test_triquad.out
x1=1.0, y1=1.0, x2=2.5, y2=3.0
x3=4.5, y3=0.5
T2[0]=4.5, T2[1]=0.5, T2[2]=1.0, T2[3]=1.0
T2[4]=2.5, T2[5]=3.0
T3[0]=2.5, T3[1]=3.0, T3[2]=4.5, T3[3]=0.5
T3[4]=1.0, T3[5]=1.0
area=3.875
triquad ready for integration over triangles
triquad.tint(1, T, X, Y, W);
x=2.666666666666665, y=1.4999999999999996, w=3.875
 
triquad.tint(2, T, X, Y, W);
x=1.682638759027739, y=1.522524275886844, w=0.7050896457420891
x=2.092616369580671, y=1.010052262695679, w=0.7050896457420891
x=2.6245409179447075, y=2.2435011278975936, w=1.2324103542579108
x=3.6002039534468775, y=1.0239223335198815, w=1.2324103542579108
 
triquad.tint(3, T, X, Y, W);
x=1.3663730719328915, y=1.3648532457606035, w=0.15032197062118613
x=1.53085134559788, y=1.159255403679364, w=0.24051515299389625
x=1.6953296192628735, y=0.953657561598126, w=0.15032197062118613
x=2.0189078390172255, y=2.0146811015206203, w=0.4935051595241087
x=2.4763328388981654, y=1.4428998516694496, w=0.789608255238574
x=2.9337578387791012, y=0.8711186018182794, w=0.4935051595241087
x=2.572553370350196, y=2.566029943950527, w=0.432561758743591
x=3.27853010121824, y=1.6835590303654722, w=0.6920988139897503
x=3.984506832086284, y=0.801088116780417, w=0.432561758743591
 
triquad.tint(4, T, X, Y, W);
x=1.229047366769562, y=1.2552602658701948, w=0.042030000806568754
x=1.3018839563285753, y=1.1642145289214318, w=0.07879626162471225
x=1.3969153653903295, y=1.0454252675942395, w=0.07879626162471225
x=1.4697519549493379, y=0.9543795306454751, w=0.042030000806568754
x=1.6824385198954024, y=1.7605389247011936, w=0.1750263819383675
x=1.8994525597157725, y=1.4892713749257311, w=0.3281328650435354
x=2.1825952784396425, y=1.1353429765208936, w=0.3281328650435354
x=2.3996093182600124, y=0.8640754267454309, w=0.1750263819383675
x=2.185155725965554, y=2.320788664695327, w=0.27425752621016647
x=2.5620327990057, y=1.8496923233951446, w=0.5141676748296337
x=3.05375213280368, y=1.2350431561476696, w=0.5141676748296337
x=3.430629205843826, y=0.7639468148474869, w=0.27425752621016647
x=2.545277694938251, y=2.722124121383429, w=0.1826548534987105
x=3.036672810316937, y=2.107880227160072, w=0.3424344360483016
x=3.677806209110473, y=1.3064634786681515, w=0.3424344360483016
x=4.169201324489159, y=0.692219584444794, w=0.1826548534987105
 
triquad.tint(5, T, X, Y, W);
x=1.157047205628331, y=1.185514450435037, w=0.014458029293304501
x=1.193279594825767, y=1.140223963938242, w=0.029207438138788126
x=1.2463377144970649, y=1.0739013143491196, w=0.034715402678931626
x=1.299395834168363, y=1.0075786647599971, w=0.029207438138788126
x=1.335628223365799, y=0.962288178263202, w=0.014458029293304501
x=1.485375178760688, y=1.5733569673038004, w=0.067855118661771
x=1.59735617398611, y=1.4333807232720228, w=0.13707775385624713
x=1.76133931661591, y=1.228401794984773, w=0.16292799802674549
x=1.9253224592457099, y=1.023422866697523, w=0.13707775385624713
x=2.037303454471132, y=0.8834466226657455, w=0.067855118661771
x=1.895767074517863, y=2.0581387671440505, w=0.13439667484308263
x=2.102429658193429, y=1.799810537549593, w=0.27150190990112916
x=2.4050629743815346, y=1.4215188923144604, w=0.32270198041776127
x=2.707696290569641, y=1.043227247079328, w=0.27150190990112916
x=2.914358874245207, y=0.7848990174848705, w=0.13439667484308263
x=2.27822237787981, y=2.509920033390007, w=0.15348164427336813
x=2.573121293724366, y=2.141296388584311, w=0.3100564772427439
x=3.00496645531598, y=1.6014899365947939, w=0.3685272021991435
x=3.4368116169075953, y=1.0616834846052785, w=0.3100564772427439
x=3.73171053275215, y=0.6930598397995815, w=0.15348164427336813
x=2.5303704015624042, y=2.8077738019725524, w=0.08885437272484188
x=2.883442433527555, y=2.3664337620161144, w=0.17949946995361338
x=3.40047535737133, y=1.720142607211399, w=0.21334963889963862
x=3.9175082812151008, y=1.0738514524066822, w=0.17949946995361338
x=4.27058031318025, y=0.6325114124502444, w=0.08885437272484188
 
