rvg-gaussian-quadrature.cpp

// Stroke-to-fill conversion program and test harness
// Copyright (C) 2020 Diego Nehab
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published
// by the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// Contact information: diego.nehab@gmail.com
//
#include "rvg-gaussian-quadrature.h"

namespace rvg {

const std::array<std::pair<double,double>,525> gaussian_quadrature_weights = {
  {
	{0.112702,0.277778},
    {0.5,0.444444},
    {0.887298,0.277778},
    {0.0694318,0.173927},
    {0.330009,0.326073},
    {0.669991,0.326073},
    {0.930568,0.173927},
    {0.0469101,0.118463},
    {0.230765,0.239314},
    {0.5,0.284444},
    {0.769235,0.239314},
    {0.95309,0.118463},
    {0.0337652,0.0856622},
    {0.169395,0.180381},
    {0.38069,0.233957},
    {0.61931,0.233957},
    {0.830605,0.180381},
    {0.966235,0.0856622},
    {0.025446,0.0647425},
    {0.129234,0.139853},
    {0.297077,0.190915},
    {0.5,0.20898},
    {0.702923,0.190915},
    {0.870766,0.139853},
    {0.974554,0.0647425},
    {0.0198551,0.0506143},
    {0.101667,0.111191},
    {0.237234,0.156853},
    {0.408283,0.181342},
    {0.591717,0.181342},
    {0.762766,0.156853},
    {0.898333,0.111191},
    {0.980145,0.0506143},
    {0.0159199,0.0406372},
    {0.0819844,0.0903241},
    {0.193314,0.130305},
    {0.337873,0.156174},
    {0.5,0.16512},
    {0.662127,0.156174},
    {0.806686,0.130305},
    {0.918016,0.0903241},
    {0.98408,0.0406372},
    {0.0130467,0.0333357},
    {0.0674683,0.0747257},
    {0.160295,0.109543},
    {0.283302,0.134633},
    {0.425563,0.147762},
    {0.574437,0.147762},
    {0.716698,0.134633},
    {0.839705,0.109543},
    {0.932532,0.0747257},
    {0.986953,0.0333357},
    {0.0108857,0.0278343},
    {0.0564687,0.0627902},
    {0.134924,0.0931451},
    {0.240452,0.116597},
    {0.365228,0.131402},
    {0.5,0.136463},
    {0.634772,0.131402},
    {0.759548,0.116597},
    {0.865076,0.0931451},
    {0.943531,0.0627902},
    {0.989114,0.0278343},
    {0.00921968,0.0235877},
    {0.0479414,0.0534697},
    {0.115049,0.0800392},
    {0.206341,0.101584},
    {0.316084,0.116746},
    {0.437383,0.124574},
    {0.562617,0.124574},
    {0.683916,0.116746},
    {0.793659,0.101584},
    {0.884951,0.0800392},
    {0.952059,0.0534697},
    {0.99078,0.0235877},
    {0.00790847,0.020242},
    {0.0412008,0.0460607},
    {0.099211,0.0694368},
    {0.178825,0.089073},
    {0.275754,0.103908},
    {0.384771,0.113142},
    {0.5,0.116276},
    {0.615229,0.113142},
    {0.724246,0.103908},
    {0.821175,0.089073},
    {0.900789,0.0694368},
    {0.958799,0.0460607},
    {0.992092,0.020242},
    {0.0068581,0.0175597},
    {0.0357826,0.040079},
    {0.0863993,0.0607593},
    {0.156354,0.0786016},
    {0.242376,0.0927692},
    {0.340444,0.102599},
    {0.445973,0.107632},
    {0.554027,0.107632},
    {0.659556,0.102599},
    {0.757624,0.0927692},
    {0.843646,0.0786016},
    {0.913601,0.0607593},
    {0.964217,0.040079},
    {0.993142,0.0175597},
    {0.00600374,0.0153766},
    {0.0313633,0.035183},
    {0.0758967,0.0535796},
    {0.137791,0.0697853},
    {0.214514,0.0831346},
    {0.302924,0.0930805},
    {0.399403,0.0992157},
    {0.5,0.101289},
    {0.600597,0.0992157},
    {0.697076,0.0930805},
    {0.785486,0.0831346},
    {0.862209,0.0697853},
    {0.924103,0.0535796},
    {0.968637,0.035183},
    {0.993996,0.0153766},
    {0.00529953,0.0135762},
    {0.0277125,0.0311268},
