Delaunay Triangulation Algorithm and Application to Terrain Generation
نویسنده
چکیده
We describe a randomized incremental algorithm for computing the Delaunay triangulation of a set of points and a recent technique of applying it to terrain generation. The algorithm is optimal, using a Directed Acyclic Graph (DAG)-based location structure for the incremental insertion which achieves an expected running time of O(n log n) and O(n) expected storage. The analysis of the expected storage is simplified, and the algorithm is implemented and tested. The implementation is done, in its integrality, with CGAL-Python which is fast and friendly, followed by numerical statistics on different distributions. The terrain generation technique is based on gaussian functions and the plotting is made with the Open Source software Blender 3D which is probably its first combination with CGAL-Python. A high quality rendering of three simple terrains is shown as a demonstration of the terrain generator. Mamaritra tetika fanamboarana ny fanatelozoroan’ i Delaunay ao aminy velarana R amin’ny fomba kisendrasendra isika ary ny fampiasana azy io aminy famoronana vohitra. Ilay tetika dia maty paika izay mampiasa grafy misy toro-lalana ary tsy misy fihodonana aminy fanatsofoana ireo teboka isan’isany, ny fandalinana ny hafainganany kosa dia natao faran’izay tsotra. Ny famolavolana dia natao, aminy akapobeny, tamin’ny CGAL-Python izay aingana sady mora ampiasaina, ny vokatra numerika dia nomena ihany koa. Ilay fanamboarana vohitra dia tsy voafetra izay afaka mamboatra tendrombohitra arak’izay ilainy mpampiasa. Ilay vohitra dia natao kisary tamin’ilay fitaovana maimaimpona Blender 3D izay mety ho voalohany aminy fampiasana azy io sy CGAL-Python miaraka. Hisy vohitra roa haseho aminy endriny farany izay kanto mba anehoana ny fahatsaran’ilay fanamboarana. Declaration I, the undersigned, hereby declare that the work contained in this essay is my original work, and that any work done by others or by myself previously has been acknowledged and referenced accordingly. Faniry Harijaona Razafindrazaka, 22 May 2009 i
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