Voronoi Diagram Essay Example | Topics and Well Written Essays - 2500 words

Voronoi Diagram - Essay ExampleTraditional GIS methods have been found to inapplicable for marine mapping. This is originally because they were built for two-dimensional land application making it hard to integrate marine features into the model. Marine objects are also likely to move over term which cannot be modeled using the traditional GIS. These limitations necessitated the development of a new modeling remains that can accurately incorporate marine features while allowing modifications to the system which does not require an overhaul of the whole model.Christopher Gold (1990) responded to the challenge by spearheading research and development of the Voronoi Diagram - a modeling system with a doubled geometric structure. Most of the literature on the development of the VD, either in 2D or in 3D, was authored by him. Voronoi diagrams that were developed were able to solve almost of the problems because of the following featuresAll of these features are available in 2D and 3D Voronoi Diagrams. This paper aims to differentiate 2D Voronoi Diagrams from 3D Voronoi Diagrams delineating their differences, advantages and disadvantages over the other. This paper also aims at pointing out the strengths and weakness of the two diagrams such that a conclusion on which iodine is more advantageous can be made.In 2D Voronoi Diagram, the cellular telephone surrounding a data point is a flat convex polygon having a defined number of neighbors (Gold and Ledoux, 1992). That is, its coordinates are only x and y with no z attribute. The analogy is the same as that of drawing figures on a piece of paper. When a plan view is done on the paper, one can see the shapes defined by the lines that were drawn. When the paper is leveled against ones visual perception, there are no figures which can be seen. This illustrates that no such elevation or learning attribute of the figures exist. The geometric dual structure of 2D Voronoi Diagrams are also flat in nature and are define d by Delaunay triangles. In descriptor 1, Delaunay Triangles are shown by the dashed lines while the solid lines defining a polygon represent the cells surrounding a data point p.Figure 1. A 2D Voronoi Sample Output (Gold, 1991)The vertices of the triangle generating each Voronoi cell must satisfy the empty circumcircle test. A circle is considered empty when there are no points in its interior but more than three points can be directly on the circle - i.e. the points are on its edges.3D Voronoi Diagram Construct3-Dimensional Voronoi Diagrams, as implied by its name, have 3 coordinates defining the space where the figure can be drawn. As opposed to 2D VDs, leveling the plane of the paper with ones eyesight provides a view of the sides of a figure. An appropriate analogy would be that of the viewing a cube held by the hand. When the figure is viewed from the top, one can see a square. When the hand is leveled against ones eyesight, one can still see the figure of a square. The figur e is a volumetric object. The convex polygon in a 2D, thru a construction algorithm, generalizes to a convex polyhedron. The geometric dual becomes a Delaunay tetrahedron. In Figure 2, the edges are the Delaunay edges joining the generator