September 16 2001 11:50:38.514 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 NDIM = 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 = 1464069145 Initializing the cell generators. Carry out the CVT iteration. Area iteration 1 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 0.720000 0.445072E-01 2 3.63636 3.24000 0.629427E-01 3 5.45455 3.74000 0.770887E-01 4 7.27273 6.98000 0.890144E-01 5 9.09091 9.68000 0.995211E-01 6 10.9091 9.48000 0.109020 7 12.7273 13.0800 0.117755 8 14.5455 16.5600 0.125885 9 16.3636 14.5800 0.133522 10 18.1818 21.9400 0.140744 Area discrepancy = 13.4290924 Area iteration 2 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.64000 0.543629E-01 2 3.63636 5.58000 0.651581E-01 3 5.45455 6.50000 0.909697E-01 4 7.27273 7.44000 0.887858E-01 5 9.09091 7.88000 0.942418E-01 6 10.9091 10.5000 0.114277 7 12.7273 11.5800 0.113502 8 14.5455 12.6200 0.115285 9 16.3636 17.7200 0.138221 10 18.1818 17.5400 0.125197 Area discrepancy = 10.6690884 Area iteration 3 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.82000 0.455895E-01 2 3.63636 3.02000 0.531534E-01 3 5.45455 6.68000 0.842102E-01 4 7.27273 6.96000 0.887056E-01 5 9.09091 8.36000 0.102289 6 10.9091 11.5000 0.117707 7 12.7273 13.9200 0.120244 8 14.5455 13.4600 0.125069 9 16.3636 15.7800 0.134224 10 18.1818 18.5000 0.128808 Area discrepancy = 6.65818167 Area iteration 4 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.66000 0.455055E-01 2 3.63636 3.72000 0.582475E-01 3 5.45455 5.48000 0.759928E-01 4 7.27273 8.14000 0.905548E-01 5 9.09091 10.0000 0.106524 6 10.9091 10.4800 0.114489 7 12.7273 11.6800 0.114823 8 14.5455 14.7200 0.129840 9 16.3636 16.6400 0.136500 10 18.1818 17.4800 0.127524 Area discrepancy = 4.67272854 Area iteration 5 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.22000 0.476554E-01 2 3.63636 3.84000 0.576265E-01 3 5.45455 6.38000 0.758655E-01 4 7.27273 7.14000 0.856507E-01 5 9.09091 8.90000 0.101633 6 10.9091 10.7600 0.116886 7 12.7273 12.7600 0.119938 8 14.5455 14.4400 0.129152 9 16.3636 15.6000 0.135450 10 18.1818 17.9600 0.130143 Area discrepancy = 3.1272738 Area iteration 6 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.90000 0.433319E-01 2 3.63636 3.28000 0.563435E-01 3 5.45455 5.46000 0.704801E-01 4 7.27273 6.34000 0.868529E-01 5 9.09091 8.64000 0.103204 6 10.9091 11.4200 0.118251 7 12.7273 13.3800 0.120352 8 14.5455 14.5200 0.130237 9 16.3636 17.4000 0.139383 10 18.1818 17.6600 0.131565 Area discrepancy = 4.57454443 Area iteration 7 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.10000 0.422613E-01 2 3.63636 3.68000 0.591472E-01 3 5.45455 4.82000 0.702333E-01 4 7.27273 7.16000 0.927431E-01 5 9.09091 9.92000 0.105545 6 10.9091 11.0000 0.115228 7 12.7273 11.1800 0.117027 8 14.5455 15.2600 0.129960 9 16.3636 15.8400 0.134762 10 18.1818 19.0400 0.133094 Area discrepancy = 5.63636398 Area iteration 8 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.24000 0.392894E-01 2 3.63636 3.82000 0.587446E-01 3 5.45455 4.70000 0.746488E-01 4 7.27273 7.88000 0.933894E-01 5 9.09091 8.02000 0.100950 6 10.9091 10.8600 0.114652 7 12.7273 13.5600 0.124755 8 14.5455 15.1200 0.126771 9 16.3636 16.2000 0.136853 10 18.1818 18.6000 0.129947 Area discrepancy = 5.23272896 Area iteration 9 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.12000 0.471680E-01 2 3.63636 3.14000 0.568243E-01 3 5.45455 5.80000 0.797292E-01 4 7.27273 6.82000 0.889502E-01 5 9.09091 10.4200 0.106558 6 10.9091 10.8800 0.113926 7 12.7273 13.3200 0.119828 8 14.5455 14.1200 0.123274 9 16.3636 16.0800 0.136364 10 18.1818 17.3000 0.127378 Area discrepancy = 5.13818169 Area iteration 10 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.86000 0.437687E-01 2 3.63636 3.70000 0.612728E-01 3 5.45455 5.04000 0.774725E-01 4 7.27273 6.80000 0.920384E-01 5 9.09091 9.34000 0.997294E-01 6 10.9091 9.56000 0.114306 7 12.7273 12.0200 0.117365 8 14.5455 15.3800 0.125367 9 16.3636 17.6400 0.137836 10 18.1818 18.6600 0.130844 Area discrepancy = 5.88727188 Area iteration 11 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.34000 0.430632E-01 2 3.63636 3.78000 0.604479E-01 3 5.45455 6.48000 