triquad.tint(6, T, X, Y, W);
x=1.1145148873257287, y=1.139941914478843, w=0.005801204849582875
x=1.1343316138552686, y=1.115171006316918, w=0.012215718593682125
x=1.1652036572511104, y=1.0765809520721155, w=0.01584399608447375
x=1.2000679861501844, y=1.033000540948273, w=0.01584399608447375
x=1.2309400295460264, y=0.9944104867034704, w=0.012215718593682125
x=1.2507567560755666, y=0.9696395785415455, w=0.005801204849582875
x=1.3617329563574894, y=1.442052589186675, w=0.029181061148359125
x=1.4243306084205654, y=1.36380552410783, w=0.06144717183692287
x=1.5218501169069114, y=1.2419061384998975, w=0.07969803352294039
x=1.6319805729428136, y=1.10424306845502, w=0.07969803352294039
x=1.7295000814291597, y=0.9823436828470876, w=0.06144717183692287
x=1.7920977334922354, y=0.9040966177682423, w=0.029181061148359125
x=1.6917958485760172, y=1.8454030540402224, w=0.06549940242630825
x=1.811510668767973, y=1.6957595288002776, w=0.13792346397695537
x=1.9980117600850589, y=1.4626331646539201, w=0.17888909329802838
x=2.208630646057191, y=1.199359557188755, w=0.17888909329802838
x=2.395131737374277, y=0.9662331930423975, w=0.13792346397695537
x=2.514846557566233, y=0.8165896678024526, w=0.06549940242630825
x=2.039296710534331, y=2.2700634369926145, w=0.09346969963305375
x=2.219146328140177, y=2.0452514149853065, w=0.19682110481511814
x=2.4993301007313047, y=1.6950216992463971, w=0.2552803414810954
x=2.8157464478629253, y=1.299501265331872, w=0.2552803414810954
x=3.095930220454053, y=0.949271549592962, w=0.19682110481511814
x=3.275779838059899, y=0.7244595275856545, w=0.09346969963305375
x=2.335412766522392, y=2.6319294681316348, w=0.08998427944423062
x=2.5665050743981084, y=2.3430640832869893, w=0.1894817824999495
x=2.926518709674826, y=1.893047039191092, w=0.24576111482795598
x=3.333088291982754, y=1.384835061306182, w=0.24576111482795598
x=3.693101927259472, y=0.9348180172102845, w=0.1894817824999495
x=3.9241942351351877, y=0.6459526323656395, w=0.08998427944423062
x=2.5215760924892425, y=2.85942872914428, w=0.04800555648310725
x=2.78488384244998, y=2.530294041693362, w=0.10108630605814325
x=3.195085208005077, y=2.017542334749488, w=0.13111066902009688
x=3.6583326561959986, y=1.438483024510835, w=0.13111066902009688
x=4.0685340217511, y=0.9257313175669619, w=0.10108630605814325
x=4.331841771711833, y=0.5965966301160426, w=0.04800555648310725
 
 
f1=x+2.0*y+3.0
1 point integral of f1=33.58333333333332
4 point integral of f1=33.583333333333314
9 point integral of f1=33.58333333333327
16 point integral of f1=33.58333333333325
25 point integral of f1=33.58333333333333
36 point integral of f1=33.58333333333339
 
f2=x*x + 2.0*x*y + 3.0*y*y + 4.0*x + 5.0*y + 6.0
1 point integral of f2=178.3576388888888
4 point integral of f2=182.93229166666652
9 point integral of f2=182.93229166666632
16 point integral of f2=182.93229166666612
25 point integral of f2=182.93229166666666
36 point integral of f2=182.93229166666703
 
f3=x*x*x + 2.0*x*x*y + 3.0*x*y*y + 4.0*y*y*y +
5.0*x*x + 6.0*x*y + 7.0*y*y + 8.0*x + 9.0*y + 10.0
1 point integral of f3=743.7488425925919
4 point integral of f3=803.0937499999989
9 point integral of f3=803.0937499999983
16 point integral of f3=803.093749999997
25 point integral of f3=803.0937500000002
36 point integral of f3=803.0937500000017
 
