Interpolation of Surfaces with Line of Curvature

Year 2021, Volume: 14 Issue: 2, 239 - 246, 29.10.2021

Ergin Bayram

https://doi.org/10.36890/iejg.890585

Abstract

We introduce a method to construct parametric surfaces interpolating given finite points and a curve as a line of curvature in 3-dimensional Euclidean space. We present an existence theorem of a $C^{0}$-Hermite interpolation of surfaces possessing the given data. We show that every parameter curve of a constructed surface is a circular helix if the given curve is a circular helix. The method is validated with illustrative examples.

Keywords

$C^{0}$-Hermite interpolation, line of curvature, parametric surface

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