December 4 2002 6:09:32.194 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 0.526316 0.245340E-01 2 2.63158 0.548597E-01 3 4.73684 0.736019E-01 4 6.84210 0.884585E-01 5 8.94737 0.101156 6 11.0526 0.112429 7 13.1579 0.122670 8 15.2632 0.132120 9 17.3684 0.140937 10 19.4737 0.149234 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 = 475832974 Initializing the cell generators. Carry out the CVT iteration. Area iteration 1 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.600000 0.245340E-01 2 2.63158 2.52000 0.548597E-01 3 4.73684 4.00000 0.736019E-01 4 6.84210 7.88000 0.884585E-01 5 8.94737 8.68000 0.101156 6 11.0526 11.0000 0.112429 7 13.1579 13.1600 0.122670 8 15.2632 15.3800 0.132120 9 17.3684 16.4600 0.140937 10 19.4737 20.3200 0.149234 Area discrepancy = 4.15369 Area iteration 2 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.460000 0.229299E-01 2 2.63158 2.52000 0.559432E-01 3 4.73684 6.32000 0.799264E-01 4 6.84210 6.06000 0.822542E-01 5 8.94737 7.72000 0.102487 6 11.0526 11.4400 0.112461 7 13.1579 12.0400 0.122402 8 15.2632 15.2600 0.131340 9 17.3684 18.6000 0.144470 10 19.4737 19.5800 0.145787 Area discrepancy = 6.61684 Area iteration 3 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.540000 0.244422E-01 2 2.63158 2.40000 0.569705E-01 3 4.73684 4.44000 0.689558E-01 4 6.84210 6.86000 0.870986E-01 5 8.94737 9.12000 0.109951 6 11.0526 10.9000 0.110158 7 13.1579 14.3000 0.127516 8 15.2632 13.6400 0.130899 9 17.3684 17.2800 0.139122 10 19.4737 20.5200 0.144887 Area discrepancy = 4.78526 Area iteration 4 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.640000 0.240527E-01 2 2.63158 3.12000 0.594634E-01 3 4.73684 5.40000 0.709939E-01 4 6.84210 7.16000 0.867044E-01 5 8.94737 8.86000 0.108554 6 11.0526 10.2600 0.110569 7 13.1579 12.0000 0.121923 8 15.2632 16.6600 0.138022 9 17.3684 17.1200 0.139027 10 19.4737 18.7800 0.140690 Area discrepancy = 5.96000 Area iteration 5 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.560000 0.219306E-01 2 2.63158 2.62000 0.549077E-01 3 4.73684 4.28000 0.668530E-01 4 6.84210 6.82000 0.852181E-01 5 8.94737 9.18000 0.109681 6 11.0526 11.9800 0.115383 7 13.1579 13.9400 0.128364 8 15.2632 13.3200 0.132827 9 17.3684 17.4800 0.140793 10 19.4737 19.8200 0.144043 Area discrepancy = 4.86737 Area iteration 6 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.460000 0.212373E-01 2 2.63158 3.18000 0.549682E-01 3 4.73684 4.86000 0.702529E-01 4 6.84210 5.96000 0.852619E-01 5 8.94737 9.48000 0.108163 6 11.0526 11.2600 0.110705 7 13.1579 12.5200 0.124573 8 15.2632 16.0600 0.142029 9 17.3684 17.7400 0.140188 10 19.4737 18.4800 0.142621 Area discrepancy = 5.16000 Area iteration 7 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.640000 0.227285E-01 2 2.63158 2.26000 0.500302E-01 3 4.73684 4.62000 0.693932E-01 4 6.84210 7.58000 0.914015E-01 5 8.94737 7.84000 0.105135 6 11.0526 10.7200 0.109738 7 13.1579 13.7600 0.127774 8 15.2632 14.5800 0.138533 9 17.3684 18.0600 0.138785 10 19.4737 19.9400 0.146482 Area discrepancy = 5.22316 Area iteration 8 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.380000 0.205497E-01 2 2.63158 2.48000 0.538255E-01 3 4.73684 5.08000 0.700555E-01 4 6.84210 6.22000 0.865796E-01 5 8.94737 9.78000 0.111980 6 11.0526 11.7200 0.111095 7 13.1579 12.6600 0.124574 8 15.2632 16.2400 0.141318 9 17.3684 15.6000 0.135695 10 19.4737 19.8400 0.144327 Area discrepancy = 6.37263 Area iteration 9 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.740000 0.241062E-01 2 2.63158 2.86000 0.552665E-01 3 4.73684 4.36000 0.674290E-01 4 6.84210 7.02000 0.905122E-01 5 8.94737 8.44000 0.106760 6 11.0526 11.0400 0.107537 7 13.1579 12.4600 0.126589 8 15.2632 15.7600 0.136559 9 17.3684 17.9800 0.142716 10 19.4737 19.3400 0.142525 Area discrepancy = 3.45684 Area iteration 10 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.480000 0.203653E-01 2 2.63158 2.42000 0.531058E-01 3 4.73684 4.78000 0.704048E-01 4 6.84210 7.24000 0.895133E-01 5 8.94737 8.62000 0.110113 6 11.0526 10.0600 0.107785 7 13.1579 14.3400 0.130312 8 15.2632 13.9600 0.134622 9 17.3684 18.5200 0.140512 10 19.4737 19.5800 0.143266 Area discrepancy = 5.76210 Area iteration 11 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.480000 