December 3 2002 9:04:08.726 AM CVT_SIZE_PRB A sample problem for the probabilistic sized Centroidal Voronoi Tesselation algorithm. Given a region in 2D, the problem is to determine GENERATORS, a set of points which define a division of the region into Voronoid cells, which are also CENTROIDS of the Voronoi cells, and which have a certain SIZE. Geometry parameters: ------------------- The spatial dimension is DIM_NUM = 2 The minimum corner of the bounding box is: 0.0000 0.0000 The maximum corner of the bounding box is: 10.0000 10.0000 CVT Algorithm parameters: ------------------------- The number of Voronoi cells to generate: 10 Number of iterations to determine CVT: 1 Number of sampling points: 5000 Voronoi cell generators are initialized by RANDOM_NUMBER. The desired CVT cell volumes and initial weights are: 1 1.81818 0.445072E-01 2 3.63636 0.629427E-01 3 5.45455 0.770887E-01 4 7.27273 0.890144E-01 5 9.09091 0.995211E-01 6 10.9091 0.109020 7 12.7273 0.117755 8 14.5455 0.125885 9 16.3636 0.133522 10 18.1818 0.140744 Nearest Neighbor Search parameters: ----------------------------------- The nearest neighbor search is not speeded up. The nearest neighbor search is done by exhaustion. Miscellaneous parameters: ------------------------ Generator and moment output files WILL be written. RANDOM_INITIALIZE Initialize RANDOM_NUMBER with arbitrary SEED = 1864081915 Initializing the cell generators. Carry out the CVT iteration. Area iteration 1 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.92000 0.445072E-01 2 3.63636 3.38000 0.629427E-01 3 5.45455 6.12000 0.770887E-01 4 7.27273 5.98000 0.890144E-01 5 9.09091 7.22000 0.995211E-01 6 10.9091 12.1000 0.109020 7 12.7273 12.7400 0.117755 8 14.5455 14.3800 0.125885 9 16.3636 16.6400 0.133522 10 18.1818 18.5200 0.140744 Area discrepancy = 7.17091 Area iteration 2 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.62000 0.350256E-01 2 3.63636 3.80000 0.651101E-01 3 5.45455 4.56000 0.725809E-01 4 7.27273 8.42000 0.979007E-01 5 9.09091 9.12000 0.111372 6 10.9091 12.0200 0.103237 7 12.7273 12.7600 0.117379 8 14.5455 15.4200 0.126266 9 16.3636 16.3600 0.132051 10 18.1818 15.9200 0.139077 Area discrepancy = 6.71636 Area iteration 3 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.38000 0.370592E-01 2 3.63636 3.20000 0.636120E-01 3 5.45455 5.08000 0.792808E-01 4 7.27273 6.74000 0.908715E-01 5 9.09091 9.48000 0.111054 6 10.9091 11.0000 0.982260E-01 7 12.7273 12.9800 0.117080 8 14.5455 13.7600 0.122478 9 16.3636 17.3800 0.131899 10 18.1818 19.0000 0.148440 Area discrepancy = 5.13454 Area iteration 4 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.96000 0.421785E-01 2 3.63636 3.64000 0.672380E-01 3 5.45455 6.04000 0.814578E-01 4 7.27273 7.54000 0.935973E-01 5 9.09091 9.62000 0.107833 6 10.9091 10.6400 0.969932E-01 7 12.7273 12.5000 0.114955 8 14.5455 14.2400 0.124862 9 16.3636 15.3200 0.126903 10 18.1818 18.5000 0.143983 Area discrepancy = 3.69091 Area iteration 5 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.86000 0.407756E-01 2 3.63636 3.72000 0.674552E-01 3 5.45455 5.90000 0.776983E-01 4 7.27273 6.84000 0.922666E-01 5 9.09091 8.62000 0.105217 6 10.9091 