Abstract
Formulation of developable patches is beneficial for modeling of the plate-metal sheet in the based-metal-industries objects. Meanwhile, installing the developable patches on a frame of the items and making a hole on these objects surface still need some practical techniques for developing. For these reasons, this research aims to introduce some methods for fitting a curve segment, cutting the developable patches, and adjusting their formulas. Using these methods can design various profile shapes of rubber filer installed on a frame of the objects and create a fissure or hole on the patches' surface. The steps are as follows. First, we define the planes containing the patches' generatrixes and orthogonal to the boundary curves. Then, it fits the Hermite and Bézier curve, via arranging some control points data on these planes, to model the rubber filler shapes. Second, we numerically evaluate a method for cutting the patches with a plane and adjusting the patches' form by modifying their formula from a linear interpolation form into a combination of curve and vectors forms. As a result, it can present some equations and procedures for plotting required curves, cutting surfaces, and modifying the extensible or narrowable shape of Hermite patches. These methods offer some advantages and contribute to designing the based-metal-sheets' object surfaces, especially modeling various forms of rubber filer profiles installed on a frame of the objects and making hole shapes on the plate-metal sheets.
Highlights
Some developable surfaces' formulas can be used to model automobile parts, ship hulls, and aircraft [1,2,3,4]
Kusno [8] discussed the construction of regular developable Bézier patches in which their boundary curves are defined by the combination of four, five, and six degrees
He developed this method by applying Hermite polynomial curves [9]
Summary
Some developable surfaces' formulas can be used to model automobile parts, ship hulls, and aircraft [1,2,3,4]. Xu et al [6] discussed the minimal surface formulation via a given boundary curve of the surface. In this case, they use a quasi-harmonic Bézier approximation and a quasi-harmonic mask. Kusno [8] discussed the construction of regular developable Bézier patches in which their boundary curves are defined by the combination of four, five, and six degrees. He developed this method by applying Hermite polynomial curves [9]. Fernández and Pérez [10] introduced the technique for designing the developable surfaces using their boundary curves in the form of NURBS curves
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