sphere_triangle_quad_test 27-Mar-2019 10:26:55 sphere_triangle_quad_test MATLAB version 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: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.28431 0.659018 V3: 0.901719 0.397757 -0.169386 QUAD_01 QUAD_02 QUAD_03 P(X,Y,Z) = 1 3.06905 3.06905 3.06905 P(X,Y,Z) = X 3.04241 1.02385 1.51463 P(X,Y,Z) = Y -0.33597 -0.113063 -0.677827 P(X,Y,Z) = Z -0.223529 -0.0752233 0.705114 P(X,Y,Z) = X^2 3.016 1.97509 1.03742 P(X,Y,Z) = Y^2 Z^2 0.000195098 0.0568326 0.0692846 P(X,Y,Z) = X^2 Y^2 Z^2 0.000191725 0.031486 0.00748156 P(X,Y,Z) = Y^2 Z^4 1.03493e-06 0.0208925 0.0308005 P(X,Y,Z) = Z^6 4.58117e-07 0.116464 0.554106 P(X,Y,Z) = X Y^2 Z^4 1.02594e-06 -0.00663518 0.0115693 P(X,Y,Z) = X^2 Y^4 Z^2 2.29758e-06 0.00252144 0.00127823 P(X,Y,Z) = X^6 Y^2 0.0349039 0.109428 0.00540225 P(X,Y,Z) = Z^8 2.43015e-09 0.046748 0.44805 P(X,Y,Z) = X^6 Z^4 8.19592e-05 0.0485087 0.0164461 P(X,Y,Z) = X^4 Y^6 Z^2 2.70575e-08 0.000148405 3.58269e-05 P(X,Y,Z) = X^2 Y^4 Z^8 3.42959e-13 0.000131797 0.000122125 P(X,Y,Z) = X^16 2.6694 0.224836 0.243061 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: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.28431 0.659018 V3: 0.901719 0.397757 -0.169386 QUAD_MC1 QUAD_MC2 QUAD_MC3 P(X,Y,Z) = 1 3.06905 3.06905 3.06905 P(X,Y,Z) = X 1.49039 1.45444 1.45637 P(X,Y,Z) = Y -1.07421 -1.0461 -1.0444 P(X,Y,Z) = Z 1.26596 1.3098 1.32544 P(X,Y,Z) = X^2 1.2901 1.27525 1.27829 P(X,Y,Z) = Y^2 Z^2 0.19287 0.17703 0.182439 P(X,Y,Z) = X^2 Y^2 Z^2 0.0247888 0.0252832 0.0248802 P(X,Y,Z) = Y^2 Z^4 0.0837552 0.0861373 0.0851929 P(X,Y,Z) = Z^6 0.531964 0.479835 0.482496 P(X,Y,Z) = X Y^2 Z^4 0.00442363 0.00506373 0.00505596 P(X,Y,Z) = X^2 Y^4 Z^2 0.0066843 0.00717428 0.00725439 P(X,Y,Z) = X^6 Y^2 0.055871 0.0555553 0.0568885 P(X,Y,Z) = Z^8 0.37485 0.374319 0.377645 P(X,Y,Z) = X^6 Z^4 0.0158417 0.0150701 0.0150134 P(X,Y,Z) = X^4 Y^6 Z^2 0.000639512 0.000723393 0.000713386 P(X,Y,Z) = X^2 Y^4 Z^8 0.000443024 0.000452401 0.000453963 P(X,Y,Z) = X^16 0.379094 0.335969 0.339363 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: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.28431 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 1 3.0690548 2.05e-12 2 4 3.0690548 2.05e-12 4 16 3.0690548 2.05e-12 8 64 3.0690548 2.03e-12 16 256 3.0690548 2.01e-12 32 1024 3.0690548 1.91e-12 P(X,Y,Z) = X 1 1 3.0424097 1.58e+00 2 4 1.4580608 7.06e-03 4 16 1.4909482 2.58e-02 8 64 1.4715879 6.47e-03 16 256 1.4633045 1.81e-03 32 1024 1.4646303 4.88e-04 