G3 Shape Adjustable GHT-Bezier Developable Surfaces and Their Applications

In this article, we proposed a novel method for the construction of generalized hybrid trigonometric (GHT-Bezier) developable surfaces to tackle the issue of modeling and shape designing in engineering. The GHT-Bezier developable surface is obtained by using the duality principle between the points and planes with GHT-Bezier curve. With different shape control parameters in their domain, a class of GHT-Bezier developable surfaces can be established (such as enveloping developable GHT-Bezier surfaces, spine curve developable GHT-Bezier surfaces, geodesic interpolating surfaces for GHT-Bezier surface and developable GHT-Bezier canal surfaces), which possess many properties of GHT-Bezier surfaces. By changing the values of shape parameters the effect on the developable surface is obvious. In addition, some useful geometric properties of GHT-Bezier developable surface and the G(1), G(2) (Farin-Boehm and Beta) and G(3) continuity conditions between any two GHT-Bezier developable surfaces are derived. Furthermore, various useful and representative numerical examples demonstrate the convenience and efficiency of the proposed method.

Automated summary

This article introduces a novel method for constructing generalized hybrid trigonometric (GHT-Bezier) developable surfaces, which allows for the establishment of a class of GHT-Bezier developable surfaces with different shape control parameters and possess many properties of GHT-Bezier surfaces. The article also derives the continuity conditions between GHT-Bezier developable surfaces.