0.212506E-01 2 2.63158 2.78000 0.551848E-01 3 4.73684 5.34000 0.698409E-01 4 6.84210 7.34000 0.867143E-01 5 8.94737 8.86000 0.111792 6 11.0526 11.8000 0.112582 7 13.1579 12.1200 0.124388 8 15.2632 15.5600 0.140273 9 17.3684 17.0200 0.135597 10 19.4737 18.7000 0.142376 Area discrepancy = 4.58737 Area iteration 12 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.560000 0.223069E-01 2 2.63158 2.42000 0.538235E-01 3 4.73684 3.88000 0.659401E-01 4 6.84210 6.36000 0.839274E-01 5 8.94737 9.88000 0.112618 6 11.0526 10.3400 0.109227 7 13.1579 14.0400 0.129924 8 15.2632 15.0600 0.139270 9 17.3684 16.8000 0.137315 10 19.4737 20.6600 0.145649 Area discrepancy = 6.06947 Area iteration 13 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.400000 0.215230E-01 2 2.63158 2.72000 0.558608E-01 3 4.73684 5.00000 0.725126E-01 4 6.84210 6.46000 0.866373E-01 5 8.94737 9.18000 0.106663 6 11.0526 11.8200 0.112392 7 13.1579 12.8400 0.125179 8 15.2632 15.6400 0.139541 9 17.3684 17.2600 0.138956 10 19.4737 18.6800 0.140734 Area discrepancy = 3.45684 Area iteration 14 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.600000 0.246636E-01 2 2.63158 2.90000 0.548896E-01 3 4.73684 4.46000 0.705070E-01 4 6.84210 7.02000 0.890723E-01 5 8.94737 8.20000 0.105196 6 11.0526 10.3400 0.108572 7 13.1579 12.9600 0.126591 8 15.2632 15.9600 0.137710 9 17.3684 17.5800 0.139251 10 19.4737 19.9800 0.143547 Area discrepancy = 3.86947 Area iteration 15 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.540000 0.230886E-01 2 2.63158 2.42000 0.522629E-01 3 4.73684 5.36000 0.726279E-01 4 6.84210 6.28000 0.878948E-01 5 8.94737 8.66000 0.109833 6 11.0526 11.6600 0.112198 7 13.1579 14.2200 0.127493 8 15.2632 14.7400 0.134606 9 17.3684 18.0200 0.138344 10 19.4737 18.1000 0.141650 Area discrepancy = 5.91579 Area iteration 16 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.420000 0.227816E-01 2 2.63158 2.36000 0.544696E-01 3 4.73684 4.48000 0.682379E-01 4 6.84210 7.02000 0.916935E-01 5 8.94737 8.62000 0.111579 6 11.0526 10.7000 0.109177 7 13.1579 12.8000 0.122572 8 15.2632 15.5200 0.136899 9 17.3684 17.8400 0.135745 10 19.4737 20.2400 0.146846 Area discrepancy = 3.34526 Area iteration 17 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.600000 0.253412E-01 2 2.63158 3.08000 0.571546E-01 3 4.73684 4.82000 0.697230E-01 4 6.84210 7.36000 0.899517E-01 5 8.94737 9.12000 0.112959 6 11.0526 10.8200 0.110259 7 13.1579 12.6200 0.123488 8 15.2632 15.9000 0.134903 9 17.3684 16.1200 0.133092 10 19.4737 19.5600 0.143128 Area discrepancy = 4.03789 Area iteration 18 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.560000 0.238544E-01 2 2.63158 2.48000 0.530979E-01 3 4.73684 4.90000 0.694688E-01 4 6.84210 6.66000 0.871683E-01 5 8.94737 9.50000 0.112451 6 11.0526 10.7200 0.112003 7 13.1579 13.6000 0.126730 8 15.2632 14.6600 0.132843 9 17.3684 17.5000 0.138849 10 19.4737 19.4200 0.143535 Area discrepancy = 2.64631 Area iteration 19 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.400000 0.231352E-01 2 2.63158 2.06000 0.547186E-01 3 4.73684 4.90000 0.683301E-01 4 6.84210 7.06000 0.883877E-01 5 8.94737 9.16000 0.109176 6 11.0526 11.4200 0.113773 7 13.1579 13.1200 0.124704 8 15.2632 14.7600 0.135603 9 17.3684 17.5000 0.138382 10 19.4737 19.6200 0.143791 Area discrepancy = 2.47790 Area iteration 20 Desired, Actual, Linear Cell Volume Volume Weight 1 0.526316 0.660000 0.263717E-01 2 2.63158 3.16000 0.614584E-01 3 4.73684 4.54000 0.667621E-01 4 6.84210 6.34000 0.864681E-01 5 8.94737 9.46000 0.107225 6 11.0526 10.2200 0.111227 7 13.1579 13.4600 0.124102 8 15.2632 15.9400 0.137031 9 17.3684 16.4200 0.136997 10 19.4737 19.8000 0.142357 Area discrepancy = 4.96000 Cell generators: 1 0.680574E+01 0.961584E+01 2 0.530428E+01 0.362766E+01 3 0.534934E+01 0.900839E+01 4 0.852306E+01 0.887463E+01 5 0.128994E+01 0.536941E+01 6 0.190406E+01 0.858488E+01 7 0.458817E+01 0.630598E+01 8 0.818232E+01 0.577004E+01 9 0.764155E+01 0.185260E+01 10 0.248444E+01 0.184454E+01 Cell volumes: 1 0.660000E+00 2 0.316000E+01 3 0.454000E+01 4 0.634000E+01 5 0.946000E+01 6 0.102200E+02 7 0.134600E+02 8 0.159400E+02 9 0.164200E+02 10 0.198000E+02 CVT_SIZE_PRB Normal end of execution. December 4 2002 6:09:50.320 AM