Quasi-quintic trigonometric Bézier curves with two shape parameters

In this work, we propose a family of six new quasi-quintic trigonometric blending functions with two shape parameters. Based on these blending functions, a class of quasi-quintic trigonometric Bézier curve is proposed, which has some properties analogous to the classical quintic Bézier curves. For the same control points, the resulting quasi-quintic trigonometric Bézier curves can be closer to the control polygon than the classical quintic Bézier curves. The shape of the quasi-quintic trigonometric Bézier curves can be flexibly adjusted by altering the values of the two shape parameters without changing their control points. Under the C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C^2}$$\end{document} smooth connection conditions, the resulting composite quasi-quintic trigonometric Bézier curves can automatically reach C2∩FC3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C^2} \cap F{C^3}$$\end{document} continuity.