15 June 2014 11:19:11 AM
TRIANGLE_NCC_RULE_PRB:
C++ version
Test the TRIANGLE_NCC_RULE library.
TEST01
TRIANGLE_NCC_RULE_NUM returns the number of rules;
TRIANGLE_NCC_DEGREE returns the degree of a rule;
TRIANGLE_NCC_ORDER_NUM returns the order of a rule.
Number of available rules = 9
Rule Degree Order
1 0 1
2 1 3
3 2 3
4 3 10
5 4 12
6 5 21
7 6 25
8 7 36
9 8 42
TEST02
TRIANGLE_NCC_RULE returns the points and weights
of an NCC rule for the triangle.
In this test, we simply check that the weights
sum to 1.
Number of available rules = 9
Rule Order Sum of weights
1 1 1
2 3 1
3 3 1
4 10 1
5 12 1
6 21 1
7 25 1
8 36 1
9 42 1
TEST03
TRIANGLE_NCC_RULE returns the points and weights
of an NCC rule for the triangle.
In this test, we simply check that, for each
quadrature point, the barycentric coordinates
add up to 1.
Rule Suborder Sum of coordinates
1 1
1
2 1
1
3 1
1
4 3
1
1
1
5 3
1
1
1
6 5
1
1
1
1
1
7 6
1
1
0.9999999999999999
1
0.9999999999999999
1
8 8
1
1
1
1
1
1
1
0.9999999999999999
9 9
1
1
1
1
1
1
1
1
1
TEST04
TRIANGLE_NCC_RULE returns the points and weights of
an NCC rule for the unit triangle.
This routine uses those rules to estimate the
integral of monomomials in the unit triangle.
Integrate 2 * X^0 * Y^0
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 1 0
7 1 2.220446049250313e-16
8 0.9999999999999997 3.33066907387547e-16
9 1 2.220446049250313e-16
Integrate 6 * X^0 * Y^1
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 1 0
7 1 2.220446049250313e-16
8 1 0
9 1 4.440892098500626e-16
Integrate 12 * X^0 * Y^2
Rule QUAD ERROR
1 0.6666666666666666 0.3333333333333334
2 2 1
3 1 0
4 1 0
5 1 0
6 1 0
7 1 0
8 1 2.220446049250313e-16
9 1 0
Integrate 20 * X^0 * Y^3
Rule QUAD ERROR
1 0.3703703703703703 0.6296296296296297
2 3.333333333333333 2.333333333333333
3 0.8333333333333333 0.1666666666666667
4 0.9999999999999999 1.110223024625157e-16
5 0.9999999999999999 1.110223024625157e-16
6 1 2.220446049250313e-16
7 0.9999999999999999 1.110223024625157e-16
8 0.9999999999999999 1.110223024625157e-16
9 0.9999999999999999 1.110223024625157e-16
Integrate 30 * X^0 * Y^4
Rule QUAD ERROR
1 0.1851851851851852 0.8148148148148149
2 5 4
3 0.625 0.375
4 1.055555555555555 0.05555555555555536
5 0.9999999999999998 2.220446049250313e-16
6 1 0
7 1 2.220446049250313e-16
8 0.9999999999999999 1.110223024625157e-16
9 1 2.220446049250313e-16
Integrate 42 * X^0 * Y^5
Rule QUAD ERROR
1 0.08641975308641975 0.9135802469135803
2 7 6
3 0.4375 0.5625
4 1.166666666666667 0.1666666666666667
5 0.9843750000000002 0.01562499999999978
6 0.9999999999999999 1.110223024625157e-16
7 1 0
8 0.9999999999999999 1.110223024625157e-16
9 0.9999999999999996 4.440892098500626e-16
Integrate 56 * X^0 * Y^6
Rule QUAD ERROR
1 0.03840877914951989 0.9615912208504801
2 9.333333333333332 8.333333333333332
3 0.2916666666666666 0.7083333333333334
4 1.325102880658436 0.325102880658436
5 0.9479166666666667 0.05208333333333326
6 1.005866666666667 0.005866666666666687
7 1 2.220446049250313e-16
8 1 4.440892098500626e-16
9 0.9999999999999994 5.551115123125783e-16
Integrate 72 * X^0 * Y^7
Rule QUAD ERROR
1 0.01646090534979424 0.9835390946502057
