(2) PH-spline is employed as an approximation for a given Bézier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bézier curve. The errors between PH-spline and the Bézier curve, the offset to PH-spline and the offset to the given Bézier curve are also estimated. A new algorithm for constructing offset to the...

In this article, we proposed a novel method for the construction of generalized hybrid trigonometric (GHT-Bézier) developable surfaces to tackle issue modeling and shape designing in engineering. The GHT-Bézier surface is obtained by using duality principle between points planes with curve. With different control parameters their domain, class can be established (such as enveloping surfaces, sp...

A new type of cubic trigonometric Bézier curve has been introduced in [1]. This trigonometric curve has two global shape parameters λ and μ. We give a lower boundary to the shape parameters where the curve has lost the variation diminishing property. In this paper the relationship of the two shape parameters and their geometric effect on the curve is discussed. These shape parameters are indepe...

A planar Bézier curve whose control points are disks is called a disk Bézier curve. It can be looked as a parametric curve with tolerance in the plane. It is an effective tool to measure or control the error. Based on minimum mean square error, this paper presents an algorithm for optimal multi-degree reduction of disk Bézier curves in L2 norm. First, applying the orthogonal property of Jacobi ...