30 September 2016 1:45:05.117 PM CVT_TRIANGULATION: FORTRAN90 version Apply simple CVT sampling routines to produce a set of sample points in regions from the TEST_TRIANGULATION package. 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 -0.563163 0.912635 0.659018 0.123391 -0.169386 -0.867763 -0.484844 -0.780086 -0.912342 0.267931 -0.876546 -0.100922 Estimated Voronoi energy (before projection): 1 0.273087E-01 2 0.159164E-01 3 0.140472E-01 4 0.132121E-01 5 0.127796E-01 6 0.125674E-01 7 0.124193E-01 8 0.122576E-01 9 0.121645E-01 10 0.121113E-01 11 0.120562E-01 12 0.120001E-01 13 0.119514E-01 14 0.119095E-01 15 0.118864E-01 16 0.118737E-01 17 0.118620E-01 18 0.118450E-01 19 0.118230E-01 20 0.118103E-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 0.152021E-01 2 0.108765E-01 3 0.957554E-02 4 0.908533E-02 5 0.881248E-02 6 0.862946E-02 7 0.854488E-02 8 0.849366E-02 9 0.846618E-02 10 0.842468E-02 11 0.838690E-02 12 0.836916E-02 13 0.835877E-02 14 0.835573E-02 15 0.834564E-02 16 0.831968E-02 17 0.830549E-02 18 0.827612E-02 19 0.827446E-02 20 0.825945E-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 0.659018 0.561695 -0.876546 0.449539 -0.197387 0.754673 0.594574 0.183837E-02 0.795008 0.350752 0.645775 0.267132 Estimated Voronoi energy (before projection): 1 0.161534E-01 2 0.115882E-01 3 0.111638E-01 4 0.109612E-01 5 0.108009E-01 6 0.106208E-01 7 0.104924E-01 8 0.104696E-01 9 0.104076E-01 10 0.103271E-01 11 0.102928E-01 12 0.102486E-01 13 0.102083E-01 14 0.102372E-01 15 0.101776E-01 16 0.101781E-01 17 0.101644E-01 18 0.101442E-01 19 0.100997E-01 20 0.101202E-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 5.17592 -1.62983 -1.33035 -4.60329 -3.80796 -4.34026 -7.16552 -1.19621 -1.55028 -0.471959 6.24398 -2.89549 5.64068 0.450847E-01 -6.06855 -2.89023 Estimated Voronoi energy (before projection): 1 23.3777 2 20.5402 3 20.4565 4 20.4336 5 20.4671 6 20.4368 7 20.4058 8 20.4062 9 20.3990 10 20.3860 11 20.3808 12 20.4111 13 20.3898 14 20.3666 15 20.3827 16 20.3523 17 20.3947 18 20.4103 19 20.4079 20 20.3843 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 0.829509 0.319359E-01 0.897504 -0.772563E-01 0.859097 0.176436 0.822887 -0.120541 Estimated Voronoi energy (before projection): 1 0.326642E-02 2 0.250509E-02 3 0.237927E-02 4 0.232967E-02 5 0.229333E-02 6 0.227179E-02 7 0.223767E-02 8 0.222890E-02 9 0.222118E-02 10 0.222091E-02 11 0.221522E-02 12 0.221259E-02 13 0.221147E-02 14 0.221293E-02 15 0.220764E-02 16 0.220621E-02 17 0.220673E-02 18 0.220828E-02 19 0.220553E-02 20 0.220349E-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 = 0.743433 1.07047