2 12 11
3 0.1875 0.8125
4 1.525925925925926 0.5259259259259259
5 0.8929687500000001 0.1070312499999999
6 1.02336 0.02336000000000027
7 0.9981481481481488 0.001851851851851216
8 1 4.440892098500626e-16
9 1 2.220446049250313e-16
Integrate 90 * X^0 * Y^8
Rule QUAD ERROR
1 0.006858710562414265 0.9931412894375857
2 15 14
3 0.1171875 0.8828125
4 1.767489711934157 0.7674897119341566
5 0.82470703125 0.17529296875
6 1.056 0.05600000000000027
7 0.9918981481481485 0.008101851851851527
8 1.000709738289318 0.0007097382893181958
9 0.9999999999999997 3.33066907387547e-16
Integrate 110 * X^0 * Y^9
Rule QUAD ERROR
1 0.002794289488390997 0.997205710511609
2 18.33333333333333 17.33333333333333
3 0.07161458333333333 0.9283854166666666
4 2.049611339734797 1.049611339734797
5 0.7485961914062499 0.2514038085937501
6 1.10528 0.1052800000000003
7 0.9792238225880212 0.02077617741197879
8 1.003534525013671 0.003534525013670686
9 0.9997647603352864 0.0002352396647136157
Integrate 132 * X^0 * Y^10
Rule QUAD ERROR
1 0.001117715795356399 0.9988822842046436
2 22 21
3 0.04296875 0.95703125
4 2.372351775643957 1.372351775643957
5 0.6693725585937498 0.3306274414062502
6 1.17142784 0.1714278400000002
7 0.9591049382716056 0.04089506172839441
8 1.01016401086525 0.01016401086525032
9 0.9987297058105473 0.001270294189452681
Integrate 6 * X^1 * Y^0
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 1 0
7 1 2.220446049250313e-16
8 1 0
9 1 2.220446049250313e-16
Integrate 24 * X^1 * Y^1
Rule QUAD ERROR
1 1.333333333333333 0.3333333333333333
2 0 1
3 1 0
4 1 0
5 1 0
6 1 2.220446049250313e-16
7 0.9999999999999999 1.110223024625157e-16
8 1 2.220446049250313e-16
9 1 0
Integrate 60 * X^1 * Y^2
Rule QUAD ERROR
1 1.111111111111111 0.1111111111111112
2 0 1
3 1.25 0.25
4 1 0
5 1 0
6 1 0
7 1 2.220446049250313e-16
8 0.9999999999999998 2.220446049250313e-16
9 0.9999999999999998 2.220446049250313e-16
Integrate 120 * X^1 * Y^3
Rule QUAD ERROR
1 0.7407407407407407 0.2592592592592593
2 0 1
3 1.25 0.25
4 0.8888888888888888 0.1111111111111112
5 1 0
6 1 0
7 0.9999999999999999 1.110223024625157e-16
8 1 0
9 1 0
Integrate 210 * X^1 * Y^4
Rule QUAD ERROR
1 0.4320987654320987 0.5679012345679013
2 0 1
3 1.09375 0.09375
4 0.7777777777777777 0.2222222222222223
5 1.0390625 0.0390625
6 1 0
7 1 4.440892098500626e-16
8 0.9999999999999999 1.110223024625157e-16
9 0.9999999999999998 2.220446049250313e-16
Integrate 336 * X^1 * Y^5
Rule QUAD ERROR
1 0.2304526748971193 0.7695473251028807
2 0 1
3 0.875 0.125
4 0.691358024691358 0.308641975308642
5 1.09375 0.09375
6 0.9824000000000002 0.01759999999999984
7 1 2.220446049250313e-16
8 1 0
9 0.9999999999999997 3.33066907387547e-16
Integrate 504 * X^1 * Y^6
Rule QUAD ERROR
1 0.1152263374485597 0.8847736625514403
2 0 1
3 0.65625 0.34375
4 0.6222222222222221 0.3777777777777779
5 1.140234375 0.1402343749999999
6 0.9446400000000003 0.05535999999999974
7 1.006481481481482 0.006481481481481755
8 0.9999999999999999 1.110223024625157e-16
9 1 0
Integrate 720 * X^1 * Y^7
Rule QUAD ERROR
1 0.05486968449931412 0.9451303155006858
2 0 1
3 0.46875 0.53125
4 0.559670781893004 0.440329218106996
5 1.166015625 0.166015625
