10-May-2023 16:53:50 sphere_triangle_quad_test(): MATLAB/Octave version 5.2.0 Test sphere_triangle_quad(). TEST01 Approximate an integral on a random spherical triangle. QUAD_01 uses centroids of spherical triangles. QUAD_02 uses vertices of spherical triangles. QUAD_03 uses midsides of spherical triangles. Vertices of random spherical triangle: V1: -0.660748 0.750486 -0.0134808 V2: 0.269576 0.545313 0.793701 V3: 0.944285 0.273317 0.183365 QUAD_01 QUAD_02 QUAD_03 P(X,Y,Z) = 1 0.848012 0.848012 0.848012 P(X,Y,Z) = X 0.243959 0.156349 0.198658 P(X,Y,Z) = Y 0.692083 0.443543 0.634912 P(X,Y,Z) = Z 0.425004 0.272377 0.342709 P(X,Y,Z) = X^2 0.0701831 0.396003 0.171785 P(X,Y,Z) = Y^2 Z^2 0.141872 0.0536915 0.0737185 P(X,Y,Z) = X^2 Y^2 Z^2 0.0117416 0.00449384 0.012443 P(X,Y,Z) = Y^2 Z^4 0.0356353 0.033382 0.0180589 P(X,Y,Z) = Z^6 0.0134385 0.0706789 0.0126585 P(X,Y,Z) = X Y^2 Z^4 0.0102517 0.0090151 0.00101682 P(X,Y,Z) = X^2 Y^4 Z^2 0.00782062 0.00119871 0.00443083 P(X,Y,Z) = X^6 Y^2 0.000320189 0.0282517 0.00671014 P(X,Y,Z) = Z^8 0.00337546 0.0445186 0.00364166 P(X,Y,Z) = X^6 Z^4 3.0329e-05 0.000269605 0.00289103 P(X,Y,Z) = X^4 Y^6 Z^2 0.000431106 2.96282e-05 0.000314795 P(X,Y,Z) = X^2 Y^4 Z^8 0.000123934 0.000286081 8.91408e-05 P(X,Y,Z) = X^16 1.86657e-09 0.113335 0.000739652 TEST02 Approximate an integral on a random spherical triangle. QUAD_MC1 uses a Monte Carlo method with 1000 points. QUAD_MC2 uses a Monte Carlo method with 10000 points. QUAD_MC3 uses a Monte Carlo method with 100000 points. Vertices of random spherical triangle: V1: -0.824372 -0.179426 0.536858 V2: 0.53017 0.736883 0.419432 V3: -0.62227 -0.651271 0.434311 QUAD_MC1 QUAD_MC2 QUAD_MC3 P(X,Y,Z) = 1 0.729032 0.729032 0.729032 P(X,Y,Z) = X -0.231098 -0.231989 -0.232762 P(X,Y,Z) = Y 0.0682027 0.0820155 0.0767847 P(X,Y,Z) = Z 0.591306 0.585119 0.583082 P(X,Y,Z) = X^2 0.150956 0.151736 0.150752 P(X,Y,Z) = Y^2 Z^2 0.057481 0.0557179 0.0558709 P(X,Y,Z) = X^2 Y^2 Z^2 0.00661942 0.00647231 0.00644222 P(X,Y,Z) = Y^2 Z^4 0.0338553 0.0347492 0.0353258 P(X,Y,Z) = Z^6 0.254606 0.259405 0.259227 P(X,Y,Z) = X Y^2 Z^4 -0.00252159 -0.00290138 -0.00290975 P(X,Y,Z) = X^2 Y^4 Z^2 0.00147098 0.00138512 0.00137861 P(X,Y,Z) = X^6 Y^2 0.00195548 0.0021097 0.00212922 P(X,Y,Z) = Z^8 0.202303 0.207236 0.204798 P(X,Y,Z) = X^6 Z^4 0.00487076 0.00509717 0.00504989 P(X,Y,Z) = X^4 Y^6 Z^2 9.53429e-05 9.16966e-05 9.56389e-05 P(X,Y,Z) = X^2 Y^4 Z^8 0.000146131 0.000151474 0.000154804 P(X,Y,Z) = X^16 0.000893608 0.000923185 0.000901365 SPHERE_TRIANGLE_QUAD_TEST03 SPHERE01_TRIANGLE_QUAD_ICOS1C approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a centroid rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: 0.307292 -0.622674 0.719617 