December 3 2002 9:07:41.485 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 4.00000 0.666667E-01 2 4.00000 0.666667E-01 3 4.00000 0.666667E-01 4 4.00000 0.666667E-01 5 4.00000 0.666667E-01 6 16.0000 0.133333 7 16.0000 0.133333 8 16.0000 0.133333 9 16.0000 0.133333 10 16.0000 0.133333 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 = 1866209499 Initializing the cell generators. Carry out the CVT iteration. Area iteration 1 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 2.90000 0.666667E-01 2 4.00000 4.16000 0.666667E-01 3 4.00000 4.72000 0.666667E-01 4 4.00000 3.26000 0.666667E-01 5 4.00000 3.56000 0.666667E-01 6 16.0000 16.6200 0.133333 7 16.0000 14.4200 0.133333 8 16.0000 13.3400 0.133333 9 16.0000 16.5200 0.133333 10 16.0000 20.5000 0.133333 Area discrepancy = 13.0400 Area iteration 2 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 5.36000 0.770738E-01 2 4.00000 4.96000 0.643515E-01 3 4.00000 4.42000 0.604136E-01 4 4.00000 4.20000 0.726937E-01 5 4.00000 3.88000 0.695634E-01 6 16.0000 15.9000 0.128780 7 16.0000 16.2600 0.138256 8 16.0000 16.9000 0.143743 9 16.0000 14.9600 0.129170 10 16.0000 13.1600 0.115955 Area discrepancy = 8.20000 Area iteration 3 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.30000 0.671829E-01 2 4.00000 3.40000 0.583113E-01 3 4.00000 3.84000 0.579907E-01 4 4.00000 4.40000 0.715825E-01 5 4.00000 4.52000 0.712688E-01 6 16.0000 15.7000 0.130352 7 16.0000 17.1800 0.138384 8 16.0000 16.4400 0.141127 9 16.0000 15.1800 0.134791 10 16.0000 15.0400 0.129011 Area discrepancy = 5.68000 Area iteration 4 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.32000 0.649049E-01 2 4.00000 3.54000 0.633528E-01 3 4.00000 3.92000 0.592850E-01 4 4.00000 4.00000 0.683649E-01 5 4.00000 3.62000 0.671557E-01 6 16.0000 16.0600 0.131810 7 16.0000 17.0200 0.133770 8 16.0000 15.8400 0.139457 9 16.0000 15.8800 0.138614 10 16.0000 15.8000 0.133286 Area discrepancy = 2.80000 Area iteration 5 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.74000 0.622475E-01 2 4.00000 4.46000 0.671199E-01 3 4.00000 4.38000 0.596883E-01 4 4.00000 3.56000 0.681381E-01 5 4.00000 4.60000 0.703583E-01 6 16.0000 16.1600 0.131127 7 16.0000 15.3400 0.129269 8 16.0000 15.9400 0.139695 9 16.0000 15.7800 0.138675 10 16.0000 16.0400 0.133682 Area discrepancy = 3.28000 Area iteration 6 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.98000 0.644765E-01 2 4.00000 4.06000 0.636647E-01 3 4.00000 3.46000 0.571304E-01 4 4.00000 3.72000 0.723403E-01 5 4.00000 3.90000 0.657131E-01 6 16.0000 15.6600 0.130683 7 16.0000 15.4600 0.132229 8 16.0000 17.3000 0.140178 9 16.0000 16.4200 0.139859 10 16.0000 16.0400 0.133726 Area discrepancy = 3.64000 Area iteration 7 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.32000 0.643898E-01 2 4.00000 4.20000 0.629496E-01 3 4.00000 4.26000 0.611908E-01 4 4.00000 4.54000 0.747249E-01 5 4.00000 4.46000 0.662943E-01 6 16.0000 15.7000 0.131586 7 16.0000 16.7400 0.134002 8 16.0000 14.5600 0.134290 9 16.0000 15.7400 0.137528 10 16.0000 15.4800 0.133045 Area discrepancy = 5.04000 Area iteration 8 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.06000 0.623239E-01 2 4.00000 3.58000 0.617942E-01 3 4.00000 4.82000 0.596432E-01 4 4.00000 3.68000 0.705533E-01 5 4.00000 3.10000 0.631522E-01 6 16.0000 16.8000 0.133619 7 16.0000 15.4600 0.131778 8 16.0000 16.0200 0.141603 9 16.0000 16.2400 0.139475 10 16.0000 16.2400 0.136058 Area discrepancy = 4.36000 Area iteration 9 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.84000 0.614762E-01 2 4.00000 3.36000 0.649115E-01 3 4.00000 4.06000 0.539949E-01 4 4.00000 4.20000 0.730986E-01 5 4.00000 3.78000 0.712891E-01 6 16.0000 16.0200 0.129586 7 16.0000 17.6000 0.133224 8 16.0000 16.4200 0.140633 9 16.0000 14.4600 0.137578 10 16.0000 16.2600 0.134208 Area discrepancy = 5.12000 Area iteration 10 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.80000 0.624295E-01 2 4.00000 4.66000 0.704694E-01 3 4.00000 3.76000 0.533259E-01 4 4.00000 4.08000 0.709795E-01 5 4.00000 4.52000 0.729669E-01 6 16.0000 15.2600 0.128857 7 16.0000 15.7600 0.126388 8 16.0000 16.1400 0.138127 9 16.0000 16.6000 0.143994 10 16.0000 15.4200 0.132463 Area discrepancy = 4.00000 Area iteration 11 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.14000 