15 June 2020 7:29:38.746 AM
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