V2: 0.645019 -0.761137 -0.0679805 V3: 0.139509 0.228791 -0.963427 FACTOR N RESULT P(X,Y,Z) = 1 1 1 0.078031728 1.92e-12 2 4 0.078031728 1.93e-12 4 16 0.078031728 1.90e-12 8 64 0.078031728 1.90e-12 16 256 0.078031728 1.83e-12 32 1024 0.078031728 1.59e-12 P(X,Y,Z) = X 1 1 0.052600937 6.59e-03 2 4 0.043046332 2.97e-03 4 16 0.04553762 4.75e-04 8 64 0.045957429 5.52e-05 16 256 0.045999913 1.27e-05 32 1024 0.046009602 3.03e-06 P(X,Y,Z) = Y 1 1 -0.05564579 1.17e-02 2 4 -0.042471786 1.44e-03 4 16 -0.043844467 6.50e-05 8 64 -0.043952984 4.35e-05 16 256 -0.043921404 1.19e-05 32 1024 -0.043912338 2.87e-06 P(X,Y,Z) = Z 1 1 -0.015021254 7.62e-03 2 4 -0.019186856 3.46e-03 4 16 -0.021843943 8.00e-04 8 64 -0.022474673 1.70e-04 16 256 -0.022602386 4.19e-05 32 1024 -0.02263425 1.00e-05 P(X,Y,Z) = X^2 1 1 0.035458122 7.50e-03 2 4 0.024701824 3.26e-03 4 16 0.027336422 6.23e-04 8 64 0.027889175 7.00e-05 16 256 0.027943536 1.57e-05 32 1024 0.027955482 3.73e-06 P(X,Y,Z) = Y^2 Z^2 1 1 0.0014704943 2.24e-03 2 4 0.0030099255 6.98e-04 4 16 0.0035107729 1.97e-04 8 64 0.0036965693 1.13e-05 16 256 0.0037069423 9.41e-07 32 1024 0.003707653 2.31e-07 P(X,Y,Z) = X^2 Y^2 Z^2 1 1 0.00066820214 6.02e-04 2 4 0.00083020585 4.40e-04 4 16 0.0011496326 1.21e-04 8 64 0.0012583947 1.19e-05 16 256 0.0012691265 1.14e-06 32 1024 0.0012699922 2.72e-07 P(X,Y,Z) = Y^2 Z^4 1 1 5.449207e-05 1.08e-03 2 4 0.0007213668 4.10e-04 4 16 0.0011105869 2.06e-05 8 64 0.0011379272 6.77e-06 16 256 0.001130554 6.08e-07 32 1024 0.0011310106 1.51e-07 P(X,Y,Z) = Z^6 1 1 3.9708281e-06 7.93e-03 2 4 0.01265765 4.73e-03 4 16 0.0084444552 5.12e-04 8 64 0.0079472649 1.49e-05 16 256 0.0079380919 5.75e-06 32 1024 0.0079337158 1.37e-06 P(X,Y,Z) = X Y^2 Z^4 1 1 3.6732929e-05 5.88e-04 2 4 0.00034088044 2.83e-04 4 16 0.00058899618 3.53e-05 8 64 0.00062853664 4.23e-06 16 256 0.0006238943 4.08e-07 32 1024 0.00062420021 1.02e-07 P(X,Y,Z) = X^2 Y^4 Z^2 1 1 0.00033980521 1.03e-04 2 4 0.00041575521 2.67e-05 4 16 0.00041811006 2.44e-05 8 64 0.00043665919 5.83e-06 16 256 0.00044242385 6.82e-08 32 1024 0.00044247806 1.40e-08 P(X,Y,Z) = X^6 Y^2 1 1 0.0037232905 1.82e-03 2 4 0.0018090875 9.65e-05 4 16 0.0018444903 6.11e-05 8 64 0.0018987033 6.93e-06 16 256 0.0019040162 1.61e-06 32 1024 0.0019052469 3.82e-07 P(X,Y,Z) = Z^8 1 1 1.4714687e-07 5.90e-03 2 4 0.010077683 4.18e-03 4 16 0.0061427215 2.41e-04 8 64 0.005908618 7.08e-06 16 256 0.0059070261 5.49e-06 32 1024 0.005902843 1.31e-06 P(X,Y,Z) = X^6 Z^4 1 1 1.0054134e-05 2.25e-04 2 4 0.0001039614 1.31e-04 4 16 0.0002277773 7.54e-06 8 64 0.00023694485 1.62e-06 16 256 0.00023490447 4.15e-07 32 1024 0.00023521702 1.03e-07 P(X,Y,Z) = X^4 Y^6 Z^2 1 1 7.8522971e-05 1.14e-05 2 4 6.8494848e-05 1.40e-06 4 16 6.9573129e-05 