0.642841E-01 2 4.00000 3.68000 0.655259E-01 3 4.00000 3.86000 0.552013E-01 4 4.00000 3.68000 0.705355E-01 5 4.00000 3.52000 0.688909E-01 6 16.0000 16.2600 0.132423 7 16.0000 16.0600 0.127809 8 16.0000 15.5600 0.138027 9 16.0000 16.9200 0.141881 10 16.0000 16.3200 0.135422 Area discrepancy = 3.40000 Area iteration 12 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.10000 0.628343E-01 2 4.00000 4.32000 0.679333E-01 3 4.00000 4.10000 0.558791E-01 4 4.00000 4.06000 0.731270E-01 5 4.00000 3.88000 0.730271E-01 6 16.0000 17.1000 0.130625 7 16.0000 15.0600 0.126857 8 16.0000 15.3400 0.139182 9 16.0000 15.3800 0.137198 10 16.0000 16.6600 0.133337 Area discrepancy = 4.68000 Area iteration 13 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.20000 0.621119E-01 2 4.00000 4.54000 0.654200E-01 3 4.00000 3.60000 0.552367E-01 4 4.00000 4.56000 0.726414E-01 5 4.00000 4.68000 0.742058E-01 6 16.0000 15.4800 0.126453 7 16.0000 15.9000 0.130858 8 16.0000 15.7400 0.142256 9 16.0000 16.2200 0.140046 10 16.0000 15.0800 0.130772 Area discrepancy = 4.40000 Area iteration 14 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.12000 0.609850E-01 2 4.00000 3.82000 0.617811E-01 3 4.00000 4.04000 0.585800E-01 4 4.00000 3.46000 0.684502E-01 5 4.00000 4.16000 0.690221E-01 6 16.0000 15.8000 0.129344 7 16.0000 16.1600 0.132070 8 16.0000 16.3600 0.144301 9 16.0000 15.5200 0.139942 10 16.0000 16.5600 0.135524 Area discrepancy = 2.80000 Area iteration 15 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.28000 0.599428E-01 2 4.00000 3.30000 0.630647E-01 3 4.00000 3.60000 0.581461E-01 4 4.00000 4.28000 0.734174E-01 5 4.00000 4.10000 0.675155E-01 6 16.0000 16.0000 0.129841 7 16.0000 15.5600 0.131092 8 16.0000 17.6800 0.142354 9 16.0000 15.5200 0.141741 10 16.0000 16.6800 0.132886 Area discrepancy = 5.48000 Area iteration 16 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.12000 0.657460E-01 2 4.00000 4.46000 0.689601E-01 3 4.00000 4.48000 0.608749E-01 4 4.00000 4.08000 0.704930E-01 5 4.00000 4.38000 0.662339E-01 6 16.0000 15.0000 0.128958 7 16.0000 17.3200 0.132029 8 16.0000 15.9000 0.134502 9 16.0000 16.0400 0.142938 10 16.0000 14.2200 0.129264 Area discrepancy = 5.76000 Area iteration 17 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.04000 0.650683E-01 2 4.00000 3.46000 0.655964E-01 3 4.00000 4.36000 0.577762E-01 4 4.00000 3.74000 0.701077E-01 5 4.00000 3.56000 0.635759E-01 6 16.0000 17.1600 0.133778 7 16.0000 15.6000 0.127461 8 16.0000 14.5400 0.135522 9 16.0000 17.0000 0.143392 10 16.0000 16.5400 0.137724 Area discrepancy = 6.20000 Area iteration 18 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 4.56000 0.643913E-01 2 4.00000 4.64000 0.701439E-01 3 4.00000 3.30000 0.550368E-01 4 4.00000 5.06000 0.721070E-01 5 4.00000 4.18000 0.670217E-01 6 16.0000 15.0000 0.128470 7 16.0000 15.0800 0.128378 8 16.0000 16.6600 0.141385 9 16.0000 15.9000 0.138350 10 16.0000 15.6200 0.134716 Area discrepancy = 6.20000 Area iteration 19 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.56000 0.606532E-01 2 4.00000 4.02000 0.654998E-01 3 4.00000 4.16000 0.609405E-01 4 4.00000 3.62000 0.644780E-01 5 4.00000 4.12000 0.659382E-01 6 16.0000 16.7600 0.133443 7 16.0000 15.8000 0.132993 8 16.0000 15.9200 0.139350 9 16.0000 15.3400 0.139579 10 16.0000 16.7000 0.137125 Area discrepancy = 3.52000 Area iteration 20 Desired, Actual, Linear Cell Volume Volume Weight 1 4.00000 3.72000 0.641115E-01 2 4.00000 4.00000 0.651530E-01 3 4.00000 4.62000 0.595890E-01 4 4.00000 3.68000 0.675872E-01 5 4.00000 3.74000 0.647881E-01 6 16.0000 17.0000 0.130016 7 16.0000 16.5600 0.133456 8 16.0000 15.5600 0.139307 9 16.0000 15.8600 0.142149 10 16.0000 15.2600 0.133843 Area discrepancy = 4.36000 Cell generators: 1 0.102687E+01 0.893038E+01 2 0.895884E+01 0.496347E+01 3 0.617390E+01 0.492965E+01 4 0.914086E+00 0.265157E+01 5 0.104254E+01 0.880898E+00 6 0.802622E+01 0.211176E+01 7 0.422824E+01 0.201750E+01 8 0.198380E+01 0.554323E+01 9 0.442817E+01 0.811143E+01 10 0.817678E+01 0.779422E+01 Cell volumes: 1 0.372000E+01 2 0.400000E+01 3 0.462000E+01 4 0.368000E+01 5 0.374000E+01 6 0.170000E+02 7 0.165600E+02 8 0.155600E+02 9 0.158600E+02 10 0.152600E+02 CVT_SIZE_PRB Normal end of execution. December 3 2002 9:07:59.145 AM