6 0.8928000000000003 0.1071999999999997
7 1.023148148148149 0.02314814814814858
8 0.9971610468427269 0.002838953157273116
9 0.9999999999999997 3.33066907387547e-16
Integrate 990 * X^1 * Y^8
Rule QUAD ERROR
1 0.02514860539551897 0.974851394604481
2 0 1
3 0.322265625 0.677734375
4 0.4979423868312756 0.5020576131687244
5 1.167205810546875 0.167205810546875
6 0.8342400000000004 0.1657599999999996
7 1.048932613168725 0.04893261316872488
8 0.9879981980297325 0.01200180197026746
9 1.001058578491211 0.00105857849121116
Integrate 1320 * X^1 * Y^9
Rule QUAD ERROR
1 0.01117715795356399 0.988822842046436
2 0 1
3 0.21484375 0.78515625
4 0.4359091601889955 0.5640908398110045
5 1.14471435546875 0.14471435546875
6 0.7745408000000006 0.2254591999999994
7 1.079818244170097 0.07981824417009675
8 0.9703870957557772 0.0296129042442228
9 1.004940032958984 0.004940032958984153
Integrate 12 * X^2 * Y^0
Rule QUAD ERROR
1 0.6666666666666666 0.3333333333333334
2 2 1
3 1 0
4 1 0
5 1 0
6 1 2.220446049250313e-16
7 1 0
8 1 0
9 1 2.220446049250313e-16
Integrate 60 * X^2 * Y^1
Rule QUAD ERROR
1 1.111111111111111 0.1111111111111109
2 0 1
3 1.25 0.25
4 0.9999999999999998 2.220446049250313e-16
5 1 0
6 1 0
7 1 0
8 0.9999999999999999 1.110223024625157e-16
9 0.9999999999999998 2.220446049250313e-16
Integrate 180 * X^2 * Y^2
Rule QUAD ERROR
1 1.111111111111111 0.1111111111111112
2 0 1
3 1.875 0.875
4 1.166666666666667 0.1666666666666665
5 1 0
6 0.9999999999999999 1.110223024625157e-16
7 1 2.220446049250313e-16
8 1 2.220446049250313e-16
9 1 0
Integrate 420 * X^2 * Y^3
Rule QUAD ERROR
1 0.8641975308641975 0.1358024691358025
2 0 1
3 2.1875 1.1875
4 1.166666666666667 0.1666666666666665
5 0.984375 0.015625
6 1 2.220446049250313e-16
7 1 0
8 0.9999999999999999 1.110223024625157e-16
9 0.9999999999999999 1.110223024625157e-16
Integrate 840 * X^2 * Y^4
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
2 0 1
3 2.1875 1.1875
4 1.123456790123457 0.1234567901234567
5 1.057291666666667 0.05729166666666652
6 1.034666666666667 0.03466666666666685
7 1 2.220446049250313e-16
8 0.9999999999999999 1.110223024625157e-16
9 1 0
Integrate 1512 * X^2 * Y^5
Rule QUAD ERROR
1 0.345679012345679 0.654320987654321
2 0 1
3 1.96875 0.96875
4 1.088888888888889 0.08888888888888902
5 1.205859375 0.2058593750000002
6 1.07712 0.0771200000000003
7 0.9916666666666668 0.008333333333333193
8 0.9999999999999997 3.33066907387547e-16
9 1 4.440892098500626e-16
Integrate 2520 * X^2 * Y^6
Rule QUAD ERROR
1 0.1920438957475994 0.8079561042524006
2 0 1
3 1.640625 0.640625
4 1.065843621399177 0.06584362139917688
5 1.3876953125 0.3876953125
6 1.1072 0.1072000000000004
7 0.9868827160493832 0.01311728395061684
8 1.007229130719343 0.007229130719343058
9 1 0
Integrate 3960 * X^2 * Y^7
Rule QUAD ERROR
1 0.1005944215820759 0.8994055784179241
2 0 1
3 1.2890625 0.2890625
4 1.041152263374485 0.04115226337448541
5 1.5670166015625 0.5670166015625
6 1.119360000000001 0.1193600000000006
7 1.001543209876544 0.00154320987654355
8 1.024447013290947 0.02444701329094734
9 0.9978205362955731 0.002179463704426898
Integrate 5940 * X^2 * Y^8
Rule QUAD ERROR
1 0.05029721079103795 0.949702789208962
