December 3 2002 8:43:24.546 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 5.00000 0.732051E-01 2 5.00000 0.732051E-01 3 5.00000 0.732051E-01 4 5.00000 0.732051E-01 5 5.00000 0.732051E-01 6 15.0000 0.126795 7 15.0000 0.126795 8 15.0000 0.126795 9 15.0000 0.126795 10 15.0000 0.126795 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 = 1851640114 Initializing the cell generators. Carry out the CVT iteration. Area iteration 1 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 6.90000 0.732051E-01 2 5.00000 4.82000 0.732051E-01 3 5.00000 4.62000 0.732051E-01 4 5.00000 4.94000 0.732051E-01 5 5.00000 5.38000 0.732051E-01 6 15.0000 16.2800 0.126795 7 15.0000 13.3000 0.126795 8 15.0000 15.4200 0.126795 9 15.0000 14.0600 0.126795 10 15.0000 14.2800 0.126795 Area discrepancy = 7.96000 Area iteration 2 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.00000 0.623419E-01 2 5.00000 5.04000 0.745901E-01 3 5.00000 5.16000 0.761875E-01 4 5.00000 4.88000 0.736786E-01 5 5.00000 4.20000 0.706014E-01 6 15.0000 16.0600 0.121758 7 15.0000 15.0600 0.134710 8 15.0000 15.3400 0.125108 9 15.0000 15.2600 0.131019 10 15.0000 14.0000 0.130006 Area discrepancy = 3.84000 Area iteration 3 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.02000 0.621222E-01 2 5.00000 4.68000 0.740317E-01 3 5.00000 4.40000 0.747327E-01 4 5.00000 4.96000 0.743161E-01 5 5.00000 4.80000 0.767610E-01 6 15.0000 13.5200 0.117257 7 15.0000 15.4400 0.133968 8 15.0000 14.5200 0.123277 9 15.0000 15.8200 0.129440 10 15.0000 16.8400 0.134094 Area discrepancy = 6.24000 Area iteration 4 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.34000 0.617149E-01 2 5.00000 6.26000 0.761710E-01 3 5.00000 5.50000 0.793011E-01 4 5.00000 5.22000 0.742741E-01 5 5.00000 5.62000 0.779857E-01 6 15.0000 15.8800 0.122944 7 15.0000 13.9000 0.131441 8 15.0000 14.0400 0.124726 9 15.0000 15.1400 0.125465 10 15.0000 13.1000 0.125978 Area discrepancy = 7.92000 Area iteration 5 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.90000 0.600607E-01 2 5.00000 4.40000 0.684657E-01 3 5.00000 5.12000 0.760446E-01 4 5.00000 4.34000 0.731093E-01 5 5.00000 5.32000 0.739806E-01 6 15.0000 14.8600 0.120174 7 15.0000 14.6600 0.137327 8 15.0000 14.2600 0.129659 9 15.0000 15.8600 0.125600 10 15.0000 16.2800 0.135578 Area discrepancy = 5.16000 Area iteration 6 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.90000 0.604339E-01 2 5.00000 4.90000 0.727002E-01 3 5.00000 4.86000 0.748553E-01 4 5.00000 5.92000 0.781658E-01 5 5.00000 4.90000 0.714415E-01 6 15.0000 15.3800 0.120268 7 15.0000 14.6000 0.138369 8 15.0000 15.6000 0.132463 9 15.0000 14.2600 0.121671 10 15.0000 14.6800 0.129632 Area discrepancy = 3.80000 Area iteration 7 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.82000 0.610991E-01 2 5.00000 5.12000 0.735004E-01 3 5.00000 5.34000 0.759900E-01 4 5.00000 4.30000 0.718965E-01 5 5.00000 5.06000 0.722279E-01 6 15.0000 14.1200 0.118874 7 15.0000 16.1800 0.140370 8 15.0000 15.6600 0.130000 9 15.0000 15.3600 0.124894 10 15.0000 14.0400 0.131148 Area discrepancy = 5.44000 Area iteration 8 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.52000 0.621296E-01 2 5.00000 5.34000 0.725174E-01 3 5.00000 4.64000 0.734130E-01 4 5.00000 5.48000 0.774035E-01 5 5.00000 5.02000 0.716831E-01 6 15.0000 15.6400 0.122325 7 15.0000 15.3200 0.134938 8 15.0000 13.8600 0.127027 9 15.0000 15.1000 0.123223 10 15.0000 15.0800 0.135340 Area discrepancy = 3.96000 Area iteration 9 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.06000 0.653152E-01 2 5.00000 4.80000 0.701385E-01 3 5.00000 4.98000 0.761727E-01 4 5.00000 5.92000 0.739019E-01 5 5.00000 5.24000 0.715072E-01 6 15.0000 15.9400 0.119741 7 15.0000 13.4400 0.133460 8 15.0000 15.0200 0.132087 9 15.0000 14.7400 0.122758 10 15.0000 14.8600 0.134919 Area discrepancy = 4.36000 Area iteration 10 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.70000 0.649826E-01 2 5.00000 4.98000 0.716463E-01 3 5.00000 5.66000 0.763910E-01 4 5.00000 4.16000 0.679755E-01 5 5.00000 4.38000 0.699104E-01 6 15.0000 14.2800 0.116257 7 15.0000 16.0800 0.141114 8 15.0000 14.7200 0.132112 9 15.0000 14.8200 0.123942 10 15.0000 16.2200 0.135669 Area discrepancy = 5.92000 Area iteration 11 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.98000 