10.8800 0.985786E-01 7 12.7273 12.5200 0.116428 8 14.5455 14.7000 0.126665 9 16.3636 16.8200 0.131644 10 18.1818 18.1400 0.143272 Area discrepancy = 2.36364 Area iteration 6 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.28000 0.403031E-01 2 3.63636 3.68000 0.666736E-01 3 5.45455 5.50000 0.746862E-01 4 7.27273 6.78000 0.951132E-01 5 9.09091 9.94000 0.108021 6 10.9091 10.9400 0.986821E-01 7 12.7273 12.8200 0.117355 8 14.5455 15.0400 0.125961 9 16.3636 15.7400 0.129808 10 18.1818 18.2800 0.143396 Area discrepancy = 3.30909 Area iteration 7 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.18000 0.477853E-01 2 3.63636 3.70000 0.659334E-01 3 5.45455 5.18000 0.739913E-01 4 7.27273 7.82000 0.979979E-01 5 9.09091 9.08000 0.102769 6 10.9091 10.0600 0.980316E-01 7 12.7273 12.2600 0.116323 8 14.5455 14.9000 0.123231 9 16.3636 17.2600 0.131669 10 18.1818 17.5600 0.142269 Area discrepancy = 4.44727 Area iteration 8 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.38000 0.437450E-01 2 3.63636 3.66000 0.655213E-01 3 5.45455 5.22000 0.761096E-01 4 7.27273 7.88000 0.947341E-01 5 9.09091 7.84000 0.103078 6 10.9091 11.2600 0.102331 7 12.7273 12.8000 0.118805 8 14.5455 14.5800 0.122049 9 16.3636 15.9600 0.128513 10 18.1818 18.4200 0.145115 Area discrepancy = 3.77818 Area iteration 9 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.16000 0.382827E-01 2 3.63636 3.84000 0.653913E-01 3 5.45455 5.86000 0.778982E-01 4 7.27273 5.80000 0.911247E-01 5 9.09091 10.6200 0.111137 6 10.9091 12.2400 0.100850 7 12.7273 12.9400 0.118615 8 14.5455 13.4200 0.122057 9 16.3636 15.9000 0.130291 10 18.1818 18.2200 0.144354 Area discrepancy = 7.44000 Area iteration 10 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.00000 0.474829E-01 2 3.63636 3.06000 0.631411E-01 3 5.45455 5.68000 0.745730E-01 4 7.27273 8.06000 0.101250 5 9.09091 8.46000 0.102029 6 10.9091 10.2400 0.944718E-01 7 12.7273 12.5800 0.116725 8 14.5455 14.3400 0.126088 9 16.3636 17.9400 0.131153 10 18.1818 17.6400 0.143086 Area discrepancy = 5.54182 Area iteration 11 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 3.10000 0.452029E-01 2 3.63636 4.06000 0.687243E-01 3 5.45455 5.10000 0.729646E-01 4 7.27273 7.24000 0.960287E-01 5 9.09091 9.18000 0.105601 6 10.9091 10.2400 0.973581E-01 7 12.7273 13.3800 0.117224 8 14.5455 13.8800 0.126791 9 16.3636 15.6000 0.125064 10 18.1818 18.2200 0.145041 Area discrepancy = 4.97091 Area iteration 12 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.72000 0.348257E-01 2 3.63636 4.18000 0.654301E-01 3 5.45455 5.80000 0.759107E-01 4 7.27273 7.00000 0.968226E-01 5 9.09091 8.30000 0.105717 6 10.9091 10.0000 0.101091 7 12.7273 12.3200 0.115015 8 14.5455 14.8800 0.130573 9 16.3636 16.5400 0.128857 10 18.1818 19.2600 0.145758 Area discrepancy = 4.95637 Area iteration 13 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.60000 0.357648E-01 2 3.63636 3.06000 0.609570E-01 3 5.45455 5.40000 0.735308E-01 4 7.27273 7.94000 0.985774E-01 5 9.09091 10.8200 0.110512 6 10.9091 12.1000 0.105465 7 12.7273 12.1600 0.116766 8 14.5455 16.3000 0.128949 9 16.3636 13.8000 0.128021 10 18.1818 16.8200 0.141457 Area discrepancy = 10.6836 Area