Construction of Generalized Hybrid Trigonometric Bézier Surfaces with Shape Parameters and Their Applications

To tackle the problem of modeling and shape designing of complex engineering surfaces, the continuity constraints between generalized hybrid trigonometric Bézier (GHT-Bézier for short) surfaces with three different shape parameters are proposed in this study. Initially, we describe the basic properties of GHT-Bézier surface and influence of shape parameters. Some special triangular surfaces and biangular surfaces by varying the different values of shape control parameters are described. G2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G^{2}$$\end{document} continuity conditions in various directions between two adjacent GHT-Bézier surfaces with graphical representation are studied. Finally, the construction of some free-form complex engineering surfaces such as cylindrical surface, swung surface, ruled surface, and swept surface by using GHT-Bézier surfaces is also studied. Some graphical examples ensure that the proposed method greatly improves the ability to design complex surfaces and is easy to implement.