    {0.0671844,0.0475793},
    {0.122298,0.0623145},
    {0.191062,0.074798},
    {0.270992,0.0845783},
    {0.359198,0.0913017},
    {0.452494,0.0947253},
    {0.547506,0.0947253},
    {0.640802,0.0913017},
    {0.729008,0.0845783},
    {0.808938,0.074798},
    {0.877702,0.0623145},
    {0.932816,0.0475793},
    {0.972288,0.0311268},
    {0.9947,0.0135762},
    {0.00471226,0.0120742},
    {0.0246622,0.0277298},
    {0.0598804,0.0425181},
    {0.109243,0.0559419},
    {0.171164,0.0675682},
    {0.243655,0.0770229},
    {0.324384,0.0840021},
    {0.410758,0.0882814},
    {0.5,0.0897232},
    {0.589242,0.0882814},
    {0.675616,0.0840021},
    {0.756345,0.0770229},
    {0.828836,0.0675682},
    {0.890757,0.0559419},
    {0.94012,0.0425181},
    {0.975338,0.0277298},
    {0.995288,0.0120742},
    {0.00421742,0.010808},
    {0.022088,0.0248573},
    {0.0536988,0.0382129},
    {0.0981475,0.050471},
    {0.154156,0.0612776},
    {0.220115,0.0703215},
    {0.294124,0.0773423},
    {0.374057,0.0821382},
    {0.457612,0.0845712},
    {0.542388,0.0845712},
    {0.625943,0.0821382},
    {0.705876,0.0773423},
    {0.779885,0.0703215},
    {0.845844,0.0612776},
    {0.901852,0.050471},
    {0.946301,0.0382129},
    {0.977912,0.0248573},
    {0.995783,0.010808},
    {0.00379658,0.00973089},
    {0.0198959,0.0224071},
    {0.048422,0.0345223},
    {0.0886427,0.045745},
    {0.139517,0.0557833},
    {0.199727,0.064377},
    {0.267715,0.0713034},
    {0.341718,0.076383},
    {0.419821,0.0794844},
    {0.5,0.0805272},
    {0.580179,0.0794844},
    {0.658282,0.076383},
    {0.732285,0.0713034},
    {0.800273,0.064377},
    {0.860483,0.0557833},
    {0.911357,0.045745},
    {0.951578,0.0345223},
    {0.980104,0.0224071},
    {0.996203,0.00973089},
    {0.0034357,0.008807},
    {0.018014,0.0203007},
    {0.0438828,0.031336},
    {0.0804415,0.0416384},
    {0.126834,0.0509651},
    {0.181973,0.0590973},
    {0.244566,0.0658443},
    {0.313147,0.0710481},
    {0.386107,0.0745865},
    {0.461737,0.0763767},
    {0.538263,0.0763767},
    {0.613893,0.0745865},
    {0.686853,0.0710481},
    {0.755434,0.0658443},
    {0.818027,0.0590973},
    {0.873166,0.0509651},
    {0.919558,0.0416384},
    {0.956117,0.031336},
    {0.981986,0.0203007},
    {0.996564,0.008807},
    {0.00312391,0.00800861},
    {0.0163866,0.0184769},
    {0.0399503,0.0285672},
    {0.0733183,0.0380501},
    {0.11578,0.0467222},
    {0.166431,0.0543986},
    {0.224191,0.0609157},
    {0.287829,0.0661345},
    {0.355989,0.0699437},
    {0.427219,0.0722622},
    {0.5,0.0730406},
    {0.572781,0.0722622},
    {0.644011,0.0699437},
    {0.712171,0.0661345},
    {0.775809,0.0609157},
    {0.833569,0.0543986},
    {0.88422,0.0467222},
    {0.926682,0.0380501},
    {0.96005,0.0285672},
    {0.983613,0.0184769},
    {0.996876,0.00800861},
    {0.00285271,0.007314},
    {0.0149698,0.0168875},
    {0.0365216,0.0261467},
    {0.0670937,0.0348982},
    {0.106092,0.0429708},
    {0.152756,0.0502071},
    {0.20618,0.0564661},
    {0.265322,0.0616262},
    {0.329032,0.0655868},
    {0.39607,0.0682707},
    {0.46513,0.0696259},
    {0.53487,0.0696259},
    {0.60393,0.0682707},
    {0.670968,0.0655868},
    {0.734678,0.0616262},
    {0.79382,0.0564661},
    {0.847244,0.0502071},
    {0.893908,0.0429708},
    {0.932906,0.0348982},
    {0.963478,0.0261467},
    {0.98503,0.0168875},
    {0.997147,0.007314},
    {0.00261533,0.00670593},
