Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 18:05:36 sphere_triangle_quad_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 Test sphere_triangle_quad(). 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: 0.644843 -0.43356 0.629447 V2: 0.569693 -0.34481 -0.746026 V3: 0.788822 0.554693 0.264718 QUAD_01 QUAD_02 QUAD_03 P(X,Y,Z) = 1 1.0549 1.0549 1.0549 P(X,Y,Z) = X 1.04557 0.70445 0.920676 P(X,Y,Z) = Y -0.116739 -0.0786527 -0.113301 P(X,Y,Z) = Z 0.0773153 0.0520909 0.0410814 P(X,Y,Z) = X^2 1.03632 0.479141 0.805435 P(X,Y,Z) = Y^2 Z^2 6.93946e-05 0.0570381 0.00195837 P(X,Y,Z) = X^2 Y^2 Z^2 6.8172e-05 0.023159 0.0015174 P(X,Y,Z) = Y^2 Z^4 3.72761e-07 0.0238572 0.000230948 P(X,Y,Z) = Z^6 1.63504e-07 0.082611 0.00806371 P(X,Y,Z) = X Y^2 Z^4 3.69463e-07 0.0144875 0.000202953 P(X,Y,Z) = X^2 Y^4 Z^2 8.34862e-07 0.00439636 0.000150684 P(X,Y,Z) = X^6 Y^2 0.0122479 0.0322474 0.0409971 P(X,Y,Z) = Z^8 8.7828e-10 0.0424119 0.00216911 P(X,Y,Z) = X^6 Z^4 2.88578e-05 0.00810826 0.0127979 P(X,Y,Z) = X^4 Y^6 Z^2 1.00439e-08 0.000472546 2.76543e-05 P(X,Y,Z) = X^2 Y^4 Z^8 1.29399e-13 0.000282597 5.84864e-08 P(X,Y,Z) = X^16 0.915073 0.00825993 0.161078 sphere_triangle_quad_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: -0.857905 -0.260281 -0.443004 V2: 0.393645 -0.0882797 0.915014 V3: 0.716351 -0.133888 -0.684774 QUAD_MC1 QUAD_MC2 QUAD_MC3 P(X,Y,Z) = 1 4.51299 4.51299 4.51299 P(X,Y,Z) = X 0.465126 0.384866 0.397749 P(X,Y,Z) = Y -2.88625 -2.84894 -2.8546 P(X,Y,Z) = Z 0.0570498 -0.0313473 -0.024124 P(X,Y,Z) = X^2 1.3323 1.24392 1.2421 P(X,Y,Z) = Y^2 Z^2 0.393136 0.39099 0.390197 P(X,Y,Z) = X^2 Y^2 Z^2 0.052035 0.0522911 0.0525974 P(X,Y,Z) = Y^2 Z^4 0.159278 0.159584 0.159395 P(X,Y,Z) = Z^6 0.400987 0.390324 0.392717 P(X,Y,Z) = X Y^2 Z^4 0.00716643 0.00507658 0.00486415 P(X,Y,Z) = X^2 Y^4 Z^2 0.0202882 0.0195339 0.019366 P(X,Y,Z) = X^6 Y^2 0.0832973 0.0823184 0.0823194 P(X,Y,Z) = Z^8 0.271268 0.271266 0.268699 P(X,Y,Z) = X^6 Z^4 0.0103227 0.0104104 0.0106619 P(X,Y,Z) = X^4 Y^6 Z^2 0.00197205 0.00203638 0.00205235 P(X,Y,Z) = X^2 Y^4 Z^8 0.000900475 0.000919279 0.000888059 P(X,Y,Z) = X^16 0.100894 0.0944964 0.0956831 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: 0.123025 -0.528229 -0.840142 V2: -0.9997 0.023931 -0.005298 V3: 0.18234 -0.580609 -0.793502 FACTOR N RESULT P(X,Y,Z) = 1 1 1 0.080263218 1.57e-12 2 4 0.080263218 1.57e-12 4 16 0.080263218 1.56e-12 8 64 0.080263218 1.57e-12 16 256 0.080263218 1.58e-12 32 1024 0.080263218 1.47e-12 P(X,Y,Z) = X 1 1 -0.026734864 7.47e-03 2 4 -0.031166126 3.04e-03 4 16 -0.033634319 5.70e-04 8 64 -0.034064904 1.40e-04 