June 6 2002 3:54:07.423 PM SCVT_MAIN A sample problem for the probabilistic Spherical Centroidal Voronoi Tessellation algorithm. Given a unit sphere in 3D, the problem is to determine a set of GENERATORS, that is, a set of points which lie on the sphere, and which implicitly define a division of the surface into Voronoi cells. It is also desired that each generator point actually be the centroid of its cell. SCVT Algorithm parameters: ------------------------- The number of Voronoi cells to generate: 32 Number of iterations to determine CVT: 2000 Number of sampling points: 160000 RANDOM_INITIALIZE Initialize RANDOM_NUMBER with user SEED = 1 Initialize the Voronoi cell generators by... ...SPIRAL POINTS Initial generators: 0.000000 0.000000 -1.000000 -0.080609 0.344053 -0.935484 -0.490833 0.022314 -0.870968 -0.303989 -0.507175 -0.806452 0.266774 -0.615112 -0.741935 0.703513 -0.214879 -0.677419 0.690005 0.385024 -0.612903 0.247757 0.798679 -0.548387 -0.361953 0.796780 -0.483871 -0.820041 0.389454 -0.419355 -0.908726 -0.219788 -0.354839 -0.593076 -0.750982 -0.290323 -0.014788 -0.974060 -0.225806 0.581158 -0.797647 -0.161290 0.950339 -0.295789 -0.096774 0.943923 0.328585 -0.032258 0.563592 0.825423 0.032258 -0.040114 0.994498 0.096774 -0.624506 0.764184 0.161290 -0.947989 0.224341 0.225806 -0.868749 -0.401233 0.290323 -0.412914 -0.838804 0.354839 0.218942 -0.881026 0.419355 0.722269 -0.494162 0.483871 0.825409 0.134056 0.548387 0.449013 0.650182 0.612903 -0.189645 0.710730 0.677419 -0.627288 0.236732 0.741935 -0.446331 -0.387846 0.806452 0.209206 -0.444576 0.870968 0.276985 0.219430 0.935484 0.000000 0.000000 1.000000 Wrote generators to file: initial.xyz Discrepancy between generator and centroid, STEP = 1 Generator motions: Total = 0.671193 Average = 0.209748E-01 Minimum = 0.207160E-02 Maximum = 0.103848 Discrepancy between generator and centroid, STEP = 2 Generator motions: Total = 0.424974 Average = 0.132805E-01 Minimum = 0.241687E-02 Maximum = 0.364240E-01 Discrepancy between generator and centroid, STEP = 3 Generator motions: Total = 0.287070 Average = 0.897094E-02 Minimum = 0.234172E-02 Maximum = 0.246383E-01 Discrepancy between generator and centroid, STEP = 4 Generator motions: Total = 0.237442 Average = 0.742007E-02 Minimum = 0.845728E-03 Maximum = 0.160467E-01 Discrepancy between generator and centroid, STEP = 5 Generator motions: Total = 0.209276 Average = 0.653989E-02 Minimum = 0.158221E-02 Maximum = 0.148747E-01 Discrepancy between generator and centroid, STEP = 6 Generator motions: Total = 0.180169 Average = 0.563028E-02 Minimum = 0.345267E-03 Maximum = 0.123479E-01 Discrepancy between generator and centroid, STEP = 206 Generator motions: Total = 0.123108 Average = 0.384713E-02 Minimum = 0.488281E-03 Maximum = 0.797860E-02 Discrepancy between generator and centroid, STEP = 406 Generator motions: Total = 0.119041 Average = 0.372003E-02 Minimum = 0.00000 Maximum = 0.820693E-02 Discrepancy between generator and centroid, STEP = 606 Generator motions: Total = 0.113193 Average = 0.353727E-02 Minimum = 0.114512E-02 Maximum = 0.631943E-02 Discrepancy between generator and centroid, STEP = 806 Generator motions: Total = 0.103392 Average = 0.323101E-02 Minimum = 0.976563E-03 Maximum = 0.662338E-02 Discrepancy between generator and centroid, STEP = 1006 Generator motions: Total = 0.129291 Average = 0.404035E-02 Minimum = 0.345267E-03 Maximum = 0.732424E-02 Discrepancy between generator and centroid, STEP = 1206 Generator motions: Total = 0.124015 Average = 0.387546E-02 Minimum = 0.845728E-03 Maximum = 0.655099E-02 Discrepancy between generator and centroid, STEP = 1406 Generator motions: Total = 0.125368 Average = 0.391776E-02 Minimum = 0.772040E-03 Maximum = 0.775893E-02 Discrepancy between generator and centroid, STEP = 1606 Generator motions: Total = 0.111245 Average = 0.347642E-02 Minimum = 0.00000 Maximum = 0.822144E-02 Discrepancy between generator and centroid, STEP = 1806 Generator motions: Total = 0.106977 Average = 0.334302E-02 Minimum = 0.488281E-03 Maximum = 0.102132E-01 Discrepancy between generator and centroid, STEP = 2000 Generator motions: Total = 0.103340 Average = 0.322939E-02 Minimum = 0.00000 Maximum = 0.842907E-02 Wrote generators to file: generators.xyz Motion of generators from initial to final. Generator motions: Total = 4.69762 Average = 0.146801 Minimum = 0.421554E-01 Maximum = 0.265063 June 6 2002 4:56:11.696 PM SCVT_MAIN Normal end of execution.