L-system is a tool commonly used for modeling and simulating the growth of fractal plants. The aim of this paper is to join some problems of the computational geometry with the fractal geometry by using the L-system technique to generate fractal plant in 3D. L-system constructs the fractal structure by applying rewriting rules sequentially and this technique depends on recursion process with large number of iterations to get different shapes of 3D fractal plants. Instead, it was reiterated a specific number of iterations up to three iterations. The vertices generated from the last stage of the Lsystem rewriting process are used as input to the triangulation algorithm to construct the triangulation shape of these vertices. The resulting shapes can be used as covers for the architectural objects and in different computer graphics fields. The paper presents a gallery of triangulation forms which application in architecture creates an alternative for domes and other traditional types of roofs.<\/p>\r\n","references":"[1] D. Hearn and M.P. Baker, Computer Graphics. C version, 2nd ed, CA: A\r\nViacom Company Upper Saddle River, New Jersey 07458, 1997, pp.\r\n362-363.\r\n[2] P. Furmanek, \"POLYHEDRAL COVERS BASED ON L-SYSTEM\r\nFRACTAL CONSTRUCTION,\" The Journal of Polish Society for\r\nGeometry and Engineering Graphics, vol. 14, 2004, pp. 40-47.\r\n[3] From Wikipedia and the free encyclopedia, \"Fractal\".\r\nOnline: http:\/\/en.wikipedia.org\/wiki\/Fractal\r\n[4] S. Sarkar, \"Introduction to Computation Geometry,\" Spring 2008.\r\nOnline: http:\/\/figment.csee.usf.edu\/~sarkar\/ComputationalGeometry\/\r\n[5] A. Lindenmayer, \"Mathematical models for cellular interaction in\r\ndevelopment,\" parts I and \u256c\u00e1, Journal of Theoretical Biology, vol. 18,\r\n1968, pp.280-315.\r\n[6] P. Prusinkiewicz and A. Lindenmayer, The algorithmic beauty of plants.\r\nNew York: Springer-Verlag, 1990, ch. 1.\r\n[7] B. D. Farkas, N. Romanyshyn, and P. Clary, \"L- Systems Construction\r\nKit\". Online:\r\nhttp:\/\/l3d.cs.colorado.edu\/~ctg\/classes\/ttt2005\/projectreports\/Lsystemrep\r\nort2.pdf\r\n[8] T. Ijiri, S. Owada, and T. Igarashi, \"The Sketch L-System: Global\r\nControl of Tree Modeling Using Free-form Strokes,\" Smart Graphics\r\n(2006), pp. 138-146.\r\n[9] P. Buser, E. Tosan, and Y. Weinand, \"Fractal Geometry and its\r\napplications in the field of construction,\" summer 2005.\r\nOnline:http:\/\/fractals-ibois.epfl.ch\/wiki\/images\/105c06_project_plan.pdf\r\n[10] D. P. Dobkin, \"Computational Geometry and Computer Graphics,\" in\r\nProc. IEEE, vol. 80, Issue 9, Sep. 1992, pp. 1400 - 1411.\r\n[11] S. Priester, \"Delaunay Triangles,\" July 19, 2005.\r\nOnline:http:\/\/www.codeguru.com\/Cpp\/data\/mfc_database\/misc\/article.p\r\nhp\/c8901\/\r\n[12] P. Bourke, \"Triangulate Efficient Triangulation Algorithm Suitable for\r\nTerrain Modelling\" or \"An Algorithm for Interpolating Irregularly-\r\nSpaced Data with Applications in Terrain Modelling,\" presented at the\r\n1989 Pan Pacific Computer Conference, Beijing, China.\r\n[13] G. Leach, \"Improving Worst-Case Optimal Delaunay Triangulation\r\nAlgorithms,\" In 4th Canadian Conference on Computational Geometry,\r\nCanada, June 15, 1992.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 20, 2008"}