P(X,Y,Z) = Y 1 1 -0.33596979 7.12e-01 2 4 -0.57944949 4.69e-01 4 16 -0.87749071 1.70e-01 8 64 -1.0211533 2.68e-02 16 256 -1.0437687 4.19e-03 32 1024 -1.0469543 1.00e-03 P(X,Y,Z) = Z 1 1 -0.2235287 1.54e+00 2 4 0.59222577 7.26e-01 4 16 1.0353422 2.83e-01 8 64 1.2736668 4.43e-02 16 256 1.3118673 6.12e-03 32 1024 1.3165379 1.45e-03 P(X,Y,Z) = X^2 1 1 3.0159959 1.73e+00 2 4 2.111525 8.30e-01 4 16 1.6276516 3.46e-01 8 64 1.3482269 6.65e-02 16 256 1.2877188 5.95e-03 32 1024 1.2831055 1.34e-03 P(X,Y,Z) = Y^2 Z^2 1 1 0.00019509813 1.82e-01 2 4 0.1117365 7.03e-02 4 16 0.13602353 4.60e-02 8 64 0.17083063 1.12e-02 16 256 0.18130698 7.58e-04 32 1024 0.1819642 1.01e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 1 0.00019172521 2.48e-02 2 4 0.024531813 4.12e-04 4 16 0.014437995 1.05e-02 8 64 0.021325852 3.62e-03 16 256 0.024844968 9.86e-05 32 1024 0.02488741 5.62e-05 P(X,Y,Z) = Y^2 Z^4 1 1 1.0349286e-06 8.52e-02 2 4 0.069416427 1.58e-02 4 16 0.065374258 1.99e-02 8 64 0.083372516 1.86e-03 16 256 0.08506338 1.72e-04 32 1024 0.085240746 4.93e-06 P(X,Y,Z) = Z^6 1 1 4.5811711e-07 4.81e-01 2 4 0.27142163 2.10e-01 4 16 0.44202683 3.92e-02 8 64 0.47344443 7.80e-03 16 256 0.48108927 1.56e-04 32 1024 0.48137563 1.30e-04 P(X,Y,Z) = X Y^2 Z^4 1 1 1.0259435e-06 5.06e-03 2 4 -0.03097895 3.60e-02 4 16 -0.016349055 2.14e-02 8 64 -0.0026907206 7.75e-03 16 256 0.0042501142 8.11e-04 32 1024 0.0049464238 1.15e-04 P(X,Y,Z) = X^2 Y^4 Z^2 1 1 2.2975787e-06 7.26e-03 2 4 0.00373937 3.52e-03 4 16 0.0044025568 2.86e-03 8 64 0.0054554699 1.81e-03 16 256 0.0071749539 8.84e-05 32 1024 0.0072419156 2.15e-05 P(X,Y,Z) = X^6 Y^2 1 1 0.034903913 2.21e-02 2 4 0.036376861 2.07e-02 4 16 0.08634931 2.93e-02 8 64 0.062460997 5.43e-03 16 256 0.056921836 1.11e-04 32 1024 0.057113046 8.05e-05 P(X,Y,Z) = Z^8 1 1 2.4301541e-09 3.80e-01 2 4 0.17056594 2.09e-01 4 16 0.38192803 2.05e-03 8 64 0.38658868 6.71e-03 16 256 0.3807194 8.37e-04 32 1024 0.38009166 2.09e-04 P(X,Y,Z) = X^6 Z^4 1 1 8.1959164e-05 1.49e-02 2 4 0.0082961901 6.64e-03 4 16 0.015349878 4.17e-04 8 64 0.018722066 3.79e-03 16 256 0.015052578 1.20e-04 32 1024 0.014907323 2.52e-05 P(X,Y,Z) = X^4 Y^6 Z^2 1 1 2.7057501e-08 7.06e-04 2 4 0.00012572515 5.81e-04 4 16 0.00025652759 4.50e-04 8 64 0.00070544929 1.02e-06 16 256 0.00076287761 5.64e-05 32 1024 0.00070378115 2.69e-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 1 3.4295905e-13 4.56e-04 2 4 0.00092039795 4.64e-04 4 16 0.00037315648 8.29e-05 8 64 0.00024128599 2.15e-04 16 256 0.00041495547 4.11e-05 