16 256 -0.034170202 3.45e-05 32 1024 -0.034196512 8.22e-06 P(X,Y,Z) = Y 1 1 -0.041773566 6.04e-03 2 4 -0.036178433 4.43e-04 4 16 -0.035899251 1.64e-04 8 64 -0.035776358 4.13e-05 16 256 -0.035745249 1.02e-05 32 1024 -0.035737467 2.43e-06 P(X,Y,Z) = Z 1 1 -0.063106262 8.72e-03 2 4 -0.054955429 5.72e-04 4 16 -0.054612546 2.29e-04 8 64 -0.054441439 5.77e-05 16 256 -0.054397998 1.43e-05 32 1024 -0.05438713 3.40e-06 P(X,Y,Z) = X^2 1 1 0.0089051121 1.46e-02 2 4 0.021862141 1.65e-03 4 16 0.023088421 4.28e-04 8 64 0.023410887 1.06e-04 16 256 0.023490453 2.62e-05 32 1024 0.02351039 6.23e-06 P(X,Y,Z) = Y^2 Z^2 1 1 0.013439971 3.38e-03 2 4 0.011029398 9.70e-04 4 16 0.010207526 1.48e-04 8 64 0.010093171 3.35e-05 16 256 0.010067974 8.29e-06 32 1024 0.010061658 1.98e-06 P(X,Y,Z) = X^2 Y^2 Z^2 1 1 0.0014911494 3.69e-04 2 4 0.00064668691 4.75e-04 4 16 0.001088255 3.36e-05 8 64 0.0011156088 6.21e-06 16 256 0.0011202854 1.54e-06 32 1024 0.0011214552 3.66e-07 P(X,Y,Z) = Y^2 Z^4 1 1 0.0083082605 2.13e-03 2 4 0.0071686646 9.93e-04 4 16 0.006300915 1.25e-04 8 64 0.0062030166 2.74e-05 16 256 0.0061824231 6.77e-06 32 1024 0.0061772624 1.61e-06 P(X,Y,Z) = Z^6 1 1 0.018960592 5.04e-03 2 4 0.016081443 2.16e-03 4 16 0.014198097 2.74e-04 8 64 0.013983522 5.93e-05 16 256 0.013938877 1.47e-05 32 1024 0.013927685 3.50e-06 P(X,Y,Z) = X Y^2 Z^4 1 1 -0.0027673973 1.61e-03 2 4 -0.0010898967 6.69e-05 4 16 -0.0011570818 2.66e-07 8 64 -0.0011528796 3.94e-06 16 256 -0.0011558668 9.49e-07 32 1024 -0.0011565911 2.24e-07 P(X,Y,Z) = X^2 Y^4 Z^2 1 1 0.00040391607 1.77e-04 2 4 0.00013812805 8.93e-05 4 16 0.00022500849 2.40e-06 8 64 0.00022611778 1.29e-06 16 256 0.00022708636 3.18e-07 32 1024 0.00022732869 7.56e-08 P(X,Y,Z) = X^6 Y^2 1 1 2.9693065e-05 5.92e-04 2 4 0.00069991971 7.85e-05 4 16 0.00062886236 7.47e-06 8 64 0.0006187564 2.64e-06 16 256 0.00062073133 6.60e-07 32 1024 0.00062123415 1.58e-07 P(X,Y,Z) = Z^8 1 1 0.011720973 2.94e-03 2 4 0.010611409 1.83e-03 4 16 0.0089820107 2.00e-04 8 64 0.0088268068 4.53e-05 16 256 0.0087927476 1.12e-05 32 1024 0.0087842096 2.67e-06 P(X,Y,Z) = X^6 Z^4 1 1 4.1889831e-05 3.68e-04 2 4 0.00030273123 1.07e-04 4 16 0.00039786358 1.19e-05 8 64 0.00040771702 2.09e-06 16 256 0.00040928901 5.22e-07 32 1024 0.00040968651 1.25e-07 P(X,Y,Z) = X^4 Y^6 Z^2 1 1 1.2139029e-05 1.10e-06 2 4 4.1740223e-06 6.87e-06 4 16 1.0195041e-05 8.47e-07 8 64 1.0972981e-05 6.95e-08 16 256 1.1024867e-05 1.76e-08 32 1024 1.1038281e-05 4.20e-09 P(X,Y,Z) = X^2 Y^4 Z^8 1 1 9.5417156e-05 5.97e-05 2 4 3.072618e-05 4.97e-06 4 16 3.8015081e-05 2.32e-06 8 64 3.5512596e-05 1.79e-07 16 256 3.564876e-05 