A class of quasi-quintic trigonometric Bézier curve with two shape parameters

Abstract

In this paper, a class of quasi-quintic trigonometric Bézier curve with two shape parameters, based on newly constructed trigonometric basis functions, is presented. The new basis functions share the properties with Bernstein basis functions, so the generated curves inherit many properties of traditional Bézier curves. The presence of shape parameters provides a local control on the shape of the curve which enables the designer to control the curve more than the ordinary Bézier curve.

A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters

“…Xiujuan et al [8] investigated special revolution surfaces and their dramatic improvement. Bashir et al [9] derived a class of quasi-quantic trigonometric Bézier curves with two shape parameters and proved their geometric features. e properties of the basis functions and curves are established, and the effect of the shape control parameters is also discussed.…”

Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

“…In recent years, many scholars have paid attention to the trigonometric Bézier curves. In [1,2], Bashir et al presented quadratic and rational quadratic trigonometric Bézier curves with single and double shape parameters, respectively. Xiao-qin and Han [3] presented cubic trigonometric polynomial curves with two shape parameters that can deal preciously with circular arc, cones, cylinders and many more.…”

“…Lasser [22] proposed an algorithm for converting a rectangular patch of a triangular Bézier surface into a tensor product Bézier representation and also discuss the corner problem of a surface. The curves and surfaces in [1][2][3][4][5][6][7][8][9][10][18][19][20][21] have several specific advantages such as they inherit the positive properties of the classical Bézier curves and surfaces. Furthermore, several local shape parameters are included and make it possible to change the local shapes of the curves and surfaces without altering the control points.…”

Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters

“…Yan expressed an algebraic-trigonometric mixed piecewise curve with two shape parameters and cubic trigonometric nonuniform B-spline curves with local shape parameters in [21] and [22], respectively. Hu et al [23] constructed geometric continuity constraints for H-Bézier curve of degree n. Recently, many researchers have developed the positivity-preserving rational quartic spline interpolation [24], cubic triangular patches scattered data interpolation [25], rational bi-cubic Ball image interpolation [26], quasiquintic trigonometric Bézier curve with shape parameters [27], curve modeling by new cubic trigonometric Bézier with shape parameters [28], continuity conditions for G 1 joint of S-λ curves and surfaces [29], generalized Bernstein basis functions for approximation of multi-degree reduction of Bézier curve [30], surface modeling in medical imaging by Ball basis functions [31], and geometric conditions for the generalized H-Bézier model [32] which have many applications in medicine, science, and engineering. Khalid and Lobiyal [33] presented the extension of Lupaş Bézier curves/surfaces and rational Lupaş Bernstein functions with shape parameters having all positive (p, q)-integers values.…”