/* triquad_int.c  compute integration points for order 1..6    */
/*                Gauss Legendre over triangle                 */ 
/*                1 <= n <=8 at this time                      */
/*                nn returned is n*n                           */
/*                integral = sum i=0 to nn-1 W[i]*f(X[i],Y[i]) */
/*                table for right regular triangle 0,0 0,1 1,0 */
/*                T[] is target x1, y1, x2, y2, x3, y3         */
/*                X[] and Y[] returned in T[] coordinates      */


#include "triquad_int.h"


int tquad_int(int n, double T[], double X[], double Y[], double W[])
{
  return triquad_int(n, T[0], T[1], T[2], T[3], T[4], T[5], X, Y, W);
}

#undef abs
#define abs(a) ((a)<0.0?(-(a)):(a))

/* data for vert = [0 0; 0 1; 1 0]  nth order */
static double tq1[1][3] = {
      {0.333333333333333, 0.333333333333333, 1.000000000000000}};

static double tq2[4][3] = {
      {0.280019915499074, 0.075031110222608, 0.181958618256023},
      {0.075031110222608, 0.280019915499074, 0.181958618256023},
      {0.666390246014701, 0.178558728263616, 0.318041381743977},
      {0.178558728263616, 0.666390246014701, 0.318041381743977}};

static double tq3[9][3] = {
      {0.188409405952072, 0.023931132287081, 0.038792766611919},
      {0.106170269119576, 0.106170269119576, 0.062068426579070},
      {0.023931132287081, 0.188409405952072, 0.038792766611919},
      {0.523979067720101, 0.066554067839164, 0.127356170199770},
      {0.295266567779633, 0.295266567779633, 0.203769872319632},
      {0.066554067839165, 0.523979067720101, 0.127356170199770},
      {0.808694385677670, 0.102717654809626, 0.111628840966088},
      {0.455706020243648, 0.455706020243648, 0.178606145545742},
      {0.102717654809626, 0.808694385677670, 0.111628840966088}};

static double tq4[16][3] = {
      {0.130056079216834, 0.009703785126946, 0.010846451821050},
      {0.093637784437329, 0.046122079906452, 0.020334519128958},
      {0.046122079906452, 0.093637784437329, 0.020334519128958},
      {0.009703785126946, 0.130056079216834, 0.010846451821050},
      {0.387497483406694, 0.028912084224389, 0.045168098564740},
      {0.278990463496509, 0.137419104134574, 0.084679449043493},
      {0.137419104134574, 0.278990463496509, 0.084679449043493},
      {0.028912084224389, 0.387497483406694, 0.045168098564740},
      {0.672946863150506, 0.050210123211370, 0.070776135796172},
      {0.484508326630433, 0.238648659731443, 0.132688432214099},
      {0.238648659731443, 0.484508326630433, 0.132688432214099},
      {0.050210123211370, 0.672946863150506, 0.070776135796172},
      {0.877428809330468, 0.065466994555014, 0.047136736386764},
      {0.631731251641125, 0.311164552244357, 0.088370177044723},
      {0.311164552244357, 0.631731251641125, 0.088370177044723},
      {0.065466994555014, 0.877428809330468, 0.047136736386764}};

static double tq5[25][3] = {
      {0.093912797333780, 0.004622288465046, 0.003731104333756},
      {0.075796602735062, 0.022738483063764, 0.007537403390655},
      {0.049267542899413, 0.049267542899413, 0.008958813594563},
      {0.022738483063764, 0.075796602735062, 0.007537403390655},
      {0.004622288465046, 0.093912797333780, 0.003731104333756},
      {0.290249932250793, 0.014285794395571, 0.017510998364328},
      {0.234259434638082, 0.070276292008282, 0.035374904220967},
      {0.152267863323182, 0.152267863323182, 0.042045934974644},
      {0.070276292008282, 0.234259434638082, 0.035374904220967},
      {0.014285794395571, 0.290249932250793, 0.017510998364328},
      {0.535660544808143, 0.026364644944471, 0.034683012862731},
      {0.432329252970360, 0.129695936782254, 0.070065009006743},
      {0.281012594876307, 0.281012594876307, 0.083277930430390},
      {0.129695936782254, 0.432329252970360, 0.070065009006743},
      {0.026364644944471, 0.535660544808143, 0.034683012862731},
      {0.764365329781281, 0.037621252345111, 0.039608166264095},
      {0.616915871859003, 0.185070710267389, 0.080014574772321},
      {0.400993291063196, 0.400993291063196, 0.095103794115908},
      {0.185070710267390, 0.616915871859003, 0.080014574772321},
      {0.037621252345111, 0.764365329781281, 0.039608166264095},
      {0.915147549378727, 0.045042593569804, 0.022930160703185},
      {0.738611533396152, 0.221578609552379, 0.046322443858997},
      {0.480095071474266, 0.480095071474266, 0.055057971328939},
      {0.221578609552379, 0.738611533396152, 0.046322443858997},
      {0.045042593569804, 0.915147549378727, 0.022930160703185}};

