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A method of constructing phyllotaxically arranged modular models by partitioning the interior of a cylinder or a cone

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Języki publikacji
EN
Abstrakty
EN
The paper describes a method of partitioning a cylinder space into three-dimensional subspaces, congruent to each other, as well as partitioning a cone space into subspaces similar to each other. The way of partitioning is of such a nature that the intersection of any two subspaces is the empty set. Subspaces are arranged with regard to phyllotaxis. Phyllotaxis lets us distinguish privileged directions and observe parastichies trending these directions. The subspaces are created by sweeping a changing cross-section along a given path, which enables us to obtain not only simple shapes but also complicated ones. Having created these subspaces, we can put modules inside them, which do not need to be obligatorily congruent or similar. The method ensures that any module does not intersect another one. An example of plant model is given, consisting of modules phyllotaxically arranged inside a cylinder or a cone.
Rocznik
Strony
21--36
Opis fizyczny
Bibliogr. 17 poz., il., wykr.
Twórcy
autor
  • Institute of Computer Science, Warsaw University of Technology, Poland
Bibliografia
  • [1] Prusinkiewicz P., Lindenmayer A.: The Algorithmic Beauty of Plants. Springer Verlag 1990.
  • [2] Douady S., Couder Y.: Phyllotaxis as a Physical Self-Organized Growth Process. Physical Review Letters. Vol. 68, 1992.
  • [3] Fowler D.R., Prusinkiewicz P., Battjes J.: A collision-based model of spiral phyllotaxis. Proc. of the 19th Annual Conference on Computer Graphics and Interactive Techniques SIGGRAPH’92, 1992.
  • [4] Zagórska-Marek B.: Phyllotaxic diversity in Magnolia flowers, Acta Soc. Bot. Poloniae 63 117-137, 1994.
  • [5] Douady S., Couder Y.: Phyllotaxis as a Dynamical Self Organizing Process. Journal of Theoretical Biology. 178, 255-274, 1996.
  • [6] Foley I. et al.: Computer Graphics: Principles and Practice. Addison-Wesley, 1996.
  • [7] Adler I., Barabe D., Jean R.V.: A History of the Study of Phyllotaxis. Annals of Botany 80: 231-244, 1997.
  • [8] Cummings F.W., Strickland J.C.: A Model of Phyllotaxis. Journal of Theoretical Biology 192, 531-544, 1998.
  • [9] Hargittai I., Pickover C.A.: Spiral symmetry. World Scientific Publishing, 2000.
  • [10] Kappraff J.: Growth in Plants: A Study in Number. Forma, 19, 335-354, 2004.
  • [11] Shipman P.D., Newell A.C.: Polygonal planforms and phyllotaxis on plants. Journal of Theoretical Biology, 236, 154-197, 2005.
  • [12] Smith R.S., Kuhlemeier C., Prusinkiewicz P.: Inhibition fields for phyllotactic pattern formation: a simulation study. Canadian Journal of Botany 84(11), pp. 1635-1649, 2006.
  • [13] Ciszak L., Stępień C.: A dynamic model of phyllotaxis for application in computer graphics. Proceedings of the XII National Conference Application of Mathematics to Biology and Medicine, Koninki, Poland, pp. 31-36, 2006.
  • [14] Newell A.C., Shipman P.D., Sun Z.: Phyllotaxis: Cooperation and competition between mechanical and biochemical processes. Journal of Theoretical Biology, 251, 421-439, 2008.
  • [15] Zagórska-Marek B., Szpak M.: Virtual phyllotaxis and real plant model cases. Functional Plant Biology, 35, 1025-1033, 2008.
  • [16] Nisoli C., Gabor N.M., Lammert P.E., Maynard J.D., Crespi V.H.: Static and Dynamical Phyllotaxis in Magnetic Cactus. Physical Review Letters. 102, 2009.
  • [17] http://www.fosterandpartners.com/Projects/1004/Default.aspx, Swiss Re H, 30 St Mary Axe (retrieved Feb. 1, 2014).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5b09000f-379c-469e-9c85-60bc88082ae5
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