test_triquad.out x1= 1.00000000000000E+00, y1= 1.00000000000000E+00, x2= 2.50000000000000E+00, y2= 3.00000000000000E+00 x3= 4.50000000000000E+00, y3= 5.00000000000000E-01 T2(0):= 4.50000000000000E+00, T2(1):= 5.00000000000000E-01, T2(2):= 1.00000000000000E+00, T2(3):= 1.00000000000000E+00 T2(4):= 2.50000000000000E+00, T2(5):= 3.00000000000000E+00 T3(0):= 2.50000000000000E+00, T3(1):= 3.00000000000000E+00, T3(2):= 4.50000000000000E+00, T3(3):= 5.00000000000000E-01 T3(4):= 1.00000000000000E+00, T3(5):= 1.00000000000000E+00 area:= 3.87500000000000E+00 triquad ready for integration over triangles triquad tint(1, T, nn, X, Y, W); x:= 2.66666666666666E+00, y:= 1.50000000000000E+00, w:= 3.87500000000000E+00 triquad tint(2, T, nn, X, Y, W); x:= 1.68263875902774E+00, y:= 1.52252427588684E+00, w:= 7.05089645742089E-01 x:= 2.09261636958067E+00, y:= 1.01005226269568E+00, w:= 7.05089645742089E-01 x:= 2.62454091794471E+00, y:= 2.24350112789759E+00, w:= 1.23241035425791E+00 x:= 3.60020395344688E+00, y:= 1.02392233351988E+00, w:= 1.23241035425791E+00 triquad tint(3, T, nn, X, Y, W); x:= 1.36637307193289E+00, y:= 1.36485324576060E+00, w:= 1.50321970621186E-01 x:= 1.53085134559788E+00, y:= 1.15925540367936E+00, w:= 2.40515152993896E-01 x:= 1.69532961926287E+00, y:= 9.53657561598126E-01, w:= 1.50321970621186E-01 x:= 2.01890783901723E+00, y:= 2.01468110152062E+00, w:= 4.93505159524109E-01 x:= 2.47633283889816E+00, y:= 1.44289985166945E+00, w:= 7.89608255238574E-01 x:= 2.93375783877910E+00, y:= 8.71118601818279E-01, w:= 4.93505159524109E-01 x:= 2.57255337035020E+00, y:= 2.56602994395053E+00, w:= 4.32561758743591E-01 x:= 3.27853010121824E+00, y:= 1.68355903036547E+00, w:= 6.92098813989750E-01 x:= 3.98450683208628E+00, y:= 8.01088116780417E-01, w:= 4.32561758743591E-01 triquad tint(4, T, nn, X, Y, W); x:= 1.22904736676956E+00, y:= 1.25526026587020E+00, w:= 4.20300008065688E-02 x:= 1.30188395632858E+00, y:= 1.16421452892143E+00, w:= 7.87962616247122E-02 x:= 1.39691536539033E+00, y:= 1.04542526759424E+00, w:= 7.87962616247122E-02 x:= 1.46975195494934E+00, y:= 9.54379530645475E-01, w:= 4.20300008065688E-02 x:= 1.68243851989540E+00, y:= 1.76053892470119E+00, w:= 1.75026381938368E-01 x:= 1.89945255971577E+00, y:= 1.48927137492573E+00, w:= 3.28132865043535E-01 x:= 2.18259527843964E+00, y:= 1.13534297652089E+00, w:= 3.28132865043535E-01 x:= 2.39960931826001E+00, y:= 8.64075426745431E-01, w:= 1.75026381938368E-01 x:= 2.18515572596555E+00, y:= 2.32078866469533E+00, w:= 2.74257526210166E-01 x:= 2.56203279900570E+00, y:= 1.84969232339514E+00, w:= 5.14167674829634E-01 x:= 3.05375213280368E+00, y:= 1.23504315614767E+00, w:= 5.14167674829634E-01 x:= 3.43062920584383E+00, y:= 7.63946814847487E-01, w:= 2.74257526210166E-01 x:= 2.54527769493825E+00, y:= 2.72212412138343E+00, w:= 1.82654853498710E-01 x:= 3.03667281031694E+00, y:= 2.10788022716007E+00, w:= 3.42434436048302E-01 x:= 3.67780620911047E+00, y:= 1.30646347866815E+00, w:= 3.42434436048302E-01 x:= 4.16920132448916E+00, y:= 6.92219584444794E-01, w:= 1.82654853498710E-01 triquad tint(5, T, nn, X, Y, W); x:= 1.15704720562833E+00, y:= 1.18551445043504E+00, w:= 1.44580292933045E-02 x:= 1.19327959482577E+00, y:= 1.14022396393824E+00, w:= 2.92074381387881E-02 x:= 1.24633771449707E+00, y:= 1.07390131434912E+00, w:= 3.47154026789316E-02 x:= 1.29939583416836E+00, y:= 1.00757866476000E+00, w:= 2.92074381387881E-02 x:= 1.33562822336580E+00, y:= 9.62288178263202E-01, w:= 1.44580292933045E-02 x:= 1.48537517876069E+00, y:= 1.57335696730380E+00, w:= 6.78551186617710E-02 x:= 1.59735617398611E+00, y:= 1.43338072327202E+00, w:= 1.37077753856247E-01 x:= 1.76133931661591E+00, y:= 1.22840179498477E+00, w:= 1.62927998026745E-01 x:= 1.92532245924571E+00, y:= 