A novel generalized trigonometric Bézier curve: Properties, continuity conditions and applications to the curve modeling

This paper presents a new class of kth degree generalized trigonometric Bernstein-like basis (or GT-Bernstein, for short). This newly introduced basis function has two shape parameters and has the same characteristics as the Bernstein basis functions. However, the intended role is identical to that of conventional basis and inherits all of its geometric properties. For this particular kind of Bézier curves, shape parameters inclusion offers more freedom than traditional types of Bézier curves. To eliminate the complexity, the required and proper conditions for C3 and G2 continuity between two continuous generalized trigonometric Bézier curves (or GT-Bézier curves, in short) are also addressed. Moreover, several practical implementations of GT-Bézier curves, such as approximation of some conic and free form geometric modeling of complex curves, are also discussed. This proposed approach is shown in many easy-to-follow modeling illustrations, and it may also model dynamic engineering curves as a backup for the expanded concept.