    {0.0137288,0.015494},
    {0.0335145,0.0240188},
    {0.0616238,0.0321162},
    {0.0975558,0.0396407},
    {0.140669,0.0464579},
    {0.190195,0.052446},
    {0.245249,0.0574983},
    {0.304849,0.0615245},
    {0.367932,0.0644529},
    {0.433372,0.066231},
    {0.5,0.0668273},
    {0.566628,0.066231},
    {0.632068,0.0644529},
    {0.695151,0.0615245},
    {0.754751,0.0574983},
    {0.809805,0.052446},
    {0.859331,0.0464579},
    {0.902444,0.0396407},
    {0.938376,0.0321162},
    {0.966486,0.0240188},
    {0.986271,0.015494},
    {0.997385,0.00670593},
    {0.00240639,0.00617061},
    {0.0126357,0.0142657},
    {0.0308627,0.0221387},
    {0.0567922,0.0296493},
    {0.089999,0.0366732},
    {0.129938,0.0430951},
    {0.175953,0.0488093},
    {0.227289,0.0537221},
    {0.283103,0.0577528},
    {0.342479,0.0608352},
    {0.404441,0.0629187},
    {0.467972,0.0639691},
    {0.532028,0.0639691},
    {0.595559,0.0629187},
    {0.657521,0.0608352},
    {0.716897,0.0577528},
    {0.772711,0.0537221},
    {0.824047,0.0488093},
    {0.870062,0.0430951},
    {0.910001,0.0366732},
    {0.943208,0.0296493},
    {0.969137,0.0221387},
    {0.987364,0.0142657},
    {0.997594,0.00617061},
    {0.00222152,0.0056969},
    {0.011668,0.0131775},
    {0.0285127,0.0204696},
    {0.052504,0.0274523},
    {0.0832787,0.0340192},
    {0.12037,0.0400704},
    {0.163217,0.0455141},
    {0.211169,0.050268},
    {0.263499,0.0542598},
    {0.319414,0.0574291},
    {0.378067,0.0597279},
    {0.438568,0.0611212},
    {0.5,0.061588},
    {0.561432,0.0611212},
    {0.621933,0.0597279},
    {0.680586,0.0574291},
    {0.736501,0.0542598},
    {0.788831,0.050268},
    {0.836783,0.0455141},
    {0.87963,0.0400704},
    {0.916721,0.0340192},
    {0.947496,0.0274523},
    {0.971487,0.0204696},
    {0.988332,0.0131775},
    {0.997778,0.0056969},
    {0.00205715,0.00527569},
    {0.0108073,0.0122089},
    {0.0264205,0.0189812},
    {0.0486811,0.0254879},
    {0.077277,0.031637},
    {0.111807,0.0373421},
    {0.151786,0.0425229},
    {0.196654,0.0471069},
    {0.24578,0.0510296},
    {0.298474,0.0542359},
    {0.353998,0.0566809},
    {0.411571,0.0583302},
    {0.470385,0.0591607},
    {0.529615,0.0591607},
    {0.588429,0.0583302},
    {0.646002,0.0566809},
    {0.701526,0.0542359},
    {0.75422,0.0510296},
    {0.803346,0.0471069},
    {0.848214,0.0425229},
    {0.888193,0.0373421},
    {0.922723,0.031637},
    {0.951319,0.0254879},
    {0.97358,0.0189812},
    {0.989193,0.0122089},
    {0.997943,0.00527569},
    {0.00191037,0.0048995},
    {0.0100383,0.0113431},
    {0.0245497,0.0176485},
    {0.0452588,0.0237247},
    {0.071896,0.0294918},
    {0.104114,0.0348744},
    {0.141493,0.0398024},
    {0.183546,0.0442116},
    {0.229724,0.0480444},
    {0.279426,0.0512508},
    {0.332003,0.0537891},
    {0.38677,0.0556262},
    {0.443014,0.0567382},
    {0.5,0.0571104},
    {0.556986,0.0567382},
    {0.61323,0.0556262},
    {0.667997,0.0537891},
    {0.720574,0.0512508},
    {0.770276,0.0480444},
    {0.816454,0.0442116},
    {0.858507,0.0398024},
    {0.895886,0.0348744},
    {0.928104,0.0294918},
    {0.954741,0.0237247},
    {0.97545,0.0176485},
    {0.989962,0.0113431},
    {0.99809,0.0048995},
    {0.00177875,0.00456214},
    {0.00934842,0.0105661},
    {0.0228704,0.0164507},
    {0.0421835,0.0221365},
    {0.0670537,0.0275537},
    {0.0971793,0.0326365},
    {0.132195,0.0373231},
    {0.171674,0.0415567},