iteration 14 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.62000 0.380490E-01 2 3.63636 3.64000 0.663172E-01 3 5.45455 4.88000 0.737532E-01 4 7.27273 7.22000 0.941554E-01 5 9.09091 7.70000 0.101095 6 10.9091 10.4400 0.999399E-01 7 12.7273 12.4000 0.119219 8 14.5455 12.9800 0.121567 9 16.3636 19.6200 0.139127 10 18.1818 19.5000 0.146777 Area discrepancy = 9.15637 Area iteration 15 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.66000 0.399365E-01 2 3.63636 3.60000 0.656712E-01 3 5.45455 5.70000 0.772532E-01 4 7.27273 6.56000 0.936248E-01 5 9.09091 9.76000 0.108831 6 10.9091 11.7400 0.101216 7 12.7273 13.2800 0.119666 8 14.5455 15.3200 0.127499 9 16.3636 15.2400 0.125883 10 18.1818 17.1400 0.140419 Area discrepancy = 6.14545 Area iteration 16 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.68000 0.417543E-01 2 3.63636 3.80000 0.659360E-01 3 5.45455 5.98000 0.754960E-01 4 7.27273 6.96000 0.984812E-01 5 9.09091 9.34000 0.104930 6 10.9091 11.1400 0.974709E-01 7 12.7273 12.3200 0.117032 8 14.5455 15.0200 0.124110 9 16.3636 16.3200 0.130311 10 18.1818 17.4400 0.144479 Area discrepancy = 3.28727 Area iteration 17 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.82000 0.434472E-01 2 3.63636 3.52000 0.645152E-01 3 5.45455 5.90000 0.721190E-01 4 7.27273 7.70000 0.100692 5 9.09091 8.80000 0.103544 6 10.9091 10.6800 0.964770E-01 7 12.7273 13.2600 0.118977 8 14.5455 14.4000 0.122161 9 16.3636 15.9800 0.130514 10 18.1818 17.9400 0.147553 Area discrepancy = 2.81455 Area iteration 18 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.46000 0.434732E-01 2 3.63636 3.50000 0.656449E-01 3 5.45455 4.96000 0.694192E-01 4 7.27273 7.28000 0.979659E-01 5 9.09091 8.96000 0.105357 6 10.9091 10.6000 0.976133E-01 7 12.7273 11.3200 0.116691 8 14.5455 14.4400 0.122912 9 16.3636 17.6800 0.132216 10 18.1818 19.8000 0.148707 Area discrepancy = 5.88364 Area iteration 19 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.60000 0.481247E-01 2 3.63636 2.88000 0.663751E-01 3 5.45455 5.84000 0.722142E-01 4 7.27273 7.92000 0.971319E-01 5 9.09091 10.0000 0.105274 6 10.9091 10.6200 0.982324E-01 7 12.7273 13.4600 0.122740 8 14.5455 14.4000 0.122371 9 16.3636 15.5400 0.126179 10 18.1818 16.7400 0.141359 Area discrepancy = 6.91273 Area iteration 20 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.42000 0.403743E-01 2 3.63636 5.16000 0.748251E-01 3 5.45455 4.94000 0.700165E-01 4 7.27273 6.92000 0.933798E-01 5 9.09091 8.04000 0.100700 6 10.9091 10.4000 0.998830E-01 7 12.7273 12.4000 0.119739 8 14.5455 13.9200 0.123386 9 16.3636 16.6400 0.129899 10 18.1818 19.1600 0.147798 Area discrepancy = 6.76000 Cell generators: 1 0.911092E+01 0.935213E+01 2 0.114593E+01 0.367679E+01 3 0.142206E+01 0.912308E+01 4 0.137465E+01 0.124225E+01 5 0.505254E+01 0.541743E+01 6 0.866187E+01 0.185165E+01 7 0.534504E+01 0.866454E+01 8 0.192948E+01 0.637275E+01 9 0.831488E+01 0.629462E+01 10 0.495161E+01 0.225180E+01 Cell volumes: 1 0.242000E+01 2 0.516000E+01 3 0.494000E+01 4 0.692000E+01 5 0.804000E+01 6 0.104000E+02 7 0.124000E+02 8 0.139200E+02 9 0.166400E+02 10 0.191600E+02 CVT_SIZE_PRB Normal end of execution. December 3 2002 9:04:26.878 AM