4.30e-08 32 1024 3.568156e-05 1.02e-08 P(X,Y,Z) = X^16 1 1 1.842889e-09 4.23e-03 2 4 0.0034639622 7.71e-04 4 16 0.0040249072 2.10e-04 8 64 0.0042136421 2.09e-05 16 256 0.0042293718 5.17e-06 32 1024 0.0042333111 1.23e-06 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: -0.255563 0.679728 -0.687501 V2: 0.188659 -0.840768 -0.507462 V3: -0.143309 0.314892 -0.938246 FACTOR N RESULT P(X,Y,Z) = 1 1 3 0.033926138 2.04e-12 2 12 0.033926138 2.02e-12 4 48 0.033926138 2.02e-12 8 192 0.033926138 1.97e-12 16 768 0.033926138 2.01e-12 32 3072 0.033926138 1.92e-12 P(X,Y,Z) = X 1 3 -0.00260986 2.67e-04 2 12 -0.002457555 1.15e-04 4 48 -0.0023668749 2.44e-05 8 192 -0.0023485544 6.10e-06 16 768 -0.0023439683 1.51e-06 32 3072 -0.002342818 3.60e-07 P(X,Y,Z) = Y 1 3 0.0004044543 1.02e-03 2 12 8.0398953e-05 6.91e-04 4 48 -0.00046630024 1.44e-04 8 192 -0.00057466147 3.61e-05 16 768 -0.00060182675 8.95e-06 32 3072 -0.00060864416 2.13e-06 P(X,Y,Z) = Z 1 3 -0.03125506 5.78e-05 2 12 -0.030535255 6.62e-04 4 48 -0.031067612 1.30e-04 8 192 -0.031164918 3.24e-05 16 768 -0.031189267 8.03e-06 32 3072 -0.031195381 1.91e-06 P(X,Y,Z) = X^2 1 3 0.0005190745 1.02e-06 2 12 0.00062352757 1.05e-04 4 48 0.000537941 1.99e-05 8 192 0.00052299983 4.94e-06 16 768 0.00051928507 1.23e-06 32 3072 0.00051835124 2.92e-07 P(X,Y,Z) = Y^2 Z^2 1 3 0.0034188992 2.95e-04 2 12 0.0036798521 5.56e-04 4 48 0.00322898 1.05e-04 8 192 0.0031497273 2.54e-05 16 768 0.0031306082 6.32e-06 32 3072 0.0031257971 1.51e-06 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 8.7932602e-05 2.30e-05 2 12 8.555293e-05 2.06e-05 4 48 6.8993513e-05 4.04e-06 8 192 6.6072761e-05 1.12e-06 16 768 6.5231343e-05 2.76e-07 32 3072 6.5020755e-05 6.58e-08 P(X,Y,Z) = Y^2 Z^4 1 3 0.0026547351 3.51e-04 2 12 0.002567113 2.63e-04 4 48 0.002358646 5.47e-05 8 192 0.0023171457 1.32e-05 16 768 0.0023072232 3.29e-06 32 3072 0.0023047188 7.85e-07 P(X,Y,Z) = Z^6 1 3 0.022216317 5.60e-04 2 12 0.020683305 2.09e-03 4 48 0.022376841 4.00e-04 8 192 0.022678598 9.80e-05 16 768 0.022752286 2.43e-05 32 3072 0.022770822 5.80e-06 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.00027413255 1.48e-04 2 12 -0.00014078412 1.44e-05 4 48 -0.00013019052 3.85e-06 8 192 -0.00012818737 1.84e-06 16 768 -0.00012679961 4.55e-07 32 3072 -0.00012645269 1.08e-07 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 2.2650874e-05 5.08e-06 2 12 2.4548472e-05 6.98e-06 4 48 1.9177807e-05 1.61e-06 8 192 1.7986061e-05 4.14e-07 16 768 1.7674264e-05 1.02e-07 32 3072 1.7596571e-05 2.43e-08 P(X,Y,Z) = X^6 Y^2 1 3 2.180393e-07 6.66e-08 2 12 1.9990867e-07 4.84e-08 4 48 1.6870245e-07 