2 0 1
3 0.966796875 0.033203125
4 1.003429355281207 0.003429355281207025
5 1.721099853515625 0.721099853515625
6 1.1159808 0.1159808000000004
7 1.044688786008231 0.04468878600823123
8 1.048571841421759 0.04857184142175908
9 0.9927921295166016 0.007207870483398438
Integrate 20 * X^3 * Y^0
Rule QUAD ERROR
1 0.3703703703703703 0.6296296296296297
2 3.333333333333333 2.333333333333333
3 0.8333333333333333 0.1666666666666667
4 1 0
5 1 0
6 1 4.440892098500626e-16
7 1 2.220446049250313e-16
8 0.9999999999999999 1.110223024625157e-16
9 0.9999999999999997 3.33066907387547e-16
Integrate 120 * X^3 * Y^1
Rule QUAD ERROR
1 0.7407407407407407 0.2592592592592593
2 0 1
3 1.25 0.25
4 0.8888888888888888 0.1111111111111112
5 1 0
6 1 2.220446049250313e-16
7 1 0
8 0.9999999999999998 2.220446049250313e-16
9 1 2.220446049250313e-16
Integrate 420 * X^3 * Y^2
Rule QUAD ERROR
1 0.8641975308641975 0.1358024691358025
2 0 1
3 2.1875 1.1875
4 1.166666666666667 0.1666666666666665
5 0.984375 0.015625
6 1 0
7 1 2.220446049250313e-16
8 1 2.220446049250313e-16
9 0.9999999999999999 1.110223024625157e-16
Integrate 1120 * X^3 * Y^3
Rule QUAD ERROR
1 0.7681755829903978 0.2318244170096022
2 0 1
3 2.916666666666667 1.916666666666667
4 1.267489711934156 0.2674897119341564
5 0.875 0.125
6 0.9600000000000001 0.03999999999999992
7 1 0
8 0.9999999999999999 1.110223024625157e-16
9 1 2.220446049250313e-16
Integrate 2520 * X^3 * Y^4
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
2 0 1
3 3.28125 2.28125
4 1.296296296296296 0.2962962962962961
5 0.861328125 0.138671875
6 0.9696000000000002 0.03039999999999976
7 1.00462962962963 0.004629629629629983
8 0.9999999999999998 2.220446049250313e-16
9 0.9999999999999998 2.220446049250313e-16
Integrate 5040 * X^3 * Y^5
Rule QUAD ERROR
1 0.3840877914951988 0.6159122085048012
2 0 1
3 3.28125 2.28125
4 1.325102880658436 0.3251028806584357
5 0.984375 0.015625
6 1.0176 0.01760000000000028
7 0.981481481481482 0.01851851851851805
8 0.9882489438924252 0.01175105610757476
9 0.9999999999999997 3.33066907387547e-16
Integrate 9240 * X^3 * Y^6
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0 1
3 3.0078125 2.0078125
4 1.373113854595336 0.3731138545953361
5 1.2125244140625 0.2125244140624998
6 1.07712 0.0771200000000003
7 0.9317558299039784 0.06824417009602157
8 0.9737708494476507 0.02622915055234931
9 1.00268809000651 0.002688090006510269
Integrate 15840 * X^3 * Y^7
Rule QUAD ERROR
1 0.1341258954427678 0.8658741045572321
2 0 1
3 2.578125 1.578125
4 1.428440786465478 0.4284407864654776
5 1.49853515625 0.49853515625
6 1.132032 0.1320320000000004
7 0.8798868312757204 0.1201131687242796
8 0.9692717927297054 0.03072820727029457
9 1.0030517578125 0.0030517578125
Integrate 30 * X^4 * Y^0
Rule QUAD ERROR
1 0.1851851851851852 0.8148148148148149
2 5 4
3 0.625 0.375
4 1.055555555555555 0.05555555555555536
5 0.9999999999999998 2.220446049250313e-16
6 1 0
7 1 2.220446049250313e-16
8 0.9999999999999999 1.110223024625157e-16
9 1 0
Integrate 210 * X^4 * Y^1
Rule QUAD ERROR
1 0.4320987654320987 0.5679012345679013
2 0 1
3 1.09375 0.09375
4 0.7777777777777777 0.2222222222222223