1.02342286669752E+00, w:= 1.37077753856247E-01 x:= 2.03730345447113E+00, y:= 8.83446622665745E-01, w:= 6.78551186617710E-02 x:= 1.89576707451786E+00, y:= 2.05813876714405E+00, w:= 1.34396674843083E-01 x:= 2.10242965819343E+00, y:= 1.79981053754959E+00, w:= 2.71501909901129E-01 x:= 2.40506297438154E+00, y:= 1.42151889231446E+00, w:= 3.22701980417761E-01 x:= 2.70769629056964E+00, y:= 1.04322724707933E+00, w:= 2.71501909901129E-01 x:= 2.91435887424521E+00, y:= 7.84899017484871E-01, w:= 1.34396674843083E-01 x:= 2.27822237787981E+00, y:= 2.50992003339001E+00, w:= 1.53481644273368E-01 x:= 2.57312129372437E+00, y:= 2.14129638858431E+00, w:= 3.10056477242744E-01 x:= 3.00496645531598E+00, y:= 1.60148993659479E+00, w:= 3.68527202199143E-01 x:= 3.43681161690760E+00, y:= 1.06168348460528E+00, w:= 3.10056477242744E-01 x:= 3.73171053275215E+00, y:= 6.93059839799582E-01, w:= 1.53481644273368E-01 x:= 2.53037040156240E+00, y:= 2.80777380197255E+00, w:= 8.88543727248419E-02 x:= 2.88344243352755E+00, y:= 2.36643376201611E+00, w:= 1.79499469953613E-01 x:= 3.40047535737133E+00, y:= 1.72014260721140E+00, w:= 2.13349638899639E-01 x:= 3.91750828121510E+00, y:= 1.07385145240668E+00, w:= 1.79499469953613E-01 x:= 4.27058031318025E+00, y:= 6.32511412450244E-01, w:= 8.88543727248419E-02 triquad tint(6, T, nn, X, Y, W); x:= 1.11451488732573E+00, y:= 1.13994191447884E+00, w:= 5.80120484958288E-03 x:= 1.13433161385527E+00, y:= 1.11517100631692E+00, w:= 1.22157185936821E-02 x:= 1.16520365725111E+00, y:= 1.07658095207212E+00, w:= 1.58439960844737E-02 x:= 1.20006798615018E+00, y:= 1.03300054094827E+00, w:= 1.58439960844737E-02 x:= 1.23094002954603E+00, y:= 9.94410486703471E-01, w:= 1.22157185936821E-02 x:= 1.25075675607557E+00, y:= 9.69639578541545E-01, w:= 5.80120484958288E-03 x:= 1.36173295635749E+00, y:= 1.44205258918667E+00, w:= 2.91810611483591E-02 x:= 1.42433060842057E+00, y:= 1.36380552410783E+00, w:= 6.14471718369229E-02 x:= 1.52185011690691E+00, y:= 1.24190613849990E+00, w:= 7.96980335229404E-02 x:= 1.63198057294281E+00, y:= 1.10424306845502E+00, w:= 7.96980335229404E-02 x:= 1.72950008142916E+00, y:= 9.82343682847088E-01, w:= 6.14471718369229E-02 x:= 1.79209773349224E+00, y:= 9.04096617768242E-01, w:= 2.91810611483591E-02 x:= 1.69179584857602E+00, y:= 1.84540305404022E+00, w:= 6.54994024263083E-02 x:= 1.81151066876797E+00, y:= 1.69575952880028E+00, w:= 1.37923463976955E-01 x:= 1.99801176008506E+00, y:= 1.46263316465392E+00, w:= 1.78889093298028E-01 x:= 2.20863064605719E+00, y:= 1.19935955718875E+00, w:= 1.78889093298028E-01 x:= 2.39513173737428E+00, y:= 9.66233193042398E-01, w:= 1.37923463976955E-01 x:= 2.51484655756623E+00, y:= 8.16589667802452E-01, w:= 6.54994024263083E-02 x:= 2.03929671053433E+00, y:= 2.27006343699261E+00, w:= 9.34696996330538E-02 x:= 2.21914632814018E+00, y:= 2.04525141498531E+00, w:= 1.96821104815118E-01 x:= 2.49933010073131E+00, y:= 1.69502169924640E+00, w:= 2.55280341481095E-01 x:= 2.81574644786292E+00, y:= 1.29950126533187E+00, w:= 2.55280341481095E-01 x:= 3.09593022045405E+00, y:= 9.49271549592962E-01, w:= 1.96821104815118E-01 x:= 3.27577983805990E+00, y:= 7.24459527585654E-01, w:= 9.34696996330538E-02 x:= 2.33541276652239E+00, y:= 2.63192946813163E+00, w:= 8.99842794442306E-02 x:= 2.56650507439811E+00, y:= 2.34306408328699E+00, w:= 1.89481782499950E-01 x:= 2.92651870967483E+00, y:= 1.89304703919109E+00, w:= 2.45761114827956E-01 x:= 3.33308829198275E+00, y:= 1.38483506130618E+00, w:= 2.45761114827956E-01 x:= 3.69310192725947E+00, y:= 9.34818017210284E-01, w:= 1.89481782499950E-01 x:= 3.92419423513519E+00, y:= 6.45952632365639E-01, w:= 8.99842794442306E-02 x:= 2.52157609248924E+00, y:= 2.85942872914428E+00, w:= 4.80055564831073E-02 x:= 