6 October 2025 6:04:32.952 PM cvt_triangulation(): Fortran90 version Apply simple CVT sampling routines to produce a set of sample points in regions from test_triangulation(). Skipping test01() Skipping test02() Skipping test03() TEST04 Try to get an approximate CVT mesh in a region that also has many points ON the boundary. Here, we only rerun cases which involve fixed points, and show how to handle them. Title: "#3: The unit square with circular hole." P03: Strang and Persson example #3 The unit square, with a hole. The hole is a concentric circle of radius 0.4. A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 2 Number of fixed points = 4 Number of holes = 1 Number of fixed points = 4 Initial points (first 10 only) Row 1 2 Col -1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 0.200254E-01 -0.662235 -0.739412E-01 0.518871 0.739245 0.598141 0.907089 0.996829 -0.430750 -0.292422 -0.184859 -0.603066 Estimated Voronoi energy (before projection): 1 0.249138E-01 2 0.153317E-01 3 0.137744E-01 4 0.129668E-01 5 0.125188E-01 6 0.122757E-01 7 0.121223E-01 8 0.120113E-01 9 0.119466E-01 10 0.118859E-01 11 0.118681E-01 12 0.118359E-01 13 0.117739E-01 14 0.117440E-01 15 0.117080E-01 16 0.117098E-01 17 0.117019E-01 18 0.116965E-01 19 0.116791E-01 20 0.116687E-01 Creating data file "cvt_p03_boundary_fixed.txt". Creating graphics file "cvt_p03_boundary_fixed.eps". TEST04 Try to get an approximate CVT mesh in a region that also has many points ON the boundary. Here, we only rerun cases which involve fixed points, and show how to handle them. Title: "#4: The unit hexagon with hexagonal hole." P04: Strang and Persson example #4 The hexagon with hexagonal hole. Radius of outer hexagon R1 = 1.00000 Radius of outer hexagon R2 = 0.500000 A uniform mesh density is requested. Element sizes tried were ? Number of boundary segments = 2 Number of fixed points = 12 Number of holes = 1 Number of fixed points = 12 Initial points (first 10 only) Row 1 2 Col 0.500000 -0.866025 1.00000 0.00000 0.500000 0.866025 -0.500000 0.866025 -1.00000 0.122465E-15 -0.500000 -0.866025 0.433013 -0.250000 -0.918485E-16 -0.500000 -0.433013 -0.250000 -0.433013 0.250000 Estimated Voronoi energy (before projection): 1 0.156922E-01 2 0.102910E-01 3 0.922893E-02 4 0.895046E-02 5 0.882238E-02 6 0.866853E-02 7 0.849977E-02 8 0.840599E-02 9 0.836699E-02 10 0.829200E-02 11 0.827725E-02 12 0.821175E-02 13 0.819462E-02 14 0.818607E-02 15 0.816190E-02 16 0.814471E-02 17 0.813507E-02 18 0.809485E-02 19 0.807543E-02 20 0.807958E-02 Creating data file "cvt_p04_boundary_fixed.txt". Creating graphics file "cvt_p04_boundary_fixed.eps". TEST04 Try to get an approximate CVT mesh in a region that also has many points ON the boundary. Here, we only rerun cases which involve fixed points, and show how to handle them. Title: "#5: The horn." P05: Strang and Persson example #5 The horn. Circle C1 has center = (0,0) Radius R1 = 1.00000 Circle C2 has center = (-0.4,0) Radius R2 = 0.550000 Points in the region are: in C1 and not in C2 and have 0 <= Y. A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 1 Number of fixed points = 4 Number of holes = 0 Number of fixed points = 4 Initial points (first 10 only) Row 1 2 Col -1.00000 0.00000 -0.950000 0.00000 0.150000 0.00000 1.00000 0.00000 -0.125802 0.518942 0.213774 0.402353E-01 0.224166 0.922241 -0.272529 0.700213 0.668413E-01 0.817960 -0.880673 0.354221 Estimated Voronoi energy (before projection): 1 0.167145E-01 2 0.111195E-01 3 0.106494E-01 4 0.104974E-01 5 0.104221E-01 6 0.103710E-01 7 0.103472E-01 8 0.103111E-01 9 0.102762E-01 10 0.102658E-01 11 0.102660E-01 12 0.102398E-01 13 0.102200E-01 14 0.102132E-01 15 