On geometry of isophote curves in Galilean space

Zuhal Küçükarslan Yüzbașı; Dae Won Yoon; Zuhal Küçükarslan Yüzbașı; Dae Won Yoon

doi:10.3934/math.2021005

AIMS Mathematics

2021, Volume 6, Issue 1: 66-76. doi: 10.3934/math.2021005

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Research article

On geometry of isophote curves in Galilean space

Zuhal Küçükarslan Yüzbașı ¹,
Dae Won Yoon ^{2
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1.
Department of Mathematics, F?rat University, 23119 Elazig, Turkey
2.
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Republic of Korea

Received: 17 July 2020 Accepted: 07 September 2020 Published: 28 September 2020
MSC : 53A35, 53Z05

In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an isotropic or a non-isotropic vector. We also give a method to compute isophote curves of surfaces of revolution. Subsequently, we show the relationship between isophote curves and slant (general) helices on surfaces of revolution obtained by revolving a curve by Euclidean rotations. Finally, we give some characterizations for isophote curves lying on surfaces of revolution.
- Galilean space,
- isophote curve,
- surfaces of revolution
Citation: Zuhal Küçükarslan Yüzbașı, Dae Won Yoon. On geometry of isophote curves in Galilean space[J]. AIMS Mathematics, 2021, 6(1): 66-76. doi: 10.3934/math.2021005

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Abstract

In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an isotropic or a non-isotropic vector. We also give a method to compute isophote curves of surfaces of revolution. Subsequently, we show the relationship between isophote curves and slant (general) helices on surfaces of revolution obtained by revolving a curve by Euclidean rotations. Finally, we give some characterizations for isophote curves lying on surfaces of revolution.

References

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