http:^^www.cs.cornell.edu^info^people^chew^delaunay.html

来自「This data set contains WWW-pages collect」· HTML 代码 · 共 84 行

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<head> <title> Voronoi/Delaunay Applet </title> </head><body><h1> <font color=magenta> Voronoi Diagram </font> / <font color=green>Delaunay Triangulation </font> </h1><applet code="geometry.Delaunay.class" width=550 height=400>If you were running a Java-compatible Web browser, suchas Netscape 2, then you would see a Voronoi Diagram /Delaunay Triangulation here.  </applet><p><ul><li> <b> The mouse: </b> Click the mouse in the drawing region to addnew sites to the Voronoi diagram or Delaunay triangulation.<li> <b> The Voronoi Diagram and Delaunay Triangulation checkboxes:</b> These toggle between the Voronoi diagram and the Delaunaytriangulation.  Your current set of sites remains the same for bothdiagrams.<li> <b> The Clear button: </b> Press this to begin a new diagram withno sites.<li> <b> The Show Empty Circles button: </b> Press this to see theempty circles for your set of sites.  Each Voronoi vertex (or Delaunaytriangle) has a corresponding empty circumcircle.</ul><h3> What is it? </h3><p> The <em> Voronoi diagram </em> has the property that for each site(clicked with the mouse) every point in the region around that site iscloser to that site than to any of the other sites.<p> The <em> Delaunay triangulation </em> is the geometric dual of theVoronoi diagram.  Alternately, it can be defined as a triangulation ofthe sites with the additional property that for each triangle of thetriangulation, the circumcircle of that triangle is empty of all othersites.<p> These closely related data structures have been found to be amongthe most useful data structures of the field of Computational Geometry.<h3> Additional Information </h3><p> The actual data structure here is a Delaunay triangulation.  TheVoronoi diagram is built on-the-fly from the Delaunay triangulation.<p> The Delaunay triangulation is built within a large triangle whosevertices are well off-screen.  That's why in the Delaunaytriangulation there are lines heading off to the upper left, the upperright, and down.  This technique makes the code simpler, sinceotherwise additional code would be needed to handle new sites that areoutside the convex hull of the previous sites.<p> <b> The algorithm: </b> To insert a new site, we walk across thetriangulation, starting from the most recently created triangle, untilwe find the triangle that contains the new site.  This triangle andany adjacent triangles that contain this new site in theircircumcircle are eliminated and the resulting empty spot isretriangulated.  This site-insertion technique is commonly called theBowyer-Watson Algorithm.  The expected time to insert a new site isroughly O(n<sup>1/2</sup>) where n is the current number of sites.<p><address> Author: <!WA0><!WA0><!WA0><!WA0><ahref="http://www.cs.cornell.edu/Info/People/chew/chew.html">PaulChew</a>, <!WA1><!WA1><!WA1><!WA1><a href="mailto:chew@cs.cornell.edu">chew@cs.cornell.edu</a></address></body>

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