August 31 2010 11:33:00.821 AM STRIPACK_PRB2 FORTRAN90 version A sample application of the data produced by STRIPACK. Here, we have STRIPACK compute the Voronoi diagram of a set of points on the unit sphere, and then we do a simple check by computing the polygonal area and summing. Data points: Row 1 2 3 Col 1: 0.915568 -0.257797 -0.308668 2: -0.171751 0.901345 0.397592 3: 0.541822 0.447986 -0.711152 4: -0.620052 -0.745456 0.244603 5: 0.262807E-01 -0.894727 0.445840 6: 0.167158E-01 -0.591520 0.806117 7: 0.987108 0.846611E-01 0.135834 8: -0.220974 0.974193 0.460176E-01 9: 0.679580 -0.416543 -0.603873 10: 0.936980 -0.375368E-01 0.347361 Vertices/Triangles/Arcs: Row 1 2 3 4 5 6 7 8 9 Col 1: 1 7 10 9 2 5 8 1 4 2: 1 10 5 16 3 1 24 2 1 3: 1 5 9 14 4 2 18 3 2 4: 1 9 3 11 5 3 12 5 3 5: 1 3 7 13 1 4 16 4 5 6: 2 8 4 12 7 10 13 6 10 7: 2 4 6 15 8 6 20 7 6 8: 2 6 10 16 9 7 22 9 7 9: 2 10 7 1 10 8 8 11 9 10: 2 7 8 13 6 9 15 10 11 11: 3 9 4 14 12 4 19 14 12 12: 3 4 8 6 13 11 13 17 14 13: 3 8 7 10 5 12 15 16 17 14: 4 9 5 3 15 11 18 21 19 15: 4 5 6 16 7 14 23 20 21 16: 5 10 6 8 15 2 22 23 24 Voronoi vertices Row 1 2 3 Col 1: 0.894880 0.272171 -0.353714 2: 0.957150 -0.282520 0.636153E-01 3: 0.681801 -0.699920 0.212744 4: 0.572625 -0.819641 -0.169977E-01 5: 0.768862 0.433521E-01 -0.637943 6: 0.586700 0.805359 0.847331E-01 7: -0.952677 0.242288 0.183586 8: -0.672512 0.115158 0.731072 9: 0.283872 0.286265 0.915133 10: 0.569882 0.645792 0.508122 11: -0.503978 -0.184997 -0.843672 12: -0.676982 0.725273E-01 -0.732417 13: 0.590866 0.806005 0.351105E-01 14: -0.665695E-01 -0.891729 -0.447646 15: -0.352343 -0.720626 0.597120 16: 0.615704 -0.594756 0.516889 Voronoi polygon orders: 1: 5 2: 5 3: 5 4: 6 5: 5 6: 4 7: 5 8: 4 9: 4 10: 5 Voronoi polygons: 1: 1 2 3 4 5 2: 6 7 8 9 10 3: 5 11 12 13 1 4: 11 14 15 8 7 12 5: 14 4 3 16 15 6: 16 9 8 15 7: 1 13 6 10 2 8: 6 13 12 7 9: 4 14 11 5 10: 10 9 16 3 2 Voronoi polygon areas: 1: 0.52459823 2: 1.5326507 3: 1.6660720 4: 2.2691220 5: 0.87769666 6: 1.2207519 7: 0.61070171 8: 1.6049351 9: 1.3343416 10: 0.92550055 Sphere area from Voronoi polygons = 12.566371 Exact area from spherical geometry = 12.566371 Voronoi polygon centroids: Row 1 2 3 Col 1: 0.915797 -0.332282 -0.225619 2: -0.203119 0.712487 0.671643 3: 0.301128 0.471796 -0.828692 4: -0.857935 -0.509699 -0.644505E-01 5: 0.175448 -0.956881 0.231510 6: -0.203405E-01 -0.311993 0.949867 7: 0.916114 0.390013 0.928748E-01 8: -0.470777 0.849122 -0.239502 9: 0.327245 -0.576910 -0.748389 10: 0.797686 -0.434066E-01 0.601509 VORONOI_TRAVERSE Visit each Voronoi polygon. Compute the (spherical) area of each subtriangle Add up to get the area of each polygon. Polygon 1 Subtriangle 1 area = 0.104144 Subtriangle 2 area = 0.986511E-01 Subtriangle 3 area = 0.107405 Subtriangle 4 area = 0.122250 Subtriangle 5 area = 0.921488E-01 Polygon area = 0.524598 Polygon 2 Subtriangle 1 area = 0.191820 Subtriangle 2 area = 0.365037 Subtriangle 3 area = 0.505555 Subtriangle 4 area = 0.274782 Subtriangle 5 area = 0.195457 Polygon area = 1.53265 Polygon 3 Subtriangle 1 area = 0.378880 Subtriangle 2 area = 0.261213 Subtriangle 3 area = 0.721344 Subtriangle 4 area = 0.212487 Subtriangle 5 area = 0.921488E-01 Polygon area = 1.66607 Polygon 4 Subtriangle 1 area = 0.524212 Subtriangle 2 area = 0.218559 Subtriangle 3 area = 0.230908 Subtriangle 4 area = 0.365037 Subtriangle 5 area = 0.669193 Subtriangle 6 area = 0.261213 Polygon area = 2.26912 Polygon 5 Subtriangle 1 area = 0.309000 Subtriangle 2 area = 0.107405 Subtriangle 3 area = 0.117237 Subtriangle 4 area = 0.125495 Subtriangle 5 area = 0.218559 Polygon area = 0.877697 Polygon 6 Subtriangle 1 area = 0.358795 Subtriangle 2 area = 0.505555 Subtriangle 3 area = 0.230908 Subtriangle 4 area = 0.125495 Polygon area = 1.22075 Polygon 7 Subtriangle 1 area = 0.212487 Subtriangle 2 area = 0.225784E-01 Subtriangle 3 area = 0.195457 Subtriangle 4 area = 0.760357E-01 Subtriangle 5 area = 0.104144 Polygon area = 0.610702 Polygon 8 Subtriangle 1 area = 0.225784E-01 Subtriangle 2 area = 0.721344 Subtriangle 3 area = 0.669193 Subtriangle 4 area = 0.191820 Polygon area = 1.60494 Polygon 9 Subtriangle 1 area = 0.309000 Subtriangle 2 area = 0.524212 Subtriangle 3 area = 0.378880 Subtriangle 4 area = 0.122250 Polygon area = 1.33434 Polygon 10 Subtriangle 1 area = 0.274782 Subtriangle 2 area = 0.358795 Subtriangle 3 area = 0.117237 Subtriangle 4 area = 0.986511E-01 Subtriangle 5 area = 0.760357E-01 Polygon area = 0.925501 STRIPACK_PRB2: Normal end of execution. August 31 2010 11:33:00.827 AM