2.48e-06 8 64 6.5980274e-05 1.11e-06 16 256 6.708342e-05 8.81e-09 32 1024 6.7090763e-05 1.46e-09 P(X,Y,Z) = X^2 Y^4 Z^8 1 1 1.7291788e-08 1.05e-05 2 4 3.0026581e-06 7.47e-06 4 16 9.6826768e-06 7.90e-07 8 64 1.0826099e-05 3.54e-07 16 256 1.0464403e-05 8.17e-09 32 1024 1.0470849e-05 1.73e-09 P(X,Y,Z) = X^16 1 1 0.00014184933 7.49e-05 2 4 5.9049255e-05 7.94e-06 4 16 5.9999759e-05 6.99e-06 8 64 6.5535063e-05 1.46e-06 16 256 6.675507e-05 2.38e-07 32 1024 6.6936644e-05 5.69e-08 SPHERE_TRIANGLE_QUAD_TEST04 SPHERE01_TRIANGLE_QUAD_ICOS1M approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a midpoint rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: -0.405312 -0.586356 -0.701362 V2: -0.377025 -0.915019 -0.143504 V3: 0.312825 -0.212553 -0.925722 FACTOR N RESULT P(X,Y,Z) = 1 1 3 0.26813503 1.91e-12 2 12 0.26813503 1.91e-12 4 48 0.26813503 1.90e-12 8 192 0.26813503 1.90e-12 16 768 0.26813503 1.88e-12 32 3072 0.26813503 1.80e-12 P(X,Y,Z) = X 1 3 -0.045200107 1.43e-03 2 12 -0.04480523 1.03e-03 4 48 -0.044023767 2.50e-04 8 192 -0.043836586 6.26e-05 16 768 -0.04378948 1.55e-05 32 3072 -0.043777682 3.69e-06 P(X,Y,Z) = Y 1 3 -0.17506427 1.54e-04 2 12 -0.17436994 8.49e-04 4 48 -0.17500371 2.15e-04 8 192 -0.17516426 5.44e-05 16 768 -0.17520518 1.35e-05 32 3072 -0.17521546 3.22e-06 P(X,Y,Z) = Z 1 3 -0.18148194 6.16e-04 2 12 -0.18108631 1.01e-03 4 48 -0.18185479 2.43e-04 8 192 -0.18203681 6.12e-05 16 768 -0.18208286 1.52e-05 32 3072 -0.18209441 3.61e-06 P(X,Y,Z) = X^2 1 3 0.015664969 4.45e-04 2 12 0.016286936 1.07e-03 4 48 0.015472003 2.52e-04 8 192 0.01528354 6.32e-05 16 768 0.015236011 1.56e-05 32 3072 0.0152241 3.72e-06 P(X,Y,Z) = Y^2 Z^2 1 3 0.047343564 7.67e-04 2 12 0.04655688 1.55e-03 4 48 0.047767918 3.42e-04 8 192 0.048024219 8.59e-05 16 768 0.048088821 2.13e-05 32 3072 0.048105012 5.06e-06 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.0019923522 3.99e-04 2 12 0.0025259487 1.35e-04 4 48 0.0024072996 1.63e-05 8 192 0.0023949963 3.95e-06 16 768 0.0023920162 9.74e-07 32 3072 0.0023912742 2.32e-07 P(X,Y,Z) = Y^2 Z^4 1 3 0.02391729 5.64e-04 2 12 0.023676462 8.05e-04 4 48 0.024307101 1.74e-04 8 192 0.024437421 4.37e-05 16 768 0.024470284 1.08e-05 32 3072 0.024478524 2.58e-06 P(X,Y,Z) = Z^6 1 3 0.056537387 4.89e-03 2 12 0.052909161 1.26e-03 4 48 0.051967397 3.23e-04 8 192 0.051726228 8.14e-05 16 768 0.051665039 2.02e-05 32 3072 0.051649682 4.80e-06 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.0019282567 8.53e-04 2 12 -0.0027324311 4.93e-05 4 48 -0.0027653783 1.63e-05 8 192 -0.0027775141 4.18e-06 16 768 -0.0027806498 1.04e-06 32 3072 -0.0027814422 2.48e-07 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.0012347936 1.52e-06 2 12 0.0012904852 5.42e-05 4 48 