5 1.0390625 0.0390625
6 1 0
7 0.9999999999999999 1.110223024625157e-16
8 0.9999999999999999 1.110223024625157e-16
9 1 2.220446049250313e-16
Integrate 840 * X^4 * Y^2
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
2 0 1
3 2.1875 1.1875
4 1.123456790123457 0.1234567901234567
5 1.057291666666667 0.05729166666666652
6 1.034666666666667 0.03466666666666662
7 1 2.220446049250313e-16
8 0.9999999999999999 1.110223024625157e-16
9 1 2.220446049250313e-16
Integrate 2520 * X^4 * Y^3
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
2 0 1
3 3.28125 2.28125
4 1.296296296296296 0.2962962962962961
5 0.861328125 0.138671875
6 0.9696000000000001 0.03039999999999987
7 1.00462962962963 0.004629629629629983
8 0.9999999999999998 2.220446049250313e-16
9 0.9999999999999997 3.33066907387547e-16
Integrate 6300 * X^4 * Y^4
Rule QUAD ERROR
1 0.4801097393689986 0.5198902606310014
2 0 1
3 4.1015625 3.1015625
4 1.368312757201646 0.368312757201646
5 0.70068359375 0.29931640625
6 0.9392000000000004 0.06079999999999963
7 1.043595679012346 0.04359567901234573
8 1.014012018801689 0.01401201880168945
9 1 4.440892098500626e-16
Integrate 13860 * X^4 * Y^5
Rule QUAD ERROR
1 0.3520804755372656 0.6479195244627344
2 0 1
3 4.51171875 3.51171875
4 1.425925925925926 0.4259259259259256
5 0.69085693359375 0.30914306640625
6 0.9609600000000005 0.03903999999999952
7 1.055298353909465 0.05529835390946514
8 1.012385712302413 0.01238571230241292
9 0.9987856547037756 0.001214345296224439
Integrate 27720 * X^4 * Y^6
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0 1
3 4.51171875 3.51171875
4 1.513946044810242 0.5139460448102422
5 0.84124755859375 0.15875244140625
6 1.0134784 0.01347840000000033
7 1.006258573388203 0.006258573388203015
8 0.9918783840066636 0.008121615993336384
9 1.008800506591796 0.008800506591796431
Integrate 42 * X^5 * Y^0
Rule QUAD ERROR
1 0.08641975308641975 0.9135802469135803
2 7 6
3 0.4375 0.5625
4 1.166666666666667 0.1666666666666667
5 0.9843750000000002 0.01562499999999978
6 0.9999999999999998 2.220446049250313e-16
7 1 0
8 0.9999999999999999 1.110223024625157e-16
9 1 0
Integrate 336 * X^5 * Y^1
Rule QUAD ERROR
1 0.2304526748971193 0.7695473251028807
2 0 1
3 0.875 0.125
4 0.691358024691358 0.308641975308642
5 1.09375 0.09375000000000022
6 0.9824000000000001 0.01759999999999995
7 1 2.220446049250313e-16
8 1 0
9 0.9999999999999998 2.220446049250313e-16
Integrate 1512 * X^5 * Y^2
Rule QUAD ERROR
1 0.3456790123456789 0.654320987654321
2 0 1
3 1.96875 0.96875
4 1.088888888888889 0.08888888888888857
5 1.205859375 0.2058593750000002
6 1.07712 0.0771200000000003
7 0.9916666666666668 0.008333333333333193
8 0.9999999999999999 1.110223024625157e-16
9 1 2.220446049250313e-16
Integrate 5040 * X^5 * Y^3
Rule QUAD ERROR
1 0.3840877914951988 0.6159122085048012
2 0 1
3 3.28125 2.28125
4 1.325102880658436 0.3251028806584357
5 0.984375 0.015625
6 1.0176 0.01760000000000028
7 0.9814814814814817 0.01851851851851827
8 0.9882489438924253 0.01175105610757465
9 0.9999999999999999 1.110223024625157e-16
Integrate 13860 * X^5 * Y^4
Rule QUAD ERROR
1 0.3520804755372656 0.6479195244627344
2 0 1
3 4.51171875 3.51171875