2.78488384244998E+00, y:= 2.53029404169336E+00, w:= 1.01086306058143E-01 x:= 3.19508520800508E+00, y:= 2.01754233474949E+00, w:= 1.31110669020097E-01 x:= 3.65833265619600E+00, y:= 1.43848302451084E+00, w:= 1.31110669020097E-01 x:= 4.06853402175110E+00, y:= 9.25731317566962E-01, w:= 1.01086306058143E-01 x:= 4.33184177171183E+00, y:= 5.96596630116042E-01, w:= 4.80055564831073E-02 f1:=x+2.0*y+3.0 1 point integral of f1:= 3.35833333333333E+01 4 point integral of f1:= 3.35833333333333E+01 9 point integral of f1:= 3.35833333333333E+01 16 point integral of f1:= 3.35833333333333E+01 25 point integral of f1:= 3.35833333333333E+01 36 point integral of f1:= 3.35833333333334E+01 f2:=x*x + 2.0*x*y + 3.0*y*y + 4.0*x + 5.0*y + 6.0 1 point integral of f2:= 1.78357638888889E+02 4 point integral of f2:= 1.82932291666667E+02 9 point integral of f2:= 1.82932291666666E+02 16 point integral of f2:= 1.82932291666666E+02 25 point integral of f2:= 1.82932291666667E+02 36 point integral of f2:= 1.82932291666667E+02 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:= 7.43748842592592E+02 4 point integral of f3:= 8.03093749999999E+02 9 point integral of f3:= 8.03093749999998E+02 16 point integral of f3:= 8.03093749999997E+02 25 point integral of f3:= 8.03093750000000E+02 36 point integral of f3:= 8.03093750000002E+02 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:= 2.69842023533950E+03 4 point integral of f4:= 3.15066421223958E+03 9 point integral of f4:= 3.15281302083333E+03 16 point integral of f4:= 3.15281302083332E+03 25 point integral of f4:= 3.15281302083333E+03 36 point integral of f4:= 3.15281302083334E+03 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:= 8.98854288837447E+03 4 point integral of f5:= 1.16481846901041E+04 9 point integral of f5:= 1.16866044270833E+04 16 point integral of f5:= 1.16866044270833E+04 25 point integral of f5:= 1.16866044270833E+04 36 point integral of f5:= 1.16866044270834E+04 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 of f6:= 2.83564736877357E+04 4 point integral of f6:= 4.17983327551106E+04 9 point integral of f6:= 4.21923159249299E+04 16 point integral of f6:= 4.21932422045508E+04 25 point integral of f6:= 4.21932422045511E+04 36 point integral of f6:= 4.21932422045512E+04 1 point integral over T2 of f6:= 2.83564736877358E+04 4 point integral over T2 of f6:= 4.18235751408529E+04 9 point integral over T2 of f6:= 4.21924535696419E+04 16 point integral over T2 of f6:= 4.21932422045510E+04 25 point integral over T2 of f6:= 4.21932422045511E+04 36 point integral over T2 of f6:= 4.21932422045513E+04 1 point integral over T3 of f6:= 2.83564736877358E+04 4 point integral over T3 of f6:= 4.17384926791016E+04 9 point integral over T3 of f6:= 4.21920442494543E+04 16 point integral over T3 of f6:= 4.21932422045510E+04 25 point integral over T3 of f6:= 4.21932422045511E+04 36 point integral over T3 of f6:= 4.21932422045513E+04 tri_split_test center point used for numerical quadrature Tri_Split returns nntri= 4, nvert= 6 4 triangles, integral over T3 of f6:= 3.84213813389070E+04 Tri_Split returns nntri= 16, nvert= 15 16 triangles, integral over T3 of f6:= 4.12313870742102E+04 Tri_Split returns nntri= 64, nvert= 45 64 triangles, integral over T3 of f6:= 4.19516079880030E+04 Tri_Split returns nntri= 256, nvert= 153 256 triangles, integral over T3 of f6:= 4.21327606574423E+04 Tri_Split returns nntri= 1024, nvert= 561 1024 triangles, integral over T3 of f6:= 4.21781172581998E+04 Tri_Split returns nntri= 4096, nvert= 2145 4096 triangles, integral over T3 of f6:= 4.21894606830287E+04 Tri_Split returns nntri= 16384, nvert= 8385 16384 triangles, integral over T3 of f6:= 4.21922968063626E+04 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.