We propose a model for generating tessellation patterns on the sphere using the spherical Laguerre Voronoi diagram which satisfies the real-world assumptions. The generator pushing model is presented to generate the tessellation dynamically. The simulations were done for the different distribution of spherical circles on the sphere, and the results show the tendency of the distribution of resulting spherical circles.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, vol. 501. Wiley, Amsterdam (2009)
Aurenhammer, F., Klein, R., Lee, D.T.: Voronoi Diagrams and Delaunay Triangulations. World Scientific Publishing Co Inc, Singapore (2013)
Mach, P., Koehl, P.: Capturing protein sequencestructure specificity using computational sequence design. Protein. Struct. Funct. Bioinf. 81(9), 1556–1570 (2013)
Telley, H., Liebling, T.M., Mocellin, A.: The Laguerre model of grain growth in two dimensions I. Cellular structures viewed as dynamical Laguerre tessellations. Philos. Magn. B 73(3), 395–408 (1996)
Telley, H., Liebling, T.M., Mocellin, A.: The Laguerre model of grain growth in two dimensions II. Examples of coarsening simulations. Philos. Magn. B 73(3), 409–427 (1996)
Aurenhammer, F.: Power diagram: properties, algorithms, and applications. SIAM J. Comput. 16, 78–96 (1987)
Imai, H., Iri, M., Murota, K.: Voronoi diagram in the Laguerre geometry and its applications. SIAM J. Comput. 14, 93–105 (1985)
Sugihara, K.: Three-dimensional convex hull as a fruitful source of diagrams. Theor. Comput. Sci. 235(2), 325–337 (2000)
Chaidee, S., Sugihara, K.: Recognition of the spherical Laguerre Voronoi diagram. arXiv:1705.03911 (2017)
Chaidee, S., Sugihara, K.: Fitting spherical laguerre voronoi diagrams to real world tessellations using planar photographic images. In: Akiyama, J. (ed.) Discrete and Computational Geometry and Graphs (LNCS 9943), pp. 73–84. Springer, Berlin (2016)
Chaidee, S., Sugihara, K.: Spherical Laguerre Voronoi diagram approximation to tessellations without generators, graphical models. https://doi.org/10.1016/j.gmod.2017.11.002 (2017)
Pushpakumara, D.K.N.G.: Foral and fruit morphology and phenology of Artocarpus heterophyllus Lam. (Moraceae). Sri. Lankan J. Agric. Sci. 43, 82–196 (2006)
Underhill, S.J.R., Critchley, C.: The physiology and anatomy of lychee (Litchi chinensis Sonn.) pericarp during fruit development. J. Horticult. Sci. 67(4), 437–444 (1992)
Roth, I.: Fruits of angiosperms-Encyclopedia of Plant Anatomy. Gebr. Borntraeger (1977)
Reeve, R.M.: Fruit histogenesis in Rubus strigosus. I. Outer epidermis, parenchyma, and receptacle. Am. J. Bot. 41(2), 152–160 (1954)
Sugihara, K.: Laguerre Voronoi diagram on the sphere. J. Geom. Graph. 6(1), 69–81 (2002)
Chaidee, S., Sugihara, K.: Approximation of fruit skin patterns using spherical Voronoi diagrams. Pattern Anal. Appl. 20(3), 783–795 (2017)
Deserno, M.: How to generate equidistributed points on the surface of a sphere. P.-If Polymerforshung (Ed.) (2004)
This research is supported by Chiang Mai University, Thailand.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Chaidee, S., Sugihara, K. Laguerre Voronoi Diagram as a Model for Generating the Tessellation Patterns on the Sphere. Graphs and Combinatorics 36, 371–385 (2020). https://doi.org/10.1007/s00373-019-02006-5
- Spherical Laguerre Voronoi diagram
- Spherical tessellation
- Pattern formations