f4=x*x*x*x + 2.0*x*x*x*y + 3.0*x*x*y*y + 4.0*x*y*y*y + 5.0*y*y*y*y +
6.0*x*x*x + 7.0*x*x*y + 8.0*x*y*y + 9.0*y*y*y +
10.0*x*x + 11.0*x*y + 12.0*y*y + 13.0*x + 14.0*y + 15.0
1 point integral of f4=2698.420235339503
4 point integral of f4=3150.6642122395774
9 point integral of f4=3152.8130208333273
16 point integral of f4=3152.813020833319
25 point integral of f4=3152.813020833334
36 point integral of f4=3152.81302083334
 
f5=x*x*x*x*x + 2.0*x*x*x*x*y + 3.0*x*x*x*y*y + 4.0*x*x*y*y*y +
5.0*x*y*y*y*y + 6.0*y*y*y*y*y + 7.0*x*x*x*x +
8.0*x*x*x*y + 9.0*x*x*y*y + 10.0*x*y*y*y + 11.0*y*y*y*y +
12.0*x*x*x + 13.0*x*x*y + 14.0*x*y*y + 15.0*y*y*y +
16.0*x*x + 17.0*x*y + 18.0*y*y + 19.0*x + 20.0*y + 21.0
1 point integral of f5=8988.54288837447
4 point integral of f5=11648.184690104135
9 point integral of f5=11686.604427083308
16 point integral of f5=11686.604427083274
25 point integral of f5=11686.604427083337
36 point integral of f5=11686.604427083364
 
f6=x*x*x*x*x*x + 2.0*x*x*x*x*x*y + 3.0*x*x*x*x*y*y +
4.0*x*x*x*y*y*y + 5.0*x*x*y*y*y*y + 6.0*x*y*y*y*y*y + 7.0*y*y*y*y*y*y +
8.0*x*x*x*x*x + 9.0*x*x*x*x*y + 10.0*x*x*x*y*y + 11.0*x*x*y*y*y +
12.0*x*y*y*y*y + 13.0*y*y*y*y*y + 14.0*x*x*x*x +
15.0*x*x*x*y + 16.0*x*x*y*y + 17.0*x*y*y*y + 18.0*y*y*y*y +
19.0*x*x*x + 20.0*x*x*y + 21.0*x*y*y + 22.0*y*y*y +
23.0*x*x + 24.0*x*y + 25.0*y*y + 26.0*x + 27.0*y + 28.0
1 point integral over T of f6=28356.473687735714
4 point integral over T of f6=41798.33275511055
9 point integral over T of f6=42192.31592492992
16 point integral over T of f6=42193.242204550836
25 point integral over T of f6=42193.24220455111
36 point integral over T of f6=42193.24220455123
 
1 point integral over T2 of f6=28356.473687735815
4 point integral over T2 of f6=41823.5751408529
9 point integral over T2 of f6=42192.453569641875
16 point integral over T2 of f6=42193.24220455103
25 point integral over T2 of f6=42193.24220455115
36 point integral over T2 of f6=42193.24220455127
 
1 point integral over T3 of f6=28356.473687735797
4 point integral over T3 of f6=41738.492679101604
9 point integral over T3 of f6=42192.04424945431
16 point integral over T3 of f6=42193.24220455103
25 point integral over T3 of f6=42193.24220455114
36 point integral over T3 of f6=42193.24220455124
 
 
tri_split_test  center point used for numerical quadrature
tri_split returns nntri=4, nvert=6
4 triangles, integral over T3 of f6=38421.381338907035
tri_split returns nntri=16, nvert=15
16 triangles, integral over T3 of f6=41231.387074210186
tri_split returns nntri=64, nvert=45
64 triangles, integral over T3 of f6=41951.607988003016
tri_split returns nntri=256, nvert=153
256 triangles, integral over T3 of f6=42132.760657442304
tri_split returns nntri=1024, nvert=561
1024 triangles, integral over T3 of f6=42178.11725819984
tri_split returns nntri=4096, nvert=2145
4096 triangles, integral over T3 of f6=42189.46068302873
tri_split returns nntri=16384, nvert=8385
16384 triangles, integral over T3 of f6=42192.29680636259
 
compare accuracy of this 16384 equal area integration
coordinates with the accuracy of the 36 Gauss Legendre
integration coordinates in the previous set.
 
P.S. No, you do not get better accuracy using many 
triangles with a higher order method used in each triangle.