9 May 2025 8:59:15.443 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 -0.571853 -0.245473 0.349182 -0.365253 0.966516 -0.723555 0.743731 -0.966363 -0.466287 -0.921601 -0.370618 0.851245 Estimated Voronoi energy (before projection): 1 0.269649E-01 2 0.153426E-01 3 0.137496E-01 4 0.131825E-01 5 0.129134E-01 6 0.127443E-01 7 0.126071E-01 8 0.125185E-01 9 0.124010E-01 10 0.122366E-01 11 0.121581E-01 12 0.121507E-01 13 0.120960E-01 14 0.120723E-01 15 0.120070E-01 16 0.119841E-01 17 0.119697E-01 18 0.119596E-01 19 0.119582E-01 20 0.119437E-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 0.154703E-01 2 0.102231E-01 3 0.923616E-02 4 0.891043E-02 5 0.873387E-02 6 0.863914E-02 7 0.856975E-02 8 0.848988E-02 9 0.839494E-02 10 0.834945E-02 11 0.831156E-02 12 0.829076E-02 13 0.828295E-02 14 0.827447E-02 15 0.826700E-02 16 0.826879E-02 17 0.824935E-02 18 0.824365E-02 19 0.824410E-02 20 0.824265E-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 0.314537 0.690473 -0.460607 0.621815 0.957932 0.208859 0.636760 0.249627E-01 -0.479359 0.789499 0.229817 0.879061 Estimated Voronoi energy (before projection): 1 0.159537E-01 2 0.112209E-01 3 0.107986E-01 4 0.104963E-01 5 0.103393E-01 6 0.102602E-01 7 0.102520E-01 8 0.101898E-01 9 0.101746E-01 10 0.101669E-01 11 0.101503E-01 12 0.101324E-01 13 0.101309E-01 14 0.101121E-01 15 0.100667E-01 16 0.100720E-01 17 0.100505E-01 18 0.100278E-01 19 0.100321E-01 20 0.100082E-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 5.92830 -2.38076 1.02021 -0.520431E-01 2.44074 -4.54790 -5.85880 -0.814108 0.991501 0.420636 0.731506 -1.87401 1.13142 -1.64721 2.94084 -4.13989 Estimated Voronoi energy (before projection): 1 23.5087 2 20.5452 3 20.5285 4 20.4653 5 20.4671 6 20.4870 7 20.4296 8 20.4402 9 20.4515 10 20.4108 11 20.3932 12 20.4500 13 20.4350 14 20.4247 15 20.3970 16 20.3962 17 20.3587 18 20.4273 19 20.4055 20 20.3795 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 0.416816 0.893705E-01 0.706503 0.451985E-01 0.319038 -0.354158E-01 0.787109 0.167389 Estimated Voronoi energy (before projection): 1 0.341746E-02 2 0.252736E-02 3 0.238962E-02 4 0.230525E-02 5 0.224594E-02 6 0.223776E-02 7 0.222082E-02 8 0.221413E-02 9 0.220799E-02 10 0.220364E-02 11 0.220558E-02 12 0.219668E-02 13 0.219722E-02 14 0.219743E-02 15 0.219494E-02 16 0.219494E-02 17 0.218973E-02 18 0.218925E-02 19 0.218846E-02 20 0.218312E-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 = 0.530039E-01 0.142248