32 1024 0.00045543599 6.08e-07 P(X,Y,Z) = X^16 1 1 2.6693986 2.33e+00 2 4 1.4495431 1.11e+00 4 16 0.48851698 1.49e-01 8 64 0.33008811 9.89e-03 16 256 0.3468983 6.92e-03 32 1024 0.34127742 1.30e-03 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: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.28431 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 3 3.0690548 2.06e-12 2 12 3.0690548 2.05e-12 4 48 3.0690548 2.05e-12 8 192 3.0690548 2.05e-12 16 768 3.0690548 2.03e-12 32 3072 3.0690548 1.94e-12 P(X,Y,Z) = X 1 3 1.5146333 4.96e-02 2 12 1.3391288 1.26e-01 4 48 1.4161789 4.89e-02 8 192 1.4488356 1.62e-02 16 768 1.4577767 7.25e-03 32 3072 1.4632315 1.80e-03 P(X,Y,Z) = Y 1 3 -0.67782654 3.70e-01 2 12 -0.69417318 3.54e-01 4 48 -0.86528596 1.83e-01 8 192 -1.0080416 3.98e-02 16 768 -1.0396664 8.23e-03 32 3072 -1.0459044 1.99e-03 P(X,Y,Z) = Z 1 3 0.7051138 6.13e-01 2 12 0.81458139 5.03e-01 4 48 1.0349595 2.83e-01 8 192 1.2585004 5.94e-02 16 768 1.3067144 1.12e-02 32 3072 1.3152153 2.69e-03 P(X,Y,Z) = X^2 1 3 1.0374204 2.44e-01 2 12 1.6738428 3.92e-01 4 48 1.5465109 2.65e-01 8 192 1.3502163 6.84e-02 16 768 1.2911961 9.37e-03 32 3072 1.284031 2.21e-03 P(X,Y,Z) = Y^2 Z^2 1 3 0.069284636 1.13e-01 2 12 0.1832839 1.22e-03 4 48 0.14519673 3.69e-02 8 192 0.17212931 9.93e-03 16 768 0.1810487 1.01e-03 32 3072 0.18188145 1.78e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.0074815556 1.75e-02 2 12 0.04013851 1.52e-02 4 48 0.022979464 1.96e-03 8 192 0.021748208 3.19e-03 16 768 0.024642828 2.98e-04 32 3072 0.024838585 1.02e-04 P(X,Y,Z) = Y^2 Z^4 1 3 0.030800538 5.44e-02 2 12 0.098762668 1.35e-02 4 48 0.05789829 2.73e-02 8 192 0.083586236 1.65e-03 16 768 0.085149295 8.78e-05 32 3072 0.085258738 2.16e-05 P(X,Y,Z) = Z^6 1 3 0.55410577 7.28e-02 2 12 0.30254841 1.79e-01 4 48 0.4492374 3.20e-02 8 192 0.4775641 3.70e-03 16 768 0.48244476 1.18e-03 32 3072 0.48171451 4.47e-04 P(X,Y,Z) = X Y^2 Z^4 1 3 0.011569346 6.51e-03 2 12 0.018816669 1.38e-02 4 48 -0.011699406 1.68e-02 8 192 -0.0016460618 6.70e-03 16 768 0.0039374641 1.12e-03 32 3072 0.0048384069 2.16e-04 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.0012782343 5.98e-03 2 12 0.0089719313 1.71e-03 4 48 0.0083042444 1.04e-03 8 192 0.0058443121 1.42e-03 16 768 0.0071187318 1.44e-04 32 3072 0.007224953 3.73e-05 P(X,Y,Z) = X^6 Y^2 1 3 0.0054022453 5.16e-02 2 12 0.041621761 1.54e-02 4 48 0.070345381 1.33e-02 8 192 0.062562909 5.53e-03 16 768 0.057214615 1.79e-04 32 3072 0.057160413 1.25e-04 P(X,Y,Z) = Z^8 1 3 0.44804993 6.81e-02 2 12 0.17963896 2.00e-01 4 48 0.35779942 2.21e-02 8 192 0.38604801 6.14e-03 16 768 0.38214345 2.23e-03 32 3072 0.38050427 5.95e-04 P(X,Y,Z) = X^6 Z^4 1 3 0.016446099 1.52e-03 2 12 0.015182542 2.52e-04 4 48 0.0071815261 7.75e-03 8 192 0.016523417 1.59e-03 16 768 0.014864535 6.58e-05 32 3072 0.014874167 5.62e-05 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 3.5826866e-05 6.71e-04 2 12 0.00051708151 1.89e-04 4 48 0.00065595034 5.04e-05 8 192 0.00050819874 1.98e-04 16 768 0.00073429503 2.80e-05 32 3072 0.00070163764 4.69e-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.0001221252 3.34e-04 2 12 0.0013094135 8.53e-04 4 48 0.00047634334 2.03e-05 8 192 0.00037603274 8.00e-05 16 768 0.00042676231 2.93e-05 32 3072 0.00045514102 8.80e-07 P(X,Y,Z) = X^16 1 3 0.24306136 9.70e-02 2 12 0.65894922 3.19e-01 4 48 0.6030299 2.63e-01 8 192 0.35542325 1.54e-02 16 768 0.35140892 1.14e-02 32 3072 0.34256519 2.51e-03 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: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.28431 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 3 3.0690548 2.06e-12 2 12 3.0690548 2.05e-12 4 48 3.0690548 2.05e-12 8 192 3.0690548 2.05e-12 16 768 3.0690548 2.03e-12 32 3072 3.0690548 1.94e-12 P(X,Y,Z) = X 1 3 1.0238514 4.41e-01 2 12 1.0316791 4.33e-01 4 48 1.2416257 2.23e-01 8 192 1.3779194 8.68e-02 16 768 1.4414767 2.33e-02 32 3072 1.4590637 5.70e-03 P(X,Y,Z) = Y 1 3 -0.11306273 9.35e-01 2 12 -0.74007307 3.08e-01 4 48 -0.89914013 1.49e-01 8 192 -0.98000267 6.77e-02 16 768 -1.0276643 2.00e-02 32 3072 -1.0427748 4.92e-03 P(X,Y,Z) = Z 1 3 -0.075223326 1.39e+00 2 12 0.93275388 3.85e-01 4 48 1.138119 1.80e-01 8 192 1.2318404 8.58e-02 16 768 1.2916667 2.60e-02 32 3072 1.3112717 6.38e-03 P(X,Y,Z) = X^2 1 3 1.9750865 6.93e-01 2 12 1.0140237 2.68e-01 4 48 1.217848 6.42e-02 8 192 1.3130626 3.11e-02 16 768 1.3009017 1.89e-02 32 3072 1.2867816 4.78e-03 P(X,Y,Z) = Y^2 Z^2 1 3 0.056832555 1.25e-01 2 12 0.077617823 1.04e-01 4 48 0.1871919 5.15e-03 8 192 0.18239532 3.51e-04 16 768 0.18059807 1.45e-03 32 3072 0.18163024 4.14e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.031486035 6.56e-03 2 12 0.013749622 1.12e-02 4 48 0.03523278 1.03e-02 8 192 0.028108426 3.18e-03 16 768 0.023967181 9.64e-04 32 3072 0.024698249 2.33e-04 P(X,Y,Z) = Y^2 Z^4 1 3 0.02089246 6.43e-02 2 12 0.034135797 5.11e-02 4 48 0.09983903 1.46e-02 8 192 0.082640672 2.60e-03 16 768 0.085485105 2.44e-04 32 3072 0.085305479 6.45e-05 P(X,Y,Z) = Z^6 1 3 0.11646444 3.65e-01 2 12 0.54057498 