    {0.21514,0.0452859},
    {0.262063,0.0484653},
    {0.311874,0.0510565},
    {0.363969,0.0530279},
    {0.417715,0.0543556},
    {0.47246,0.0550235},
    {0.52754,0.0550235},
    {0.582285,0.0543556},
    {0.636031,0.0530279},
    {0.688126,0.0510565},
    {0.737937,0.0484653},
    {0.78486,0.0452859},
    {0.828326,0.0415567},
    {0.867805,0.0373231},
    {0.902821,0.0326365},
    {0.932946,0.0275537},
    {0.957817,0.0221365},
    {0.97713,0.0164507},
    {0.990652,0.0105661},
    {0.998221,0.00456214},
    {0.00166028,0.00425845},
    {0.00872725,0.00986604},
    {0.0213572,0.0153702},
    {0.0394099,0.020701},
    {0.0626811,0.0257974},
    {0.0909073,0.0306015},
    {0.123769,0.035059},
    {0.160893,0.0391192},
    {0.201859,0.0427361},
    {0.246204,0.0458689},
    {0.293424,0.0484819},
    {0.342984,0.0505456},
    {0.394324,0.0520367},
    {0.446861,0.0529381},
    {0.5,0.0532397},
    {0.553139,0.0529381},
    {0.605676,0.0520367},
    {0.657016,0.0505456},
    {0.706576,0.0484819},
    {0.753796,0.0458689},
    {0.798141,0.0427361},
    {0.839107,0.0391192},
    {0.876231,0.035059},
    {0.909093,0.0306015},
    {0.937319,0.0257974},
    {0.96059,0.020701},
    {0.978643,0.0153702},
    {0.991273,0.00986604},
    {0.99834,0.00425845},
    {0.00155326,0.0039841},
    {0.00816594,0.00923323},
    {0.0199891,0.0143924},
    {0.0369,0.0193996},
    {0.0587197,0.0242013},
    {0.0852171,0.0287466},
    {0.116111,0.0329871},
    {0.151075,0.036878},
    {0.189737,0.0403779},
    {0.231688,0.0434499},
    {0.276483,0.0460613},
    {0.323648,0.0481844},
    {0.372682,0.0497967},
    {0.423065,0.0508812},
    {0.474264,0.0514263},
    {0.525736,0.0514263},
    {0.576935,0.0508812},
    {0.627318,0.0497967},
    {0.676352,0.0481844},
    {0.723517,0.0460613},
    {0.768312,0.0434499},
    {0.810263,0.0403779},
    {0.848925,0.036878},
    {0.883889,0.0329871},
    {0.914783,0.0287466},
    {0.94128,0.0242013},
    {0.9631,0.0193996},
    {0.980011,0.0143924},
    {0.991834,0.00923323},
    {0.998447,0.0039841},
    {0.00145626,0.00373542},
    {0.00765705,0.00865931},
    {0.018748,0.0135045},
    {0.0346215,0.0182161},
    {0.05512,0.0227469},
    {0.0800398,0.0270515},
    {0.109133,0.0310874},
    {0.142112,0.0348143},
    {0.178647,0.0381952},
    {0.218375,0.0411965},
    {0.260903,0.0437884},
    {0.305807,0.0459451},
    {0.352641,0.0476451},
    {0.400939,0.0488717},
    {0.450222,0.0496125},
    {0.5,0.0498603},
    {0.549778,0.0496125},
    {0.599061,0.0488717},
    {0.647359,0.0476451},
    {0.694193,0.0459451},
    {0.739097,0.0437884},
    {0.781625,0.0411965},
    {0.821353,0.0381952},
    {0.857888,0.0348143},
    {0.890867,0.0310874},
    {0.91996,0.0270515},
    {0.94488,0.0227469},
    {0.965378,0.0182161},
    {0.981252,0.0135045},
    {0.992343,0.00865931},
    {0.998544,0.00373542},
    {0.00136807,0.00350931},
    {0.00719424,0.0081372},
    {0.0176189,0.012696},
    {0.032547,0.0171369},
    {0.0518394,0.0214179},
    {0.0753162,0.025499},
    {0.102758,0.029342},
    {0.133909,0.0329111},
    {0.168478,0.0361729},
    {0.206142,0.0390969},
    {0.24655,0.041656},
    {0.289324,0.043826},
    {0.334066,0.0455869},
    {0.380356,0.0469222},
    {0.427764,0.0478194},
    {0.475846,0.04827},
    {0.524154,0.04827},
    {0.572236,0.0478194},
    {0.619644,0.0469222},
    {0.665934,0.0455869},
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};

}