1.72e-08 8 192 1.5558529e-07 4.12e-09 16 768 1.5248484e-07 1.02e-09 32 3072 1.5171087e-07 2.42e-10 P(X,Y,Z) = Z^8 1 3 0.019920742 8.11e-04 2 12 0.018498075 2.23e-03 4 48 0.0203022 4.29e-04 8 192 0.020625897 1.06e-04 16 768 0.020705197 2.62e-05 32 3072 0.020725156 6.25e-06 P(X,Y,Z) = X^6 Z^4 1 3 4.0640368e-07 1.10e-07 2 12 3.661715e-07 7.00e-08 4 48 3.1075291e-07 1.46e-08 8 192 3.0012716e-07 4.00e-09 16 768 2.9711669e-07 9.89e-10 32 3072 2.9636351e-07 2.36e-10 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 2.4660819e-07 3.26e-08 2 12 2.8870395e-07 7.47e-08 4 48 2.4473041e-07 3.07e-08 8 192 2.2109157e-07 7.07e-09 16 768 2.1576212e-07 1.74e-09 32 3072 2.1443676e-07 4.14e-10 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 7.7211237e-06 2.90e-06 2 12 6.2972428e-06 1.47e-06 4 48 5.1089379e-06 2.83e-07 8 192 4.9034568e-06 7.80e-08 16 768 4.8448297e-06 1.93e-08 32 3072 4.8301057e-06 4.60e-09 P(X,Y,Z) = X^16 1 3 1.0872637e-13 4.62e-14 2 12 2.0321564e-13 4.83e-14 4 48 1.7506223e-13 2.01e-14 8 192 1.6009839e-13 5.14e-15 16 768 1.5623558e-13 1.28e-15 32 3072 1.5526392e-13 3.04e-16 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: 0.935995 0.273468 -0.221652 V2: -0.740832 0.329275 0.585444 V3: 0.939945 -0.0771896 -0.332483 FACTOR N RESULT P(X,Y,Z) = 1 1 3 0.54396603 2.20e-12 2 12 0.54396603 2.21e-12 4 48 0.54396603 2.21e-12 8 192 0.54396603 2.20e-12 16 768 0.54396603 2.18e-12 32 3072 0.54396603 2.09e-12 P(X,Y,Z) = X 1 3 0.20581993 4.04e-02 2 12 0.21540158 3.08e-02 4 48 0.22749308 1.87e-02 8 192 0.23861064 7.58e-03 16 768 0.24403508 2.16e-03 32 3072 0.24566412 5.30e-04 P(X,Y,Z) = Y 1 3 0.095294401 2.13e-01 2 12 0.26731365 4.12e-02 4 48 0.28085506 2.77e-02 8 192 0.29669634 1.18e-02 16 768 0.3051972 3.35e-03 32 3072 0.3077293 8.15e-04 P(X,Y,Z) = Z 1 3 0.0056770675 2.01e-01 2 12 0.17833816 2.86e-02 4 48 0.1864599 2.04e-02 8 192 0.19775264 9.15e-03 16 768 0.20429919 2.60e-03 32 3072 0.20626991 6.32e-04 P(X,Y,Z) = X^2 1 3 0.41856651 1.96e-01 2 12 0.22593684 3.82e-03 4 48 0.23728561 1.52e-02 8 192 0.23381222 1.17e-02 16 768 0.22587643 3.76e-03 32 3072 0.22303798 9.20e-04 P(X,Y,Z) = Y^2 Z^2 1 3 0.0075237737 4.91e-02 2 12 0.053293112 3.36e-03 4 48 0.05313053 3.52e-03 8 192 0.0541161 2.54e-03 16 768 0.055850766 8.03e-04 32 3072 0.056459822 1.94e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.0043872773 2.71e-03 2 12 0.0091966198 2.10e-03 4 48 0.0095690414 2.47e-03 8 192 0.0079172231 8.20e-04 16 768 0.0069600653 1.37e-04 32 3072 0.0070506177 4.67e-05 P(X,Y,Z) = Y^2 Z^4 1 3 0.0023553978 2.01e-02 2 12 0.016706078 5.72e-03 4 48 0.017768129 4.65e-03 8 192 0.020837712 