static double tq6[36][3] = {
      {0.070587631527589, 0.002466697152670, 0.001497085122473},
      {0.060679268262819, 0.012375060417440, 0.003152443508047},
      {0.045243246564898, 0.027811082115361, 0.004088773183090},
      {0.027811082115361, 0.045243246564898, 0.004088773183090},
      {0.012375060417440, 0.060679268262819, 0.003152443508047},
      {0.002466697152670, 0.070587631527589, 0.001497085122473},
      {0.222974263268659, 0.007791874701286, 0.007530596425383},
      {0.191675437237121, 0.039090700732824, 0.015857334667593},
      {0.142915682993948, 0.087850454975997, 0.020567234457533},
      {0.087850454975997, 0.142915682993948, 0.020567234457533},
      {0.039090700732824, 0.191675437237121, 0.015857334667593},
      {0.007791874701286, 0.222974263268659, 0.007530596425383},
      {0.426426917861779, 0.014901563366671, 0.016903071593886},
      {0.366569507765801, 0.074758973462649, 0.035593151994053},
      {0.273318962107258, 0.168009519121192, 0.046164927302717},
      {0.168009519121192, 0.273318962107258, 0.046164927302717},
      {0.074758973462649, 0.366569507765801, 0.035593151994053},
      {0.014901563366671, 0.426426917861779, 0.016903071593886},
      {0.640628436740815, 0.022386872978031, 0.024121212808530},
      {0.550703627937892, 0.112311681780954, 0.050792543178095},
      {0.410611741642328, 0.252403568076518, 0.065878797801573},
      {0.252403568076518, 0.410611741642328, 0.065878797801573},
      {0.112311681780954, 0.550703627937892, 0.050792543178095},
      {0.022386872978031, 0.640628436740815, 0.024121212808530},
      {0.823156067318957, 0.028765333012559, 0.023221749533995},
      {0.707609913381099, 0.144311486950417, 0.048898524516116},
      {0.527603095742740, 0.324318304588776, 0.063422223181408},
      {0.324318304588776, 0.527603095742740, 0.063422223181408},
      {0.144311486950417, 0.707609913381099, 0.048898524516116},
      {0.028765333012559, 0.823156067318957, 0.023221749533995},
      {0.937908206225755, 0.032775366614460, 0.012388530705318},
      {0.806254331245388, 0.164429241594828, 0.026086788660166},
      {0.601153648467838, 0.369529924372377, 0.033835011360025},
      {0.369529924372377, 0.601153648467838, 0.033835011360025},
      {0.164429241594828, 0.806254331245388, 0.026086788660166},
      {0.032775366614460, 0.937908206225755, 0.012388530705318}};