0.0012455651 9.25e-06 8 192 0.001238604 2.29e-06 16 768 0.0012368826 5.64e-07 32 3072 0.0012364528 1.34e-07 P(X,Y,Z) = X^6 Y^2 1 3 0.00028122503 1.73e-04 2 12 0.00013326754 2.49e-05 4 48 0.00011372747 5.36e-06 8 192 0.00010969581 1.33e-06 16 768 0.00010869315 3.28e-07 32 3072 0.00010844292 7.82e-08 P(X,Y,Z) = Z^8 1 3 0.04188449 5.89e-03 2 12 0.037469092 1.47e-03 4 48 0.036369533 3.75e-04 8 192 0.036089141 9.45e-05 16 768 0.036018039 2.34e-05 32 3072 0.036000196 5.58e-06 P(X,Y,Z) = X^6 Z^4 1 3 1.775716e-05 2.06e-06 2 12 1.8427101e-05 1.39e-06 4 48 2.0199507e-05 3.83e-07 8 192 1.9932336e-05 1.16e-07 16 768 1.984662e-05 2.98e-08 32 3072 1.9823962e-05 7.18e-09 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.0001300495 5.95e-05 2 12 7.1804067e-05 1.21e-06 4 48 7.2198101e-05 1.61e-06 8 192 7.0991957e-05 4.02e-07 16 768 7.0689755e-05 9.97e-08 32 3072 7.0613819e-05 2.38e-08 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 1.530894e-05 6.42e-05 2 12 8.9112323e-05 9.56e-06 4 48 7.946527e-05 8.96e-08 8 192 7.9504331e-05 5.05e-08 16 768 7.9542188e-05 1.27e-08 32 3072 7.9551843e-05 3.03e-09 P(X,Y,Z) = X^16 1 3 6.5236843e-08 5.50e-08 2 12 2.4427254e-08 1.42e-08 4 48 1.2750553e-08 2.54e-09 8 192 1.0591492e-08 3.78e-10 16 768 1.0288324e-08 7.50e-11 32 3072 1.0230047e-08 1.67e-11 SPHERE_TRIANGLE_QUAD_TEST05 SPHERE01_TRIANGLE_QUAD_ICOS1V approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a vertex rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: -0.546508 -0.235498 0.803661 V2: 0.397715 0.585803 -0.706157 V3: 0.497766 -0.846835 -0.187346 FACTOR N RESULT P(X,Y,Z) = 1 1 3 5.9464833 2.26e-12 2 12 5.9464833 2.25e-12 4 48 5.9464833 2.26e-12 8 192 5.9464833 2.24e-12 16 768 5.9464833 2.21e-12 32 3072 5.9464833 2.07e-12 P(X,Y,Z) = X 1 3 0.69172119 1.64e+00 2 12 0.50458461 1.83e+00 4 48 0.28667234 2.05e+00 8 192 1.0042735 1.33e+00 16 768 1.3037816 1.03e+00 32 3072 1.907517 4.29e-01 P(X,Y,Z) = Y 1 3 -0.98420338 1.72e+00 2 12 -0.29256824 1.03e+00 4 48 0.38598089 3.54e-01 8 192 -0.085773165 8.25e-01 16 768 0.52123861 2.18e-01 32 3072 0.54997008 1.90e-01 P(X,Y,Z) = Z 1 3 -0.17808359 2.04e+00 2 12 0.1192643 1.74e+00 4 48 0.37661717 1.49e+00 8 192 0.47617321 1.39e+00 16 768 1.0633654 7.99e-01 32 3072 1.4931278 3.69e-01 P(X,Y,Z) = X^2 1 3 1.396668 6.05e-01 2 12 1.2389281 7.63e-01 4 48 1.287861 7.14e-01 8 192 1.5640247 4.37e-01 16 768 1.3390835 6.62e-01 32 3072 1.7863371 2.15e-01 P(X,Y,Z) = Y^2 Z^2 1 3 0.46008254 6.44e-02 2 12 0.50116513 1.05e-01 4 48 0.55969024 1.64e-01 8 192 0.35499462 4.07e-02 16 768 0.63737408 2.42e-01 32 3072 0.33008887 6.56e-02 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.087219521 3.22e-02 2 12 0.034683515 2.03e-02 4 48 0.034583576 2.04e-02 8 192 