4 1.425925925925926 0.4259259259259256
5 0.69085693359375 0.30914306640625
6 0.9609600000000007 0.0390399999999993
7 1.055298353909465 0.05529835390946536
8 1.012385712302413 0.01238571230241337
9 0.9987856547037756 0.001214345296224439
Integrate 33264 * X^5 * Y^5
Rule QUAD ERROR
1 0.2816643804298125 0.7183356195701875
2 0 1
3 5.4140625 4.4140625
4 1.478737997256516 0.4787379972565156
5 0.507568359375 0.492431640625
6 0.9539481600000006 0.0460518399999994
7 1.141589506172839 0.1415895061728394
8 1.034046188237893 0.03404618823789329
9 0.9849243164062501 0.01507568359374989
Integrate 56 * X^6 * Y^0
Rule QUAD ERROR
1 0.03840877914951989 0.9615912208504801
2 9.333333333333332 8.333333333333332
3 0.2916666666666666 0.7083333333333334
4 1.325102880658436 0.3251028806584362
5 0.9479166666666667 0.05208333333333326
6 1.005866666666667 0.005866666666666909
7 1 4.440892098500626e-16
8 1 4.440892098500626e-16
9 0.9999999999999999 1.110223024625157e-16
Integrate 504 * X^6 * Y^1
Rule QUAD ERROR
1 0.1152263374485597 0.8847736625514403
2 0 1
3 0.65625 0.34375
4 0.6222222222222221 0.3777777777777779
5 1.140234375 0.1402343749999999
6 0.9446400000000001 0.05535999999999985
7 1.006481481481482 0.006481481481481977
8 0.9999999999999998 2.220446049250313e-16
9 1 2.220446049250313e-16
Integrate 2520 * X^6 * Y^2
Rule QUAD ERROR
1 0.1920438957475994 0.8079561042524006
2 0 1
3 1.640625 0.640625
4 1.065843621399177 0.06584362139917666
5 1.3876953125 0.3876953125
6 1.1072 0.1072000000000004
7 0.9868827160493832 0.01311728395061684
8 1.007229130719343 0.007229130719343058
9 1 2.220446049250313e-16
Integrate 9240 * X^6 * Y^3
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0 1
3 3.0078125 2.0078125
4 1.373113854595336 0.3731138545953356
5 1.2125244140625 0.2125244140625
6 1.07712 0.0771200000000003
7 0.9317558299039784 0.06824417009602157
8 0.9737708494476505 0.02622915055234953
9 1.00268809000651 0.002688090006510269
Integrate 27720 * X^6 * Y^4
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0 1
3 4.51171875 3.51171875
4 1.513946044810242 0.5139460448102422
5 0.84124755859375 0.15875244140625
6 1.0134784 0.01347840000000033
7 1.006258573388203 0.006258573388203459
8 0.9918783840066635 0.008121615993336495
9 1.008800506591797 0.008800506591796653
Integrate 72 * X^7 * Y^0
Rule QUAD ERROR
1 0.01646090534979424 0.9835390946502057
2 12 11
3 0.1875 0.8125
4 1.525925925925926 0.5259259259259259
5 0.8929687500000001 0.1070312499999999
6 1.02336 0.02336000000000049
7 0.9981481481481489 0.001851851851851105
8 1 4.440892098500626e-16
9 1 4.440892098500626e-16
Integrate 720 * X^7 * Y^1
Rule QUAD ERROR
1 0.05486968449931412 0.9451303155006858
2 0 1
3 0.46875 0.53125
4 0.559670781893004 0.440329218106996
5 1.166015625 0.166015625
6 0.8928000000000005 0.1071999999999995
7 1.023148148148149 0.02314814814814881
8 0.9971610468427268 0.002838953157273227
9 0.9999999999999998 2.220446049250313e-16
Integrate 3960 * X^7 * Y^2
Rule QUAD ERROR
1 0.1005944215820759 0.8994055784179241
2 0 1
3 1.2890625 0.2890625
4 1.041152263374485 0.04115226337448519
5 1.5670166015625 0.5670166015625
6 1.11936 0.1193600000000004
