Approximations of Parallel Surfaces Along Curves

Year 2023, , 715 - 726, 29.10.2023

Büşra Köse , Yusuf Yaylı

https://doi.org/10.36890/iejg.1362590

Abstract

In this paper, we study developable surfaces which are flat and normal approximation of parallel surfaces along curves associated with three special vector fields. It is known that a surface whose points are at a constant distance along the normal of the surface is called a parallel surface. We investigate singularities of such developable surfaces. We show that under what conditions the approach surfaces are parallel. Also, we show that the approach surfaces are constant angle ruled surfaces if the curves selected on the surfaces are isophote, relatively normal-slant helix and helix.

Keywords

Parallel surfaces, developable surfaces, curves on surfaces, flat approximations, normal approximations.

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