0.058525489 3.56e-03 16 768 0.02486128 3.01e-02 32 3072 0.043293897 1.17e-02 P(X,Y,Z) = Y^2 Z^4 1 3 0.21674825 4.31e-02 2 12 0.11693743 5.67e-02 4 48 0.22379616 5.01e-02 8 192 0.11002397 6.37e-02 16 768 0.27069532 9.70e-02 32 3072 0.11982506 5.39e-02 P(X,Y,Z) = Z^6 1 3 0.77990768 1.17e-01 2 12 0.26252365 6.35e-01 4 48 0.50393879 3.93e-01 8 192 0.90508458 7.84e-03 16 768 0.55756125 3.40e-01 32 3072 1.3479046 4.51e-01 P(X,Y,Z) = X Y^2 Z^4 1 3 0.043080302 2.76e-02 2 12 0.0079671941 7.50e-03 4 48 -0.037936832 5.34e-02 8 192 0.031770586 1.63e-02 16 768 0.010957329 4.51e-03 32 3072 -0.0012854444 1.68e-02 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.028452548 9.97e-03 2 12 0.01276203 5.72e-03 4 48 0.019373856 8.92e-04 8 192 0.02985304 1.14e-02 16 768 0.0084498928 1.00e-02 32 3072 0.016287011 2.20e-03 P(X,Y,Z) = X^6 Y^2 1 3 0.027242431 7.09e-02 2 12 0.013619382 8.46e-02 4 48 0.0075054096 9.07e-02 8 192 0.077871695 2.03e-02 16 768 0.023315413 7.49e-02 32 3072 0.15227281 5.41e-02 P(X,Y,Z) = Z^8 1 3 0.46748493 2.40e-01 2 12 0.1217281 5.85e-01 4 48 0.25608378 4.51e-01 8 192 0.66042703 4.68e-02 16 768 0.33693341 3.70e-01 32 3072 1.2325423 5.25e-01 P(X,Y,Z) = X^6 Z^4 1 3 0.024017401 5.58e-04 2 12 0.049603676 2.50e-02 4 48 0.054919192 3.03e-02 8 192 0.018278003 6.30e-03 16 768 0.047827448 2.33e-02 32 3072 0.015362337 9.21e-03 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.0025940339 6.19e-04 2 12 0.0013074915 6.68e-04 4 48 0.0014435017 5.32e-04 8 192 0.0029895574 1.01e-03 16 768 0.0007518796 1.22e-03 32 3072 0.0023797465 4.05e-04 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.002600204 1.72e-03 2 12 0.00016418557 7.18e-04 4 48 0.00087290564 9.03e-06 8 192 0.0008322734 4.97e-05 16 768 0.00042372713 4.58e-04 32 3072 0.00040702018 4.75e-04 P(X,Y,Z) = X^16 1 3 0.00015444127 3.68e-01 2 12 0.0054765754 3.63e-01 4 48 0.0042170679 3.64e-01 8 192 0.002070555 3.66e-01 16 768 0.056530573 3.12e-01 32 3072 0.15056687 2.18e-01 SPHERE_TRIANGLE_QUAD_TEST06 SPHERE01_TRIANGLE_QUAD_ICOS2V approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a vertex rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: -0.0604511 0.670395 -0.739538 V2: -0.860871 0.432544 0.267969 V3: 0.704563 0.336554 0.624759 FACTOR N RESULT P(X,Y,Z) = 1 1 3 2.0261804 3.15e-12 2 12 2.0261804 3.15e-12 4 48 2.0261804 3.15e-12 8 192 2.0261804 3.13e-12 16 768 2.0261804 3.09e-12 32 3072 2.0261804 2.95e-12 P(X,Y,Z) = X 1 3 -0.14639768 3.80e-02 2 12 -0.092536271 1.59e-02 4 48 -0.10414628 4.27e-03 8 192 -0.10733694 1.08e-03 16 768 -0.10814707 2.67e-04 32 3072 -0.10835022 6.35e-05 P(X,Y,Z) = Y 1 3 0.97222425 6.75e-01 2 12 1.3842413 2.63e-01 4 48 1.5792089 6.79e-02 8 192 1.630126 1.70e-02 16 768 1.6429035 4.20e-03 32 