Research article

On geometry of isophote curves in Galilean space

  • 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.

    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

    Related Papers:

  • 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.


    加载中


    [1] A. Artykbaev, Total angle about the vertex of a cone in Galilean space, Math. Notes, 43 (1988), 379-382. doi: 10.1007/BF01158845
    [2] M. Dede, C. Ekici and W. Goemans, Surfaces of revolution with vanishing curvature in Galilean 3-space, J. Math. Phys. Anal. Geo., 14 (2018), 141-152.
    [3] F. Doğan and Y. Yaylı, On isophote curves and their characterizations, Turkish J. Math., 39 (2015), 650-664.
    [4] F. Do?an and Y. Yayl?, Isophote curves on spacelike surfaces in Lorentz-Minkowski space E13, arXiv preprint arXiv: 1203.4388, 2012.
    [5] A. Kazan and H. B. Karadag, Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density, Int. J. Anal. Appl., 16 (2018), 414-426.
    [6] K. J. Kim and I. K. Lee, Computing isophotes of surface of revolution and canal surface, ComputAided Des., 35 (2003), 215-223.
    [7] J. J. Koenderink and A. J. van Doorn, Photometric invariants related to solid shape, J. Modern Opt., 27 (1980), 981-996.
    [8] E. Molnar, The projective interpretation of the eight 3-dimensional Homogeneous geometries, Beitr. Algebra Geom., 38 (1997), 261-288.
    [9] B. J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space G3, Glas. Mat., 22 (1987), 449-457.
    [10] O. Röschel, Die Geometrie des Galileischen raumes, Habilitationsschrift, Leoben, 1984.
    [11] Z. M. Sipus, Ruled Weingarten surfaces in Galilean space, Period. Math. Hungar, 56 (2008), 213-225. doi: 10.1007/s10998-008-6213-6
    [12] T. Şahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Math. Sci., 33 (2013), 701-711.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(193) PDF downloads(42) Cited by(0)

Article outline

Figures and Tables

Figures(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog