07-Jan-2022 18:09:10 circle_segment_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2. Test CIRCLE_SEGMENT. CIRCLE_SEGMENT_TEST01 CIRCLE_SEGMENT_AREA_FROM_HEIGHT computes the area of a circle segment. R H Area 1.000000 1.000000 1.570796 1.000000 0.500000 0.614185 1.000000 0.250000 0.226656 1.000000 0.125000 0.081753 1.000000 0.062500 0.029185 1.000000 0.031250 0.010368 1.000000 0.015625 0.003674 1.000000 0.007812 0.001301 1.000000 0.003906 0.000460 1.000000 0.001953 0.000163 1.000000 0.000977 0.000058 CIRCLE_SEGMENT_TEST02 GQCIRCSEGM computes a Gauss quadrature rule for a circle segment with circle of radius R and center (0,0), with segment angles in [-theta/2,+theta/2]. Tabulate some rules. Rule of precision 0 THETA = 6.28319 Grid order: 3 Sum(W) = 3.14159 X Y W 0.926632 0 0.258589 6.12323e-17 0 2.62442 -0.926632 0 0.258589 Rule of precision 1 THETA = 6.28319 Grid order: 4 Sum(W) = 3.14159 X Y W 0.970028 0 0.0703739 0.480049 0 1.50042 -0.480049 0 1.50042 -0.970028 0 0.0703739 Rule of precision 2 THETA = 6.28319 Grid order: 10 Sum(W) = 3.14159 X Y W 0.985634 -0.0975123 0.0119222 0.716222 -0.402917 0.360189 6.12323e-17 -0.57735 0.826575 -0.716222 -0.402917 0.360189 -0.985634 -0.0975123 0.0119222 0.985634 0.0975123 0.0119222 0.716222 0.402917 0.360189 6.12323e-17 0.57735 0.826575 -0.716222 0.402917 0.360189 -0.985634 0.0975123 0.0119222 Rule of precision 3 THETA = 6.28319 Grid order: 12 Sum(W) = 3.14159 X Y W 0.992298 -0.0715201 0.00473805 0.835113 -0.317588 0.174542 0.339731 -0.543011 0.606118 -0.339731 -0.543011 0.606118 -0.835113 -0.317588 0.174542 -0.992298 -0.0715201 0.00473805 0.992298 0.0715201 0.00473805 0.835113 0.317588 0.174542 0.339731 0.543011 0.606118 -0.339731 0.543011 0.606118 -0.835113 0.317588 0.174542 -0.992298 0.0715201 0.00473805 Rule of precision 4 THETA = 6.28319 Grid order: 21 Sum(W) = 3.14159 X Y W 0.995514 -0.0732842 0.00117913 0.898628 -0.339824 0.0492883 0.558451 -0.642557 0.218402 6.12323e-17 -0.774597 0.334925 -0.558451 -0.642557 0.218402 -0.898628 -0.339824 0.0492883 -0.995514 -0.0732842 0.00117913 0.995514 -4.26715e-18 0.0018866 0.898628 -1.97871e-17 0.0788612 0.558451 -3.74145e-17 0.349444 6.12323e-17 -4.51028e-17 0.53588 -0.558451 -3.74145e-17 0.349444 -0.898628 -1.97871e-17 0.0788612 -0.995514 -4.26715e-18 0.0018866 0.995514 0.0732842 0.00117913 0.898628 0.339824 0.0492883 0.558451 0.642557 0.218402 6.12323e-17 0.774597 0.334925 -0.558451 0.642557 0.218402 -0.898628 0.339824 0.0492883 -0.995514 0.0732842 0.00117913 Rule of precision 5 THETA = 6.28319 Grid order: 24 Sum(W) = 3.14159 X Y W 0.997217 -0.057753 0.000579528 0.93462 -0.275484 0.0264176 0.697838 -0.554809 0.137205 0.261542 -0.747634 0.27213 -0.261542 -0.747634 0.27213 -0.697838 -0.554809 0.137205 -0.93462 -0.275484 0.0264176 -0.997217 -0.057753 0.000579528 0.997217 -3.36281e-18 0.000927245 0.93462 -1.60408e-17 0.0422682 0.697838 -3.23052e-17 0.219528 0.261542 -4.35329e-17 0.435409 -0.261542 -4.35329e-17 0.435409 -0.697838 -3.23052e-17 0.219528 -0.93462 -1.60408e-17 0.0422682 -0.997217 -3.36281e-18 0.000927245 0.997217 0.057753 0.000579528 0.93462 0.275484 0.0264176 0.697838 0.554809 0.137205 0.261542 0.747634 0.27213 -0.261542 0.747634 