Quasi-quintic trigonometric Bézier curves with two shape parameters

• DOI: 10.1007/s40314-019-0961-y
• Publication Date: 2019-10-03T10:10:57Z
• Authors: Xuewen Tan; Yuanpeng Zhu
• Keywords: Quintic function; Family of curves; Trigonometric polynomial; Trigonometric integral; Pythagorean trigonometric identity

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 Bezier curve is proposed, which has some properties analogous to the classical quintic Bezier curves. For the same control points, the resulting quasi-quintic trigonometric Bezier curves can be closer to the control polygon than the classical quintic Bezier curves. The shape of the quasi-quintic trigonometric Bezier curves can be flexibly adjusted by altering the values of the two shape parameters without changing their control points. Under the $${C^2}$$ smooth connection conditions, the resulting composite quasi-quintic trigonometric Bezier curves can automatically reach $${C^2} \cap F{C^3}$$ continuity.