0.102070E-01 16 0.102004E-01 17 0.102050E-01 18 0.101793E-01 19 0.101823E-01 20 0.102081E-01 Creating data file "cvt_p05_boundary_fixed.txt". Creating graphics file "cvt_p05_boundary_fixed.eps". TEST04 Try to get an approximate CVT mesh in a region that also has many points ON the boundary. Here, we only rerun cases which involve fixed points, and show how to handle them. Title: "#7: Bicycle seat (implicit)." P07: Strang and Persson example #7 Bicycle seat (implicit). A uniform mesh density is requested. The boundary is formed by two algebraic expressions. Number of boundary segments = 1 Number of fixed points = 2 Number of holes = 0 Number of fixed points = 2 Initial points (first 10 only) Row 1 2 Col -7.85398 0.00000 7.85398 0.00000 7.30075 -0.525936 0.419927E-01 0.893590 1.84873 -3.34458 5.29923 -2.80905 -4.34931 -2.20843 3.93937 -3.16030 -1.31235 -2.62150 -4.86355 -4.12540 Estimated Voronoi energy (before projection): 1 22.9325 2 20.5366 3 20.4944 4 20.4342 5 20.4488 6 20.4451 7 20.4430 8 20.4363 9 20.4459 10 20.4486 11 20.4398 12 20.3656 13 20.3821 14 20.3920 15 20.4097 16 20.4482 17 20.4443 18 20.4385 19 20.3889 20 20.3761 Creating data file "cvt_p07_boundary_fixed.txt". Creating graphics file "cvt_p07_boundary_fixed.eps". TEST04 Try to get an approximate CVT mesh in a region that also has many points ON the boundary. Here, we only rerun cases which involve fixed points, and show how to handle them. Title: "#8: Pie slice with notch and hole." P08: Strang and Persson example #8 Pie slice with notch and hole. The pie rim is a portion of a circle C1 with CENTER1 = 0.00000 0.00000 and radius R1 = 1.00000 The interior hole is a circle C2 with CENTER2 = 0.600000 0.00000 and radius R2 = 0.100000 A uniform mesh density is requested. Number of boundary segments = 2 Number of fixed points = 6 Number of holes = 1 Number of fixed points = 6 Initial points (first 10 only) Row 1 2 Col 0.00000 0.00000 0.965926 -0.258819 0.995436 -0.954356E-01 0.900000 0.00000 0.995436 0.954356E-01 0.965926 0.258819 0.440921 -0.737863E-01 0.737544 -0.190094 0.519219 -0.105383 0.578917 -0.991673E-01 Estimated Voronoi energy (before projection): 1 0.323232E-02 2 0.244851E-02 3 0.235106E-02 4 0.229731E-02 5 0.227176E-02 6 0.225397E-02 7 0.224224E-02 8 0.223695E-02 9 0.222321E-02 10 0.222570E-02 11 0.222132E-02 12 0.221133E-02 13 0.220768E-02 14 0.220762E-02 15 0.220649E-02 16 0.220793E-02 17 0.220383E-02 18 0.219368E-02 19 0.219251E-02 20 0.219240E-02 Creating data file "cvt_p08_boundary_fixed.txt". Creating graphics file "cvt_p08_boundary_fixed.eps". TEST04 Try to get an approximate CVT mesh in a region that also has many points ON the boundary. Here, we only rerun cases which involve fixed points, and show how to handle them. Title: "#9: Jeff Borggaard's Box with 2 hexagonal holes." P09: Jeff Borggaard's example A square with 2 hexagonal holes. The square has "center" at 0.500000 0.500000 and "radius" R1 = 0.500000 Hexagon 1 has "center" at 0.250000 0.750000 and "radius" R2 = 0.100000 Hexagon 2 has "center" at 0.600000 0.400000 and "radius" R3 = 0.100000 A uniform mesh density is requested. Number of boundary segments = 3 Number of fixed points = 16 Number of holes = 2 Number of fixed points = 16 Initial points (first 10 only) Row 1 2 Col 0.00000 0.00000 1.00000 0.00000 1.00000 1.00000 0.00000 1.00000 0.350000 0.750000 0.300000 0.836603 0.200000 0.836603 0.150000 0.750000 0.200000 0.663397 0.300000 0.663397 Estimated Voronoi energy (before projection): P09_SAMPLE - Fatal error! (The double hexagonal hole region) Trying to generate point J = 1 Number of rejections = 2000010 Rejection percentage = 100.000 Y = 0.179532 0.203019E-01