3072 1.6461025 1.00e-03 P(X,Y,Z) = Z 1 3 0.10346366 1.88e-01 2 12 0.24377674 4.77e-02 4 48 0.27599725 1.55e-02 8 192 0.28748055 4.02e-03 16 768 0.29050163 1.00e-03 32 3072 0.29126546 2.39e-04 P(X,Y,Z) = X^2 1 3 0.83827186 5.09e-01 2 12 0.5321817 2.03e-01 4 48 0.37350603 4.43e-02 8 192 0.33994021 1.07e-02 16 768 0.33183416 2.64e-03 32 3072 0.32982509 6.26e-04 P(X,Y,Z) = Y^2 Z^2 1 3 0.20494568 2.33e-02 2 12 0.19961306 1.80e-02 4 48 0.16859581 1.30e-02 8 192 0.17846221 3.15e-03 16 768 0.18084369 7.69e-04 32 3072 0.18143022 1.83e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.022153967 3.61e-03 2 12 0.018030425 5.14e-04 4 48 0.018553023 8.68e-06 8 192 0.018473222 7.11e-05 16 768 0.018523862 2.05e-05 32 3072 0.018539292 5.06e-06 P(X,Y,Z) = Y^2 Z^4 1 3 0.10310116 5.25e-02 2 12 0.095638673 4.50e-02 4 48 0.058356448 7.72e-03 8 192 0.051768538 1.13e-03 16 768 0.050907734 2.69e-04 32 3072 0.050702605 6.35e-05 P(X,Y,Z) = Z^6 1 3 0.15090227 1.13e-01 2 12 0.12936271 9.11e-02 4 48 0.075434235 3.72e-02 8 192 0.04825097 1.00e-02 16 768 0.040726582 2.48e-03 32 3072 0.038835086 5.92e-04 P(X,Y,Z) = X Y^2 Z^4 1 3 0.0021621751 5.79e-04 2 12 -0.010356784 1.19e-02 4 48 -0.0012729898 2.86e-03 8 192 0.00090961211 6.73e-04 16 768 0.0014190946 1.64e-04 32 3072 0.0015439554 3.89e-05 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.0032097271 6.29e-03 2 12 0.0075823157 1.92e-03 4 48 0.0084526621 1.05e-03 8 192 0.0092841276 2.18e-04 16 768 0.0094487211 5.38e-05 32 3072 0.0094896898 1.28e-05 P(X,Y,Z) = X^6 Y^2 1 3 0.06079136 4.12e-02 2 12 0.034978309 1.54e-02 4 48 0.026351309 6.79e-03 8 192 0.021061424 1.50e-03 16 768 0.019923032 3.63e-04 32 3072 0.019645938 8.60e-05 P(X,Y,Z) = Z^8 1 3 0.076122741 5.98e-02 2 12 0.070706283 5.44e-02 4 48 0.040694681 2.44e-02 8 192 0.023551673 7.23e-03 16 768 0.018141442 1.82e-03 32 3072 0.016758143 4.34e-04 P(X,Y,Z) = X^6 Z^4 1 3 0.014004534 1.30e-02 2 12 0.0035257108 2.54e-03 4 48 0.0014023672 4.22e-04 8 192 0.0010748532 9.41e-05 16 768 0.0010033819 2.26e-05 32 3072 0.00098609925 5.35e-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.0002692965 7.71e-04 2 12 0.0012403154 2.00e-04 4 48 0.00090521204 1.35e-04 8 192 0.0010152096 2.47e-05 16 768 0.00103374 6.21e-06 32 3072 0.0010384611 1.48e-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.00014491101 6.26e-05 2 12 0.00020604935 1.44e-06 4 48 0.00033584285 1.28e-04 8 192 0.00022798299 2.05e-05 16 768 0.00021213793 4.65e-06 32 3072 0.00020858408 1.09e-06 P(X,Y,Z) = X^16 1 3 0.063946119 6.17e-02 2 12 0.012249975 1.00e-02 4 48 0.0054925257 3.26e-03 8 192 0.0033257947 1.09e-03 16 768 0.0025222194 2.88e-04 32 3072 0.002303655 6.97e-05 sphere_triangle_quad_test(): Normal end of execution. 10-May-2023 17:21:41