7 1.001543209876544 0.001543209876543994
8 1.024447013290947 0.02444701329094734
9 0.9978205362955731 0.002179463704426898
Integrate 15840 * X^7 * Y^3
Rule QUAD ERROR
1 0.1341258954427678 0.8658741045572321
2 0 1
3 2.578125 1.578125
4 1.428440786465478 0.4284407864654776
5 1.49853515625 0.49853515625
6 1.132032 0.1320319999999999
7 0.8798868312757204 0.1201131687242796
8 0.9692717927297057 0.03072820727029435
9 1.0030517578125 0.003051757812499778
Integrate 90 * X^8 * Y^0
Rule QUAD ERROR
1 0.006858710562414265 0.9931412894375857
2 15 14
3 0.1171875 0.8828125
4 1.767489711934157 0.7674897119341566
5 0.82470703125 0.17529296875
6 1.056 0.05600000000000027
7 0.9918981481481485 0.008101851851851527
8 1.000709738289318 0.0007097382893184179
9 0.9999999999999999 1.110223024625157e-16
Integrate 990 * X^8 * Y^1
Rule QUAD ERROR
1 0.02514860539551897 0.974851394604481
2 0 1
3 0.322265625 0.677734375
4 0.4979423868312756 0.5020576131687244
5 1.167205810546875 0.167205810546875
6 0.8342400000000003 0.1657599999999997
7 1.048932613168724 0.04893261316872444
8 0.9879981980297325 0.01200180197026746
9 1.001058578491211 0.001058578491210938
Integrate 5940 * X^8 * Y^2
Rule QUAD ERROR
1 0.05029721079103794 0.949702789208962
2 0 1
3 0.966796875 0.033203125
4 1.003429355281207 0.003429355281206803
5 1.721099853515625 0.721099853515625
6 1.1159808 0.1159808000000004
7 1.044688786008231 0.04468878600823101
8 1.048571841421759 0.04857184142175863
9 0.9927921295166013 0.00720787048339866
Integrate 110 * X^9 * Y^0
Rule QUAD ERROR
1 0.002794289488390997 0.997205710511609
2 18.33333333333333 17.33333333333333
3 0.07161458333333333 0.9283854166666666
4 2.049611339734796 1.049611339734796
5 0.74859619140625 0.25140380859375
6 1.10528 0.1052800000000005
7 0.9792238225880213 0.02077617741197868
8 1.003534525013671 0.003534525013670908
9 0.9997647603352868 0.0002352396647131716
Integrate 1320 * X^9 * Y^1
Rule QUAD ERROR
1 0.01117715795356399 0.988822842046436
2 0 1
3 0.21484375 0.78515625
4 0.4359091601889955 0.5640908398110045
5 1.14471435546875 0.14471435546875
6 0.7745408000000005 0.2254591999999995
7 1.079818244170097 0.07981824417009653
8 0.9703870957557771 0.02961290424422292
9 1.004940032958984 0.004940032958984153
Integrate 132 * X^10 * Y^0
Rule QUAD ERROR
1 0.001117715795356399 0.9988822842046436
2 22 21
3 0.04296875 0.95703125
4 2.372351775643957 1.372351775643957
5 0.6693725585937498 0.3306274414062502
6 1.17142784 0.1714278400000004
7 0.9591049382716056 0.04089506172839441
8 1.01016401086525 0.01016401086525032
9 0.9987297058105471 0.001270294189452903
TEST05
REFERENCE_TO_PHYSICAL_T3 transforms a rule
on the unit (reference) triangle to a rule on
an arbitrary (physical) triangle.
The reference triangle:
1 0 0
2 1 0
3 0 1
Rule 3 for reference triangle
with area = 0.5
X Y W
0 0.5 0.5 0.3333333333333333
1 0.5 0 0.3333333333333333
2 0 0.5 0.3333333333333333
The physical triangle:
1 1 2
2 1 1
3 3 2
Rule 3 for physical triangle
with area = 1
X Y W
0 2 1.5 0.3333333333333333
1 1 1.5 0.3333333333333333
2 2 2 0.3333333333333333
TRIANGLE_NCC_RULE_PRB:
Normal end of execution.
15 June 2014 11:19:11 AM