5.92e-02 4 48 0.45127201 3.01e-02 8 192 0.4889184 7.59e-03 16 768 0.48667765 5.34e-03 32 3072 0.48269293 1.36e-03 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.0066351753 1.17e-02 2 12 0.0071491014 2.12e-03 4 48 0.026892267 2.19e-02 8 192 0.0066302221 1.60e-03 16 768 0.0035026674 1.53e-03 32 3072 0.0045188583 5.15e-04 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.0025214372 4.74e-03 2 12 0.001753472 5.51e-03 4 48 0.0080878156 8.29e-04 8 192 0.0091883223 1.93e-03 16 768 0.0069903895 2.69e-04 32 3072 0.0071760843 8.29e-05 P(X,Y,Z) = X^6 Y^2 1 3 0.10942767 5.24e-02 2 12 0.014609328 4.24e-02 4 48 0.029853754 2.72e-02 8 192 0.054462428 2.58e-03 16 768 0.058619457 1.57e-03 32 3072 0.057295087 2.50e-04 P(X,Y,Z) = Z^8 1 3 0.046748006 3.33e-01 2 12 0.42558335 4.56e-02 4 48 0.31203149 6.80e-02 8 192 0.37173242 8.26e-03 16 768 0.38557764 5.59e-03 32 3072 0.38169887 1.71e-03 P(X,Y,Z) = X^6 Z^4 1 3 0.048508696 3.36e-02 2 12 0.021026762 6.10e-03 4 48 0.010823045 4.10e-03 8 192 0.0067314157 8.19e-03 16 768 0.014047509 8.76e-04 32 3072 0.014777712 1.46e-04 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.00014840502 5.58e-04 2 12 5.9483385e-05 6.46e-04 4 48 0.00042602231 2.80e-04 8 192 0.0006211242 8.48e-05 16 768 0.00054976815 1.56e-04 32 3072 0.00069545584 1.05e-05 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.0001317969 3.24e-04 2 12 0.00015380922 3.02e-04 4 48 0.001232508 7.77e-04 8 192 0.00084853036 3.93e-04 16 768 0.00051863904 6.27e-05 32 3072 0.00045454955 1.40e-06 P(X,Y,Z) = X^16 1 3 0.22483589 1.15e-01 2 12 0.17674348 1.64e-01 4 48 0.4327635 9.25e-02 8 192 0.48863952 1.48e-01 16 768 0.36219129 2.19e-02 32 3072 0.34639491 6.09e-03 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: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.28431 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 3 3.0690548 8.91e-13 2 12 3.0690548 8.92e-13 4 48 3.0690548 8.93e-13 8 192 3.0690548 8.89e-13 16 768 3.0690548 8.88e-13 32 3072 3.0690548 8.31e-13 P(X,Y,Z) = X 1 3 1.0238514 4.41e-01 2 12 1.0316791 4.33e-01 4 48 1.3266931 1.38e-01 8 192 1.4296819 3.53e-02 16 768 1.4562829 8.73e-03 32 3072 1.4629299 2.08e-03 P(X,Y,Z) = Y 1 3 -0.11306273 9.35e-01 2 12 -0.74007307 3.08e-01 4 48 -0.95042145 9.75e-02 8 192 -1.0254543 2.25e-02 16 768 -1.0424257 5.51e-03 32 3072 -1.0466229 1.31e-03 P(X,Y,Z) = Z 1 3 -0.075223326 1.39e+00 2 12 0.93275388 3.85e-01 4 48 1.151618 1.66e-01 8 192 1.2690057 4.89e-02 16 768 1.3056284 1.23e-02 32 3072 1.3149559 2.93e-03 P(X,Y,Z) = X^2 1 3 