Generalized quartic H-Bézier curves: Construction and application to developable surfaces

Abstract

In this paper, certain generalized quartic H-Bézier basis functions are introduced for the purpose to construct generalized quartic H-Bézier curves with local shape parameters. Meanwhile, the rules of influence for the shape parameters on these generalized quartic H-Bézier curves, as well as the geometric continuity conditions between two adjacent generalized quartic H-Bézier curves, are investigated. To examine their usefulness, hyperbolic curves and catenary curves can be represented exactly using the generalized quartic H-Bézier curves; one advantage of such representation is that the local shape of these curves can be adjusted by altering the values of shape parameters while the control points are kept unchanged. Furthermore, generalized quartic developable H-Bézier surfaces are designed by using control planes with the generalized quartic H-Bézier basis functions, and some properties of the new developable surfaces are explored. Finally, modeling examples are provided to illustrate the new approach of using generalized quartic H-Bézier basis and compare with the existing geometric modeling methods for developable surfaces.