0.27213 -0.697838 0.554809 0.137205 -0.93462 0.275484 0.0264176 -0.997217 0.057753 0.000579528 Rule of precision 0 THETA = 3.14159 Grid order: 3 Sum(W) = 1.5708 X Y W 0.98372 0 0.0285153 0.707107 0 0.687812 0.179706 0 0.85447 Rule of precision 1 THETA = 3.14159 Grid order: 4 Sum(W) = 1.5708 X Y W 0.993717 0 0.00699072 0.866597 0 0.252172 0.499009 0 0.760526 0.111919 0 0.551108 Rule of precision 2 THETA = 3.14159 Grid order: 10 Sum(W) = 1.5708 X Y W 0.997101 -0.0439271 0.00110751 0.932985 -0.207797 0.0485584 0.707107 -0.408248 0.219222 0.359915 -0.538659 0.326297 0.0760839 -0.575677 0.190213 0.997101 0.0439271 0.00110751 0.932985 0.207797 0.0485584 0.707107 0.408248 0.219222 0.359915 0.538659 0.326297 0.0760839 0.575677 0.190213 Rule of precision 3 THETA = 3.14159 Grid order: 12 Sum(W) = 1.5708 X Y W 0.998487 -0.0317441 0.000420179 0.963239 -0.155102 0.0205674 0.824494 -0.326706 0.115731 0.565871 -0.476022 0.245691 0.268645 -0.556126 0.264417 0.0549824 -0.576477 0.138571 0.998487 0.0317441 0.000420179 0.963239 0.155102 0.0205674 0.824494 0.326706 0.115731 0.565871 0.476022 0.245691 0.268645 0.556126 0.264417 0.0549824 0.576477 0.138571 Rule of precision 4 THETA = 3.14159 Grid order: 21 Sum(W) = 1.5708 X Y W 0.999136 -0.0321849 0.000101096 0.978334 -0.160366 0.00529996 0.890587 -0.352296 0.0340918 0.707107 -0.547723 0.0893122 0.454812 -0.689846 0.130719 0.207031 -0.757815 0.118352 0.0415505 -0.773928 0.0584563 0.999136 -1.87404e-18 0.000161753 0.978334 -9.33769e-18 0.00847994 0.890587 -2.05133e-17 0.0545469 0.707107 -3.18925e-17 0.1429 0.454812 -4.0168e-17 0.20915 0.207031 -4.41256e-17 0.189363 0.0415505 -4.50639e-17 0.09353 0.999136 0.0321849 0.000101096 0.978334 0.160366 0.00529996 0.890587 0.352296 0.0340918 0.707107 0.547723 0.0893122 0.454812 0.689846 0.130719 0.207031 0.757815 0.118352 0.0415505 0.773928 0.0584563 Rule of precision 5 THETA = 3.14159 Grid order: 24 Sum(W) = 1.5708 X Y W 0.999472 -0.0251643 4.84375e-05 0.986468 -0.126996 0.0026583 0.929017 -0.28663 0.0186652 0.799536 -0.465237 0.0559976 0.600619 -0.619318 0.0992311 0.370038 -0.719613 0.117649 0.163951 -0.764115 0.0962366 0.032487 -0.774188 0.0458463 0.999472 -1.46525e-18 7.75e-05 0.986468 -7.39466e-18 0.00425327 0.929017 -1.66898e-17 0.0298643 0.799536 -2.70896e-17 0.0895962 0.600619 -3.60613e-17 0.15877 0.370038 -4.19013e-17 0.188238 0.163951 -4.44925e-17 0.153979 0.032487 -4.5079e-17 0.0733541 0.999472 0.0251643 4.84375e-05 0.986468 0.126996 0.0026583 0.929017 0.28663 0.0186652 0.799536 0.465237 0.0559976 0.600619 0.619318 0.0992311 0.370038 0.719613 0.117649 0.163951 0.764115 0.0962366 0.032487 0.774188 0.0458463 Rule of precision 0 THETA = 1.5708 Grid order: 3 Sum(W) = 0.285398 X Y W 0.996045 0 0.0034545 0.92388 0 0.101863 0.767135 0 0.180081 Rule of precision 1 THETA = 1.5708 Grid order: 4 Sum(W) = 0.285398 X Y W 0.998493 0 0.000827221 0.966468 0 0.0336787 0.864972 0 0.12862 0.744848 0 0.122272 Rule of precision 2 THETA = 1.5708 Grid order: 10 Sum(W) = 0.285398 X Y W 0.99931 -0.0214398 0.000129186 0.983493 -0.104468 0.00615 0.92388 -0.220942 0.0325636 0.823382 -0.327639 0.0604919 0.732877 -0.392807 0.0433645 0.99931 0.0214398 0.000129186 0.983493 0.104468 0.00615 