1.9750865 6.93e-01 2 12 1.0140237 2.68e-01 4 48 1.2005759 8.10e-02 8 192 1.260914 2.07e-02 16 768 1.2763565 5.24e-03 32 3072 1.2803319 1.26e-03 P(X,Y,Z) = Y^2 Z^2 1 3 0.056832555 1.25e-01 2 12 0.077617823 1.04e-01 4 48 0.14619357 3.59e-02 8 192 0.19374097 1.16e-02 16 768 0.18493249 2.82e-03 32 3072 0.18277469 6.59e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.031486035 6.53e-03 2 12 0.013749622 1.12e-02 4 48 0.027482796 2.53e-03 8 192 0.02870351 3.75e-03 16 768 0.025574439 6.17e-04 32 3072 0.025104926 1.48e-04 P(X,Y,Z) = Y^2 Z^4 1 3 0.02089246 6.44e-02 2 12 0.034135797 5.11e-02 4 48 0.040642538 4.46e-02 8 192 0.087667355 2.42e-03 16 768 0.086280136 1.03e-03 32 3072 0.085465675 2.16e-04 P(X,Y,Z) = Z^6 1 3 0.11646444 3.65e-01 2 12 0.54057498 5.94e-02 4 48 0.54617852 6.51e-02 8 192 0.45620862 2.49e-02 16 768 0.47391746 7.21e-03 32 3072 0.4794493 1.68e-03 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.0066351753 1.17e-02 2 12 0.0071491014 2.06e-03 4 48 0.00651056 1.43e-03 8 192 0.010793517 5.71e-03 16 768 0.0061026233 1.02e-03 32 3072 0.0053146691 2.30e-04 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.0025214372 4.75e-03 2 12 0.001753472 5.52e-03 4 48 0.012204383 4.94e-03 8 192 0.0080152249 7.46e-04 16 768 0.0075158286 2.47e-04 32 3072 0.0073277464 5.90e-05 P(X,Y,Z) = X^6 Y^2 1 3 0.10942767 5.24e-02 2 12 0.014609328 4.24e-02 4 48 0.080200288 2.32e-02 8 192 0.059063454 2.03e-03 16 768 0.057513361 4.78e-04 32 3072 0.057150827 1.16e-04 P(X,Y,Z) = Z^8 1 3 0.046748006 3.33e-01 2 12 0.42558335 4.58e-02 4 48 0.47845688 9.87e-02 8 192 0.36394196 1.58e-02 16 768 0.37339401 6.38e-03 32 3072 0.37833126 1.44e-03 P(X,Y,Z) = X^6 Z^4 1 3 0.048508696 3.36e-02 2 12 0.021026762 6.10e-03 4 48 0.0089657101 5.96e-03 8 192 0.012703251 2.22e-03 16 768 0.014511716 4.16e-04 32 3072 0.014825674 1.02e-04 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.00014840502 5.59e-04 2 12 5.9483385e-05 6.48e-04 4 48 0.0012643502 5.57e-04 8 192 0.0007645708 5.75e-05 16 768 0.00073367771 2.66e-05 32 3072 0.0007136572 6.57e-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.0001317969 3.24e-04 2 12 0.00015380922 3.02e-04 4 48 0.00017336717 2.83e-04 8 192 0.00053740966 8.12e-05 16 768 0.0004622165 6.01e-06 32 3072 0.00045823338 2.03e-06 P(X,Y,Z) = X^16 1 3 0.22483589 1.15e-01 2 12 0.17674348 1.63e-01 4 48 0.20910459 1.31e-01 8 192 0.33175412 8.10e-03 16 768 0.33729858 2.55e-03 32 3072 0.3392461 6.04e-04 sphere_triangle_quad_test Normal end of execution. 27-Mar-2019 10:28:27 diary off