0.667708E-01 2 5.00000 4.56000 0.715184E-01 3 5.00000 4.28000 0.715274E-01 4 5.00000 5.20000 0.742411E-01 5 5.00000 5.48000 0.744121E-01 6 15.0000 15.0200 0.118701 7 15.0000 15.8200 0.135777 8 15.0000 16.1400 0.132858 9 15.0000 13.7600 0.124221 10 15.0000 13.7600 0.129973 Area discrepancy = 7.28000 Area iteration 12 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.24000 0.609668E-01 2 5.00000 4.90000 0.747812E-01 3 5.00000 4.96000 0.771984E-01 4 5.00000 4.40000 0.726943E-01 5 5.00000 4.28000 0.709759E-01 6 15.0000 15.4800 0.118450 7 15.0000 14.0800 0.132020 8 15.0000 14.2600 0.127895 9 15.0000 15.9000 0.129510 10 15.0000 16.5000 0.135508 Area discrepancy = 6.24000 Area iteration 13 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.86000 0.592086E-01 2 5.00000 5.88000 0.751019E-01 3 5.00000 5.36000 0.770591E-01 4 5.00000 6.14000 0.770425E-01 5 5.00000 5.28000 0.762685E-01 6 15.0000 13.9000 0.115923 7 15.0000 14.7000 0.135474 8 15.0000 15.2400 0.130410 9 15.0000 15.4200 0.125061 10 15.0000 13.2200 0.128451 Area discrepancy = 6.64000 Area iteration 14 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.40000 0.603995E-01 2 5.00000 4.14000 0.696513E-01 3 5.00000 5.12000 0.748529E-01 4 5.00000 4.38000 0.699219E-01 5 5.00000 5.14000 0.746441E-01 6 15.0000 16.1400 0.121112 7 15.0000 15.0600 0.137634 8 15.0000 14.5000 0.130121 9 15.0000 13.9000 0.124053 10 15.0000 17.2200 0.137610 Area discrepancy = 7.36000 Area iteration 15 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.02000 0.639390E-01 2 5.00000 5.60000 0.760131E-01 3 5.00000 4.80000 0.734568E-01 4 5.00000 5.46000 0.741883E-01 5 5.00000 4.80000 0.731093E-01 6 15.0000 14.2000 0.115946 7 15.0000 14.9200 0.136405 8 15.0000 16.3800 0.131427 9 15.0000 15.2200 0.127973 10 15.0000 13.6000 0.127542 Area discrepancy = 5.36000 Area iteration 16 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.56000 0.638807E-01 2 5.00000 5.06000 0.719034E-01 3 5.00000 4.66000 0.750528E-01 4 5.00000 4.68000 0.710713E-01 5 5.00000 5.24000 0.746977E-01 6 15.0000 15.5200 0.119297 7 15.0000 14.8400 0.136919 8 15.0000 13.7000 0.125905 9 15.0000 14.1000 0.127183 10 15.0000 16.6400 0.134091 Area discrepancy = 6.04000 Area iteration 17 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.96000 0.604939E-01 2 5.00000 4.48000 0.713763E-01 3 5.00000 5.74000 0.776343E-01 4 5.00000 4.64000 0.733586E-01 5 5.00000 5.30000 0.728654E-01 6 15.0000 15.4800 0.117118 7 15.0000 14.7200 0.137463 8 15.0000 15.8400 0.131560 9 15.0000 15.0400 0.130996 10 15.0000 13.8000 0.127135 Area discrepancy = 4.80000 Area iteration 18 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.10000 0.606786E-01 2 5.00000 5.88000 0.753320E-01 3 5.00000 5.02000 0.723873E-01 4 5.00000 5.22000 0.760775E-01 5 5.00000 4.24000 0.707046E-01 6 15.0000 14.1200 0.115176 7 15.0000 16.1400 0.138630 8 15.0000 14.7200 0.127900 9 15.0000 16.0000 0.130695 10 15.0000 14.5600 0.132419 Area discrepancy = 6.52000 Area iteration 19 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 5.48000 0.668498E-01 2 5.00000 4.30000 0.693022E-01 3 5.00000 4.56000 0.720720E-01 4 5.00000 5.06000 0.742810E-01 5 5.00000 5.20000 0.765987E-01 6 15.0000 14.4600 0.118430 7 15.0000 14.9800 0.133328 8 15.0000 15.4200 0.128805 9 15.0000 15.3600 0.126246 10 15.0000 15.1800 0.134087 Area discrepancy = 3.40000 Area iteration 20 Desired, Actual, Linear Cell Volume Volume Weight 1 5.00000 4.52000 0.637193E-01 2 5.00000 5.54000 0.745717E-01 3 5.00000 5.00000 0.753088E-01 4 5.00000 5.60000 0.736823E-01 5 5.00000 5.10000 0.749516E-01 6 15.0000 16.2400 0.120365 7 15.0000 14.4200 0.133134 8 15.0000 15.1400 0.126769 9 15.0000 13.6200 0.124493 10 15.0000 14.8200 0.133006 Area discrepancy = 5.24000 Cell generators: 1 0.438367E+01 0.895928E+01 2 0.450761E+01 0.130156E+01 3 0.888192E+01 0.109646E+01 4 0.149556E+01 0.919952E+01 5 0.651575E+01 0.123014E+01 6 0.779006E+01 0.827337E+01 7 0.825922E+01 0.428750E+01 8 0.500385E+01 0.499661E+01 9 0.173868E+01 0.203751E+01 10 0.178658E+01 0.640073E+01 Cell volumes: 1 0.452000E+01 2 0.554000E+01 3 0.500000E+01 4 0.560000E+01 5 0.510000E+01 6 0.162400E+02 7 0.144200E+02 8 0.151400E+02 9 0.136200E+02 10 0.148200E+02 CVT_SIZE_PRB Normal end of execution. December 3 2002 8:43:41.578 AM