1.58e-03 16 768 0.022324567 9.77e-05 32 3072 0.022411368 1.09e-05 P(X,Y,Z) = Z^6 1 3 0.0075671348 1.48e-02 2 12 0.014631264 7.70e-03 4 48 0.016931259 5.40e-03 8 192 0.021733901 6.02e-04 16 768 0.022809257 4.73e-04 32 3072 0.02247237 1.37e-04 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.0016678825 2.57e-03 2 12 0.0056194061 4.72e-03 4 48 0.0034379429 2.54e-03 8 192 0.00064380017 2.57e-04 16 768 0.00052186448 3.79e-04 32 3072 0.00080260933 9.83e-05 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.00044523478 2.50e-03 2 12 0.0036231629 6.74e-04 4 48 0.0038917568 9.43e-04 8 192 0.0034347807 4.86e-04 16 768 0.0028824673 6.65e-05 32 3072 0.0029222457 2.67e-05 P(X,Y,Z) = X^6 Y^2 1 3 0.01311315 3.24e-03 2 12 0.003803199 1.26e-02 4 48 0.0097771375 6.58e-03 8 192 0.016243953 1.12e-04 16 768 0.016657397 3.02e-04 32 3072 0.016427548 7.19e-05 P(X,Y,Z) = Z^8 1 3 0.0025304078 7.97e-03 2 12 0.0051411488 5.36e-03 4 48 0.0064923545 4.01e-03 8 192 0.0099187085 5.83e-04 16 768 0.010837422 3.36e-04 32 3072 0.0105995 9.77e-05 P(X,Y,Z) = X^6 Z^4 1 3 0.0053437411 4.80e-03 2 12 0.0024555857 1.91e-03 4 48 0.0010849821 5.41e-04 8 192 0.0004699672 7.43e-05 16 768 0.00052553759 1.87e-05 32 3072 0.00054527935 1.02e-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 2.6722327e-05 2.95e-04 2 12 0.00026869617 5.28e-05 4 48 0.00029452826 2.70e-05 8 192 0.00025455899 6.70e-05 16 768 0.00030167086 1.99e-05 32 3072 0.00031808559 3.44e-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 1.6150072e-05 1.01e-04 2 12 0.00014840788 3.08e-05 4 48 0.00017065978 5.31e-05 8 192 0.00019464996 7.71e-05 16 768 0.00011885311 1.27e-06 32 3072 0.00011775756 1.76e-07 P(X,Y,Z) = X^16 1 3 0.13172946 7.60e-02 2 12 0.067885372 1.21e-02 4 48 0.088416496 3.27e-02 8 192 0.068813107 1.31e-02 16 768 0.058263031 2.53e-03 32 3072 0.056365706 6.30e-04 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: 0.643951 -0.165247 -0.747008 V2: 0.954943 -0.0305823 0.29521 V3: -0.429235 -0.896253 0.111748 FACTOR N RESULT P(X,Y,Z) = 1 1 3 1.5917027 1.98e-12 2 12 1.5917027 1.98e-12 4 48 1.5917027 1.98e-12 8 192 1.5917027 1.97e-12 16 768 1.5917027 1.96e-12 32 3072 1.5917027 1.87e-12 P(X,Y,Z) = X 1 3 0.62058305 2.31e-01 2 12 0.74599286 1.05e-01 4 48 0.8236553 2.77e-02 8 192 0.84437856 6.95e-03 16 768 0.84960937 1.72e-03 32 3072 0.85091992 4.10e-04 P(X,Y,Z) = Y 1 3 -0.57942329 4.59e-01 2 12 -0.90574753 1.33e-01 4 48 -1.0032009 3.54e-02 8 192 -1.0296817 8.95e-03 16 768 -1.036412 2.22e-03 32 3072 -1.038101 5.28e-04 P(X,Y,Z) = Z 1 3 -0.18041925 3.47e-02 2 12 -0.18912028 2.60e-02 4 48 -0.20943192 5.65e-03 8 192 -0.21376466 