A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters

Abstract

In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along with their geometric properties which are similar to the classical Bernstein basis functions. A sextic trigonometric Bézier (ST-Bézier, for short) curve with two shape parameters and their geometric characteristics is also constructed. The continuity constraints for the connection of two adjacent ST-Bézier curves segments are discussed. Shape control parameters can provide an opportunity to modify the shape of curve as designer desired. Some open and closed curves are also part of this study.

Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization

“…Because F j ðtÞ and G j ðtÞðj = 1, 2Þ should have the similar characteristics given by Equation ( 3), then from Equations ( 11), ( 12), (13), and ( 14) we obtain a 11 + a 61 = 1, a 12 + a 62 = 0, a 13 + a 63 = 0, a 14 + a 64 = 1, a 11 + a 41 + a 51 = 0, a 12 + a 42 + a 52 = 1, a 13 + a 43 + a 53 = −1, a 14 + a 44 + a 54 = 0, a 21 = 0, a 22 = 0, a 23 = 1, a 24 = 0, a 31 = 0, a 32 = 0, a 33 = 0, a 34 = −1:…”

“…In the recent years, trigonometric polynomials have received much attention within geometric modeling. Such as the trigonometric Bézier curves [11][12][13][14], the trigonometric B-spline curves [15][16][17], the trigonometric interpolation curves [18,19], etc. The curves constructed in trigonometric polynomial space have broad application prospects in engineering.…”

A quartic trigonometric interpolatory spline with local free parameters

“…However, trigonometric functions have also received very much attention within geometric modeling. Such as the trigonometric Be´zier curves, [1][2][3][4] the trigonometric B-spline curves, [5][6][7] the trigonometric Hermite curves, 8,9 the trigonometric rational curves, 10,11 etc. The curves constructed in trigonometric function space have been applied in signal analysis, 12 kitchen product design, 13 robot path planning, 14 and other engineering problems.…”