June 6 2002 10:25:40.736 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... ...SOCCER BALL CENTERS (Requires N = 32) Initial generators: 0.188492 0.356822 0.914958 -0.400983 -0.045432 0.914958 0.193492 -0.283551 0.939234 0.729968 -0.045432 0.681970 -0.386986 0.567101 0.727075 -0.223822 -0.696291 0.681969 0.642850 0.567100 0.514918 0.475145 -0.696291 0.537974 -0.861294 0.237881 0.448982 0.092495 0.888741 0.448981 -0.762436 -0.391857 0.514918 0.968622 0.237881 0.071998 0.903874 -0.391857 0.171640 -0.556308 0.815232 0.160992 0.035359 -0.984525 0.171639 -0.574642 -0.815232 0.071997 0.574642 0.815232 -0.071997 0.556308 -0.815232 -0.160992 -0.903874 0.391857 -0.171640 -0.968622 -0.237881 -0.071998 -0.035359 0.984525 -0.171639 0.762436 0.391857 -0.514918 0.861294 -0.237881 -0.448982 -0.475144 0.696291 -0.537975 -0.092495 -0.888741 -0.448981 -0.642850 -0.567100 -0.514918 0.223822 0.696291 -0.681969 0.386986 -0.567101 -0.727075 -0.729968 0.045432 -0.681970 0.400983 0.045432 -0.914958 -0.193492 0.283551 -0.939234 -0.188492 -0.356822 -0.914958 Wrote generators to file: initial.xyz Discrepancy between generator and centroid, STEP = 1 Generator motions: Total = 0.115351 Average = 0.360471E-02 Minimum = 0.109183E-02 Maximum = 0.963664E-02 Discrepancy between generator and centroid, STEP = 2 Generator motions: Total = 0.105102 Average = 0.328445E-02 Minimum = 0.488281E-03 Maximum = 0.688807E-02 Discrepancy between generator and centroid, STEP = 3 Generator motions: Total = 0.110905 Average = 0.346578E-02 Minimum = 0.976562E-03 Maximum = 0.720113E-02 Discrepancy between generator and centroid, STEP = 4 Generator motions: Total = 0.115572 Average = 0.361163E-02 Minimum = 0.598020E-03 Maximum = 0.883644E-02 Discrepancy between generator and centroid, STEP = 5 Generator motions: Total = 0.112859 Average = 0.352685E-02 Minimum = 0.345267E-03 Maximum = 0.100306E-01 Discrepancy between generator and centroid, STEP = 6 Generator motions: Total = 0.110795 Average = 0.346233E-02 Minimum = 0.00000 Maximum = 0.995308E-02 Discrepancy between generator and centroid, STEP = 206 Generator motions: Total = 0.112152 Average = 0.350475E-02 Minimum = 0.690534E-03 Maximum = 0.822868E-02 Discrepancy between generator and centroid, STEP = 406 Generator motions: Total = 0.121812 Average = 0.380662E-02 Minimum = 0.124488E-02 Maximum = 0.627210E-02 Discrepancy between generator and centroid, STEP = 606 Generator motions: Total = 0.127630 Average = 0.398843E-02 Minimum = 0.103580E-02 Maximum = 0.829362E-02 Discrepancy between generator and centroid, STEP = 806 Generator motions: Total = 0.112658 Average = 0.352057E-02 Minimum = 0.488281E-03 Maximum = 0.932224E-02 Discrepancy between generator and centroid, STEP = 1006 Generator motions: Total = 0.116991 Average = 0.365597E-02 Minimum = 0.690534E-03 Maximum = 0.755655E-02 Discrepancy between generator and centroid, STEP = 1206 Generator motions: Total = 0.127369 Average = 0.398028E-02 Minimum = 0.690534E-03 Maximum = 0.923875E-02 Discrepancy between generator and centroid, STEP = 1406 Generator motions: Total = 0.134795 Average = 0.421235E-02 Minimum = 0.345267E-03 Maximum = 0.926452E-02 Discrepancy between generator and centroid, STEP = 1606 Generator motions: Total = 0.126733 Average = 0.396040E-02 Minimum = 0.690534E-03 Maximum = 0.897697E-02 Discrepancy between generator and centroid, STEP = 1806 Generator motions: Total = 0.123904 Average = 0.387199E-02 Minimum = 0.913491E-03 Maximum = 0.656916E-02 Discrepancy between generator and centroid, STEP = 2000 Generator motions: Total = 0.120813 Average = 0.377542E-02 Minimum = 0.690534E-03 Maximum = 0.932863E-02 Wrote generators to file: generators.xyz Motion of generators from initial to final. Generator motions: Total = 0.398404 Average = 0.124501E-01 Minimum = 0.133721E-02 Maximum = 0.226727E-01 June 7 2002 0:52:27.495 AM SCVT_MAIN Normal end of execution.