0.92388 0.220942 0.0325636 0.823382 0.327639 0.0604919 0.732877 0.392807 0.0433645 Rule of precision 3 THETA = 1.5708 Grid order: 12 Sum(W) = 0.285398 X Y W 0.999642 -0.0154468 4.85453e-05 0.991066 -0.0770014 0.00252381 0.955505 -0.170305 0.0159225 0.884223 -0.26966 0.0399201 0.795097 -0.350153 0.0521886 0.725772 -0.39718 0.0320955 0.999642 0.0154468 4.85453e-05 0.991066 0.0770014 0.00252381 0.955505 0.170305 0.0159225 0.884223 0.26966 0.0399201 0.795097 0.350153 0.0521886 0.725772 0.39718 0.0320955 Rule of precision 4 THETA = 1.5708 Grid order: 21 Sum(W) = 0.285398 X Y W 0.999796 -0.0156284 1.16012e-05 0.994784 -0.0790097 0.000637003 0.972744 -0.179613 0.00446727 0.92388 -0.296425 0.013285 0.851798 -0.405788 0.0228016 0.775544 -0.488997 0.0244002 0.72123 -0.53656 0.0136746 0.999796 -9.09999e-19 1.85619e-05 0.994784 -4.60054e-18 0.0010192 0.972744 -1.04584e-17 0.00714763 0.92388 -1.72601e-17 0.0212561 0.851798 -2.3628e-17 0.0364825 0.775544 -2.84731e-17 0.0390403 0.72123 -3.12425e-17 0.0218793 0.999796 0.0156284 1.16012e-05 0.994784 0.0790097 0.000637003 0.972744 0.179613 0.00446727 0.92388 0.296425 0.013285 0.851798 0.405788 0.0228016 0.775544 0.488997 0.0244002 0.72123 0.53656 0.0136746 Rule of precision 5 THETA = 1.5708 Grid order: 24 Sum(W) = 0.285398 X Y W 0.999876 -0.0122004 5.53062e-06 0.996765 -0.0622557 0.000314896 0.982545 -0.144095 0.00236619 0.94891 -0.244421 0.00784097 0.894106 -0.346907 0.015795 0.826304 -0.436271 0.0216903 0.761651 -0.501929 0.0204689 0.718156 -0.539028 0.0107956 0.999876 -7.104e-19 8.84899e-06 0.996765 -3.62499e-18 0.000503833 0.982545 -8.39029e-18 0.00378591 0.94891 -1.4232e-17 0.0125456 0.894106 -2.01995e-17 0.0252719 0.826304 -2.5403e-17 0.0347045 0.761651 -2.92261e-17 0.0327502 0.718156 -3.13862e-17 0.0172729 0.999876 0.0122004 5.53062e-06 0.996765 0.0622557 0.000314896 0.982545 0.144095 0.00236619 0.94891 0.244421 0.00784097 0.894106 0.346907 0.015795 0.826304 0.436271 0.0216903 0.761651 0.501929 0.0204689 0.718156 0.539028 0.0107956 Rule of precision 0 THETA = 0.785398 Grid order: 3 Sum(W) = 0.0391457 X Y W 0.999018 0 0.000428449 0.980785 0 0.0132733 0.939925 0 0.0254439 Rule of precision 1 THETA = 0.785398 Grid order: 4 Sum(W) = 0.0391457 X Y W 0.999627 0 0.000102012 0.991606 0 0.0042782 0.965604 0 0.0173025 0.933986 0 0.017463 Rule of precision 2 THETA = 0.785398 Grid order: 10 Sum(W) = 0.0391457 X Y W 0.99983 -0.0106566 1.58762e-05 0.995889 -0.0522991 0.000771032 0.980785 -0.112635 0.0042464 0.954747 -0.171716 0.00831198 0.930786 -0.211059 0.00622756 0.99983 0.0106566 1.58762e-05 0.995889 0.0522991 0.000771032 0.980785 0.112635 0.0042464 0.954747 0.171716 0.00831198 0.930786 0.211059 0.00622756 Rule of precision 3 THETA = 0.785398 Grid order: 12 Sum(W) = 0.0391457 X Y W 0.999912 -0.00767229 5.9523e-06 0.997782 -0.0384299 0.000313962 0.988838 -0.086022 0.00203747 0.970585 -0.139002 0.00532004 0.947303 -0.184948 0.00727171 0.928883 -0.213835 0.00462371 0.999912 0.00767229 5.9523e-06 0.997782 0.0384299 0.000313962 0.988838 0.086022 0.00203747 0.970585 0.139002 0.00532004 0.947303 0.184948 0.00727171 0.928883 0.213835 0.00462371 Rule of precision 4 THETA = 0.785398 Grid order: 21 Sum(W) = 0.0391457 X