0.802033E-01 4 7.27273 7.36000 0.947205E-01 5 9.09091 8.64000 0.979115E-01 6 10.9091 10.9800 0.121511 7 12.7273 12.1400 0.120181 8 14.5455 13.9000 0.121324 9 16.3636 15.8400 0.132109 10 18.1818 18.5400 0.128528 Area discrepancy = 4.41454411 Area iteration 12 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.48000 0.381400E-01 2 3.63636 3.52000 0.595707E-01 3 5.45455 5.20000 0.739346E-01 4 7.27273 7.06000 0.946057E-01 5 9.09091 8.64000 0.100912 6 10.9091 10.4600 0.121695 7 12.7273 14.0600 0.123640 8 14.5455 15.5200 0.124700 9 16.3636 16.8200 0.134915 10 18.1818 17.2400 0.127887 Area discrepancy = 5.52727413 Area iteration 13 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.80000 0.420583E-01 2 3.63636 3.06000 0.602391E-01 3 5.45455 5.22000 0.753371E-01 4 7.27273 7.42000 0.955316E-01 5 9.09091 9.50000 0.102985 6 10.9091 11.0800 0.123647 7 12.7273 12.8800 0.117035 8 14.5455 14.1600 0.120107 9 16.3636 15.3600 0.132395 10 18.1818 19.5200 0.130665 Area discrepancy = 4.43636513 Area iteration 14 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.56000 0.421107E-01 2 3.63636 4.70000 0.654198E-01 3 5.45455 6.02000 0.767204E-01 4 7.27273 7.06000 0.942218E-01 5 9.09091 8.62000 0.100363 6 10.9091 10.7600 0.122227 7 12.7273 13.2600 0.115900 8 14.5455 14.0000 0.121271 9 16.3636 17.4400 0.136136 10 18.1818 16.5800 0.125631 Area discrepancy = 6.47636414 Area iteration 15 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.78000 0.455353E-01 2 3.63636 3.50000 0.576360E-01 3 5.45455 5.24000 0.731462E-01 4 7.27273 7.74000 0.957850E-01 5 9.09091 8.78000 0.103234 6 10.9091 10.7600 0.123269 7 12.7273 12.1000 0.113731 8 14.5455 13.1000 0.123811 9 16.3636 17.1400 0.132080 10 18.1818 19.8600 0.131772 Area discrepancy = 5.84363508 Area iteration 16 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.86000 0.458536E-01 2 3.63636 4.10000 0.585342E-01 3 5.45455 5.32000 0.743570E-01 4 7.27273 6.12000 0.925107E-01 5 9.09091 9.06000 0.104664 6 10.9091 11.7600 0.123668 7 12.7273 12.5800 0.116217 8 14.5455 16.6600 0.129988 9 16.3636 15.1800 0.128585 10 18.1818 17.3600 0.125622 Area discrepancy = 6.94181585 Area iteration 17 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.72000 0.452912E-01 2 3.63636 2.94000 0.550719E-01 3 5.45455 5.14000 0.752183E-01 4 7.27273 8.52000 0.100750 5 9.09091 9.08000 0.104741 6 10.9091 11.4000 0.118995 7 12.7273 11.8800 0.116782 8 14.5455 13.9800 0.121341 9 16.3636 15.8400 0.133374 10 18.1818 19.5000 0.128437 Area discrepancy = 6.11272621 Area iteration 18 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.02000 0.463889E-01 2 3.63636 3.78000 0.610149E-01 3 5.45455 5.70000 0.771911E-01 4 7.27273 7.26000 0.927295E-01 5 9.09091 9.26000 0.104405 6 10.9091 10.9400 0.115962 7 12.7273 13.8200 0.120415 8 14.5455 13.4600 0.123300 9 16.3636 16.3400 0.135045 10 18.1818 17.4200 0.123548 Area discrepancy = 3.76727104 Area iteration 19 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 2.04000 0.441644E-01 2 3.63636 3.54000 0.600535E-01 3 5.45455 5.42000 0.757746E-01 4 7.27273 6.88000 0.931351E-01 5 9.09091 9.38000 0.103809 6 10.9091 10.0000 0.116202 7 12.7273 12.2600 0.115961 8 14.5455 15.4600 0.128623 9 16.3636 16.3000 0.135615 10 18.1818 18.7200 0.126662 Area discrepancy = 3.92727208 Area iteration 20 Desired, Actual, Linear Cell Volume Volume Weight 1 1.81818 1.52000 0.416311E-01 2 3.63636 3.22000 0.607733E-01 3 5.45455 6.00000 0.759007E-01 4 7.27273 8.10000 0.956114E-01 5 9.09091 9.22000 0.102042 6 10.9091 11.3200 0.121186 7 12.7273 13.2600 0.117971 8 14.5455 14.5600 0.124572 9 16.3636 15.4200 0.135674 10 18.1818 17.3800 0.124639 Area discrepancy = 4.92000246 Cell generators: 1 0.308835E+01 0.474227E+01 2 0.538450E+01 0.762819E+00 3 0.113331E+01 0.448326E+01 4 0.448827E+01 0.284585E+01 5 0.565370E+01 0.533936E+01 6 0.535921E+01 0.849509E+01 7 0.188988E+01 0.163834E+01 8 0.860110E+01 0.742737E+01 9 0.185904E+01 0.774516E+01 10 0.824790E+01 0.236524E+01 Cell volumes: 1 0.152000E+01 2 0.322000E+01 3 0.600000E+01 4 0.810000E+01 5 0.922000E+01 6 0.113200E+02 7 0.132600E+02 8 0.145600E+02 9 0.154200E+02 10 0.173800E+02 CVT_SIZE_PRB Normal end of execution.