Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2020; 57(4): 957-971

Published online July 1, 2020 https://doi.org/10.4134/JKMS.j190456

Copyright © The Korean Mathematical Society.

Interpolation of surfaces with geodesics

Hyun Chol Lee, Jae Won Lee, Dae Won Yoon

Gyeongsang National University; Gyeongsang National University; Gyeongsang National University

Abstract

In this paper, we introduce a new method to construct a parametric surface in terms of curves and points lying on Euclidean 3-space, called a $C^0$-Hermite surface interpolation. We also prove the existence of a $C^0$-Hermite interpolation of isoparametric surfaces with the so-called marching scale functions, and give some examples. Finally, we construct ruled surfaces and surfaces foliated by a circle as an isoparametric surface.

Keywords: $C^0$-Hermite interpolation, isogeodesic, ruled surface

MSC numbers: Primary 65D17, 68U05, 53A05

Supported by: The third author was supported by Basic Science Research Program through the National
Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07046979).