Y W 0.99995 -0.00775859 1.42018e-06 0.998708 -0.0393594 7.88433e-05 0.993193 -0.090227 0.000564763 0.980785 -0.151116 0.00173302 0.962166 -0.211049 0.00309 0.942131 -0.259679 0.00343197 0.927666 -0.289242 0.00197379 0.99995 -4.51763e-19 2.27228e-06 0.998708 -2.2918e-18 0.000126149 0.993193 -5.25369e-18 0.000903621 0.980785 -8.79912e-18 0.00277284 0.962166 -1.22888e-17 0.00494399 0.942131 -1.51205e-17 0.00549115 0.927666 -1.68419e-17 0.00315806 0.99995 0.00775859 1.42018e-06 0.998708 0.0393594 7.88433e-05 0.993193 0.090227 0.000564763 0.980785 0.151116 0.00173302 0.962166 0.211049 0.00309 0.942131 0.259679 0.00343197 0.927666 0.289242 0.00197379 Rule of precision 5 THETA = 0.785398 Grid order: 24 Sum(W) = 0.0391457 X Y W 0.999969 -0.00605461 6.76235e-07 0.9992 -0.0309758 3.88389e-05 0.995654 -0.0721345 0.000296699 0.987167 -0.123697 0.0010077 0.973135 -0.178341 0.00209468 0.955502 -0.228494 0.002977 0.938444 -0.26757 0.002898 0.926843 -0.290823 0.0015602 0.999969 -3.52544e-19 1.08198e-06 0.9992 -1.80364e-18 6.21422e-05 0.995654 -4.20021e-18 0.000474719 0.987167 -7.20254e-18 0.00161233 0.973135 -1.03843e-17 0.00335148 0.955502 -1.33046e-17 0.0047632 0.938444 -1.55799e-17 0.00463681 0.926843 -1.69339e-17 0.00249633 0.999969 0.00605461 6.76235e-07 0.9992 0.0309758 3.88389e-05 0.995654 0.0721345 0.000296699 0.987167 0.123697 0.0010077 0.973135 0.178341 0.00209468 0.955502 0.228494 0.002977 0.938444 0.26757 0.002898 0.926843 0.290823 0.0015602 CIRCLE_SEGMENT_TEST03 GQCIRCSEGM computes a Gauss quadrature rule for a circle segment with circle of radius R and center (0,0), with segment angles in [-theta/2,+theta/2]. Plot some rules. Created graphics image "rule_p9_t3.14159.png". Created graphics image "rule_p9_t1.5708.png". Created graphics image "rule_p9_t0.785398.png". Created graphics image "rule_p9_t0.392699.png". CIRCLE_SEGMENT_TEST04 GQCIRCSEGM computes a Gauss quadrature rule for a circle segment with circle of radius R and center (0,0), with segment angles in [-theta/2,+theta/2]. Radius R = 1 Angle Theta = 0.785398 Estimate the integral of (x+y+2)^k using precision P rule. P: 1 3 5 7 9 11 K 0 0.965604.5 0.988838.5 0.995654.5 0.998013.5 0.998976.5 0.999422.5 1 3.853949.5 3.953072.5 3.981791.5 3.991688.5 3.995718.5 3.997585.5 2 15.382010.5 15.803171.5 15.923856.5 15.965291.5 15.982134.5 15.989929.5 3 61.393192.5 63.176242.5 63.682202.5 63.855327.5 63.925586.5 63.958070.5 4 245.034547.5 252.559280.5 254.675921.5 255.397954.5 255.690539.5 255.825699.5 5 977.990031.5 1009.654705.5 1018.492190.5 1021.498412.5 1022.714939.5 1023.276474.5 6 3903.386325.5 4036.290512.5 4073.122954.5 4085.620062.5 4090.670891.5 4093.000619.5 7 15579.325263.5 16135.854182.5 16289.109289.5 16340.986037.5 16361.928139.5 16371.581376.5 8 62180.720904.5 64506.206726.5 65142.909864.5 65357.967847.5 65444.690994.5 65484.641145.5 9 248177.760390.5 257876.072706.5 260517.541520.5 261407.968369.5 261766.678286.5 261931.827322.5 10 990535.327620.5 1030909.617060.5 1041853.819268.5 1045536.270135.5 1047018.372606.5 1047700.360943.5 11 3953457.528673.5 4121261.144528.5 4166550.069489.5 4181762.702149.5 4187880.137203.5 4190693.653162.5 CIRCLE_SEGMENT_TEST05 For circle segment