1.32e-03 16 768 -0.21476426 3.21e-04 32 3072 -0.21500925 7.62e-05 P(X,Y,Z) = X^2 1 3 0.80159839 1.65e-01 2 12 0.62105577 1.51e-02 4 48 0.6313461 4.76e-03 8 192 0.63486436 1.24e-03 16 768 0.63579652 3.11e-04 32 3072 0.63603345 7.44e-05 P(X,Y,Z) = Y^2 Z^2 1 3 0.013449887 4.35e-02 2 12 0.11793502 6.09e-02 4 48 0.075547445 1.86e-02 8 192 0.061560955 4.57e-03 16 768 0.058114401 1.12e-03 32 3072 0.057257388 2.67e-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.0043724406 9.51e-03 2 12 0.011291382 2.60e-03 4 48 0.01501012 1.12e-03 8 192 0.014107399 2.21e-04 16 768 0.013939469 5.30e-05 32 3072 0.013898997 1.26e-05 P(X,Y,Z) = Y^2 Z^4 1 3 0.0045815739 6.77e-03 2 12 0.025487177 1.41e-02 4 48 0.015242179 3.89e-03 8 192 0.0125309 1.18e-03 16 768 0.011651464 3.01e-04 32 3072 0.011422481 7.22e-05 P(X,Y,Z) = Z^6 1 3 0.092543704 7.84e-02 2 12 0.024647457 1.05e-02 4 48 0.017122241 2.95e-03 8 192 0.014970288 7.95e-04 16 768 0.014380579 2.05e-04 32 3072 0.01422509 4.93e-05 P(X,Y,Z) = X Y^2 Z^4 1 3 0.0028801579 2.54e-03 2 12 0.0061031605 6.82e-04 4 48 0.0061682774 7.48e-04 8 192 0.0056753132 2.55e-04 16 768 0.0054845258 6.38e-05 32 3072 0.0054359113 1.52e-05 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.00087923183 4.42e-03 2 12 0.00700512 1.70e-03 4 48 0.0061193676 8.19e-04 8 192 0.0054484671 1.48e-04 16 768 0.0053356763 3.52e-05 32 3072 0.005308812 8.31e-06 P(X,Y,Z) = X^6 Y^2 1 3 0.0040748375 3.91e-02 2 12 0.0078020913 3.54e-02 4 48 0.036887372 6.33e-03 8 192 0.04175177 1.46e-03 16 768 0.042856218 3.57e-04 32 3072 0.043128653 8.49e-05 P(X,Y,Z) = Z^8 1 3 0.051475348 4.59e-02 2 12 0.01109994 5.50e-03 4 48 0.0071890568 1.59e-03 8 192 0.0060092968 4.07e-04 16 768 0.0057051434 1.03e-04 32 3072 0.0056271697 2.46e-05 P(X,Y,Z) = X^6 Z^4 1 3 0.014836711 1.10e-02 2 12 0.0043398998 5.19e-04 4 48 0.0042441871 4.23e-04 8 192 0.003938414 1.18e-04 16 768 0.0038495717 2.89e-05 32 3072 0.0038275647 6.86e-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.00011760641 5.77e-04 2 12 0.0007868013 9.22e-05 4 48 0.0007730637 7.85e-05 8 192 0.00069787921 3.29e-06 16 768 0.00069535546 7.68e-07 32 3072 0.00069476849 1.81e-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 1.5908156e-05 6.81e-05 2 12 4.0794654e-05 4.32e-05 4 48 0.0001069078 2.29e-05 8 192 8.8842212e-05 4.82e-06 16 768 8.5303544e-05 1.28e-06 32 3072 8.4334016e-05 3.10e-07 P(X,Y,Z) = X^16 1 3 0.25419848 1.30e-01 2 12 0.23861063 1.14e-01 4 48 0.15352385 2.93e-02 8 192 0.13016792 5.89e-03 16 768 0.12570953 1.44e-03 32 3072 0.12461452 3.41e-04 sphere_triangle_quad_test(): Normal end of execution. 13-May-2025 18:06:56