Mathematics and Statistics Vol. 8(6), pp. 740 - 746
DOI: 10.13189/ms.2020.080615
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Fitting a Curve, Cutting Surface, and Adjusting the Shapes of Developable Hermite Patches

Kusno ^*
Department of Mathematics, University of Jember, Indonesia

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.

KEYWORDS
Fitting, Cutting, Adjusting, Curves, Surfaces, Developable Hermite Patches

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Kusno , "Fitting a Curve, Cutting Surface, and Adjusting the Shapes of Developable Hermite Patches," Mathematics and Statistics, Vol. 8, No. 6, pp. 740 - 746, 2020. DOI: 10.13189/ms.2020.080615.

(b). APA Format:
Kusno (2020). Fitting a Curve, Cutting Surface, and Adjusting the Shapes of Developable Hermite Patches. Mathematics and Statistics, 8(6), 740 - 746. DOI: 10.13189/ms.2020.080615.