Approximation of fruit skin patterns using spherical Voronoi diagrams
- 284 Downloads
In nature, there are many tessellation patterns on curved surfaces that look like Voronoi diagrams. Typical examples are the patterns found on fruit skins. Verifying that a given tessellation is a Voronoi diagram will be useful for constructing mathematical models of polygonal patterns. However, the data are usually obtained as a 2D projected image, and hence it is not easy to compare it with a Voronoi diagram on a curved surfaces. We propose a framework for using a photograph of a fruit to measure the difference between the pattern on its skin and a spherical Voronoi diagram. The problem of finding the spherical Voronoi diagram that best fits the fruit skin pattern is reduced to an optimization problem. The validity of this formulation is evaluated using jackfruit and lychee. We also propose generalizations of our problem for further research.
KeywordsSpherical Voronoi diagram Tessellation fitting Circular search Fruit skin pattern Jackfruit Lychee
The authors wish to thank Sukhumabhorn Kaewsangsai from Department of Biology, Chiang Mai University, Thailand for taking the jackfruit photos. The authors also thank Suttipong Kawilapat from the Department of Statistics, Chiang Mai University, Thailand for discussing the uses of statistical tests. The first author acknowledges the support of the MIMS Ph.D. Program of the Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, and the DPST of IPST, Ministry of Education, Thailand. This research is partly supported by the Grant-in-Aid for Basic Research No. 24360039 of MEXT.
- 1.Aloupis G et al. (2013) Fitting Voronoi diagrams to planar tessellations. IWOCA2013, LNCS8288, 349–361Google Scholar
- 6.Denis B, Bernard J, Chafika B (1996) The geometry of the inflorescence of Symplocarpus Araceae: physical or biological problem? Comptes Rendus de l’Academie des Sciences Serie III 319(8):699–704Google Scholar
- 20.Sharma MR (1963) Morphological and anatomical investigations on Artocarpus Forst: II the inflorescence. Proc Natl Inst Sci India 29:77–92Google Scholar
- 21.Sharma MR (1965) Morphological and anatomical investigations on Artocarpus Forst: III the flower. Phytomorphol 15:185–201Google Scholar
- 22.Sharma MR (1964) Morphological and anatomical investigations on Artocarpus Forst: IV the fruit. Proc Indian Acad Sci B 60(6):380–393Google Scholar
- 23.Simpson MG (2010) Plant systematics, 2nd edn. Elsevier, LondonGoogle Scholar
- 28.Underhill SJR, Critchley C (1992) The physiology and anatomy of lychee (Litchi chinensis Sonn.) pericarp during fruit development. J Hortic Sci 67(4):437–444Google Scholar