with a given radius R, CIRCLE_SEGMENT_AREA_FROM_HEIGHT computes the area A, given the height. CIRCLE_SEGMENT_HEIGHT_FROM_AREA computes height H, given the area. Check that these functions are inverses of each other using random values of R, A, and H. R H => A => H2 4.073618 7.379701 49.647207 7.379701 0.634934 1.159867 1.213136 1.159867 3.161796 0.616806 1.575825 0.616806 1.392491 1.523055 3.408909 1.523055 4.787534 9.238874 71.211089 9.238873 R A => H => A2 0.788065 1.893701 1.469136 1.893701 4.785835 34.925550 4.675885 34.925550 4.001402 7.136987 1.596692 7.136987 2.108806 12.793618 3.631115 12.793617 3.961037 47.294337 7.253986 47.294337 CIRCLE_SEGMENT_TEST06 CIRCLE_SEGMENT_SAMPLE_FROM_HEIGHT samples a circle segment. Plot 100 points from several segments. Created graphics file "sample_t3.14159.png". Created graphics file "sample_t1.5708.png". Created graphics file "sample_t0.785398.png". Created graphics file "sample_t0.392699.png". CIRCLE_SEGMENT_TEST07 For circle segment with a given radius R, CIRCLE_SEGMENT_ANGLE_FROM_HEIGHT computes the angle THETA, given the height. CIRCLE_SEGMENT_HEIGHT_FROM_ANGLE computes height H, given the angle. Check that these functions are inverses of each other using random values of R, T, and H. R H => T => H2 3.946820 2.902120 2.605819 2.902120 1.030139 0.178557 1.195276 0.178557 3.859670 1.587671 1.882815 1.587671 1.941358 2.142400 3.349079 2.142400 1.144766 1.469744 3.717272 1.469744 R T => H => T2 2.422402 0.954074 0.270438 0.954074 3.909660 0.632128 0.193660 0.632128 1.470332 1.491459 0.390236 1.491459 2.654361 0.574903 0.108910 0.574903 2.026577 0.658768 0.108945 0.658768 CIRCLE_SEGMENT_TEST08 CIRCLE_SEGMENT_CONTAINS_POINT reports whether a circle segment contains a point. Pick a circle segment at random. Compute 1000 sample points in the surrounding box. Compare the area of the segment to the percentage of points contained in the circle segment. N Omega1 Omega2 Area Estimate 1000 0.705501 4.92871 2.55296 2.572 1000 5.7974 9.71682 2.31057 2.428 1000 1.67965 6.09144 2.68348 2.764 1000 3.28266 3.87919 0.0173771 0.012 1000 2.6719 3.86032 0.130319 0.128 CIRCLE_SEGMENT_TEST09 CIRCLE_SEGMENT_AREA_FROM_CHORD and CIRCLE_SEGMENT_CENTROID_FROM_CHORD evaluate the area and centroid of a circle segment, given R, C and P1:P2. CIRCLE_SEGMENT_AREA_FROM_SAMPLE and CIRCLE_SEGMENT_CENTROID_FROM_SAMPLE give us Monte Carlo estimates. GQCIRCSEGM can estimate these values by quadrature. Start easy, with R = 1, C = (0,0), and Theta centered. Area CentroidX CentroidY 0.0391457 0.954429 5.29815e-17 0.0391457 0.954429 -0 0.0402124 0.954336 -0.00161192 CIRCLE_SEGMENT_TEST10 GQCIRCSEGM computes a Gauss quadrature rule for a circle segment with circle of radius R and center (0,0), with segment angles in [-theta/2,+theta/2]. Radius R = 1 Angle Theta = 0.785398 Estimate the integral of (x+y+2)^k using QUAD2D. K 0 0.039146.5 1 0.115653.5 2 0.342862.5 3 1.019859.5 4 3.043618.5 5 9.112436.5 6 27.367568.5 7 82.443510.5 8 249.089055.5 9 754.725272.5 10 2293.066015.5 11 6985.452528.5 CIRCLE_SEGMENT_TEST11: CIRCLE_SEGMENT_ROTATION_FROM_CHORD is given the endpoints of a chord, and is asked to determine the angle of the central radius vector. We make a table of all pairs of angles that are multiples of pi/12, determine the corresponding chord endpoints, and compute the rotation angle, also printed as a multiple of pi/12. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 0.0: 6.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1.0: 6.5 7.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 2.0: 7.0 7.5 8.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 3.0: 7.5 8.0 8.5 9.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 4.0: 8.0 8.5 9.0 9.5 10.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 5.0: 8.5 9.0 9.5 10.0 10.5 11.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 6.0: 9.0 9.5 10.0 10.5 11.0 11.5 0.0 6.5 7.0 7.5 8.0 8.5 9.0 7.0: -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 -4.5 -4.0 -3.5 -3.0 -2.5 8.0: -2.0 -1.5 -1.0 -0.5 -0.0 0.5 1.0 1.5 2.0 -3.5 -3.0 -2.5 -2.0 9.0: -1.5 -1.0 -0.5 -0.0 0.5 1.0 1.5 2.0 2.5 3.0 -2.5 -2.0 -1.5 10.0: -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 -1.5 -1.0 11.0: -0.5 -0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -0.5 12.0: -0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 CIRCLE_SEGMENT_TEST12 CIRCLE_SEGMENT_RULE_FROM_CHORD computes a quadrature rule for a circle segment of radius R, center C, chord P1:P2, algebraic precision P. Plot some such rules. Created graphics image "test12_rule1.png". Created graphics image "test12_rule2.png". CIRCLE_SEGMENT_TEST13 GAUSS computes the points and weights for a Gauss quadrature rule, given the ALPHA and BETA recursion coefficients. LEGENDRE RULE Point Weight -0.973907 0.0666713 -0.865063 0.149451 -0.67941 0.219086 -0.433395 0.269267 -0.148874 0.295524 0.148874 0.295524 0.433395 0.269267 0.67941 0.219086 0.865063 0.149451 0.973907 0.0666713 HERMITE RULE Point Weight -3.43616 7.64043e-06 -2.53273 0.00134365 -1.75668 0.0338744 -1.03661 0.240139 -0.342901 0.610863 0.342901 0.610863 1.03661 0.240139 1.75668 0.0338744 2.53273 0.00134365 3.43616 7.64043e-06 LAGUERRE RULE Point Weight 0.137793 0.308441 0.729455 0.40112 1.80834 0.218068 3.40143 0.0620875 5.5525 0.00950152 8.33015 0.000753008 11.8438 2.82592e-05 16.2793 4.24931e-07 21.9966 1.83956e-09 29.9207 9.91183e-13 CIRCLE_SEGMENT_TEST14 R_JACOBI computes recursion coefficients ALPHA and BETA for a Jacobi weight w(x)=(1-x)^A * (1+x)^B. Legendre A = 0, B = 0 Alpha Beta 0 2 0 0.333333 0 0.266667 0 0.257143 0 0.253968 0 0.252525 0 0.251748 0 0.251282 0 0.25098 0 0.250774 Chebyshev Type 1 A = -0.5, B = -0.5 Alpha Beta 0 3.14159 0 0.5 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 Chebyshev Type 2 A = 0.5, B = 0.5 Alpha Beta 0 1.5708 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 0 0.25 General Jacobi weight A = 0.5, B = 1.5 Alpha Beta 0.25 1.5708 0.0833333 0.1875 0.0416667 0.222222 0.025 0.234375 0.0166667 0.24 0.0119048 0.243056 0.00892857 0.244898 0.00694444 0.246094 0.00555556 0.246914 0.00454545 0.2475 CIRCLE_SEGMENT_TEST17 Demonstrate GQCIRCSECT. Created graphics image "test16_acute.png". Created graphics image "test16_obtuse.png". CIRCLE_SEGMENT_TEST17 Demonstrate GQCIRCSEGM. Created graphics image "test17.png". CIRCLE_SEGMENT_TEST Normal end of execution. 07-Jan-2022 18:09:34