static double tq7[49][3] = {
      {0.054830900955589, 0.001431659581333, 0.000675181513423},
      {0.048991501878362, 0.007271058658560, 0.001458485221303},
      {0.039548223967455, 0.016714336569468, 0.001991000183250},
      {0.028131280268461, 0.028131280268461, 0.002179390569663},
      {0.016714336569468, 0.039548223967455, 0.001991000183250},
      {0.007271058658560, 0.048991501878362, 0.001458485221303},
      {0.001431659581333, 0.054830900955589, 0.000675181513423},
      {0.175654279195255, 0.004586412541638, 0.003548970142876},
      {0.156947392786903, 0.023293298949990, 0.007666265146969},
      {0.126695251279609, 0.053545440457283, 0.010465334231375},
      {0.090120345868446, 0.090120345868446, 0.011455574401305},
      {0.053545440457283, 0.126695251279609, 0.010465334231375},
      {0.023293298949990, 0.156947392786903, 0.007666265146969},
      {0.004586412541638, 0.175654279195255, 0.003548970142876},
      {0.343651813106453, 0.008972904006717, 0.008595820175965},
      {0.307053470832875, 0.045571246280295, 0.018568157513777},
      {0.247867874404688, 0.104756842708482, 0.025347672004186},
      {0.176312358556585, 0.176312358556585, 0.027746093543128},
      {0.104756842708482, 0.247867874404688, 0.025347672004186},
      {0.045571246280295, 0.307053470832875, 0.018568157513777},
      {0.008972904006717, 0.343651813106453, 0.008595820175965},
      {0.533230731173959, 0.013922895156596, 0.013871085507468},
      {0.476442551784230, 0.070711074546325, 0.029963458438779},
      {0.384606636317686, 0.162546990012870, 0.040903569245020},
      {0.273576813165278, 0.273576813165278, 0.044773905009214},
      {0.162546990012870, 0.384606636317686, 0.040903569245020},
      {0.070711074546325, 0.476442551784230, 0.029963458438779},
      {0.013922895156596, 0.533230731173959, 0.013871085507468},
      {0.715527432866568, 0.018682744348843, 0.016495206027059},
      {0.639324960202548, 0.094885217012863, 0.035631920801352},
      {0.516092908865112, 0.218117268350298, 0.048641672749794},
      {0.367105088607705, 0.367105088607705, 0.053244195442767},
      {0.218117268350298, 0.516092908865112, 0.048641672749794},
      {0.094885217012863, 0.639324960202548, 0.035631920801352},
      {0.018682744348843, 0.715527432866568, 0.016495206027059},
      {0.862793031223432, 0.022527915615664, 0.014309287558192},
      {0.770907019092335, 0.114413927746761, 0.030910035325468},
      {0.622312080263295, 0.263008866575801, 0.042195755636305},
      {0.442660473419548, 0.442660473419548, 0.046188359341819},
      {0.263008866575801, 0.622312080263295, 0.042195755636305},
      {0.114413927746761, 0.770907019092335, 0.030910035325468},
      {0.022527915615664, 0.862793031223432, 0.014309287558192},
      {0.952646581185227, 0.024874032376061, 0.007246932159451},
      {0.851191316541618, 0.126329297019669, 0.015654373296990},
      {0.687121307473297, 0.290399306087990, 0.021370021202630},
      {0.488760306780644, 0.488760306780644, 0.023392073528839},
      {0.290399306087990, 0.687121307473297, 0.021370021202630},
      {0.126329297019669, 0.851191316541618, 0.015654373296990},
      {0.024874032376061, 0.952646581185227, 0.007246932159451}};

static double tq8[64][3] = {
      {0.043747744905146, 0.000886210384824, 0.000333567406495},
      {0.040096165611934, 0.004537789678036, 0.000732788081649},
      {0.034045272688803, 0.010588682601167, 0.001033723454873},
      {0.026410684460876, 0.018223270829094, 0.001195112499231},
      {0.018223270829094, 0.026410684460876, 0.001195112499231},
      {0.010588682601167, 0.034045272688803, 0.001033723454873},
      {0.004537789678036, 0.040096165611934, 0.000732788081649},
      {0.000886210384824, 0.043747744905146, 0.000333567406495},
      {0.141499854650117, 0.002866402392029, 0.001806210919037},
      {0.129689007248651, 0.014677249793495, 0.003967923150289},
      {0.110117702008052, 0.034248555034093, 0.005597437144935},
      {0.085424014895553, 0.058942242146592, 0.006471331441725},
      {0.058942242146592, 0.085424014895553, 0.006471331441725},
      {0.034248555034093, 0.110117702008052, 0.005597437144935},
      {0.014677249793495, 0.129689007248651, 0.003967923150289},
      {0.002866402392029, 0.141499854650117, 0.001806210919037},
      {0.281129831011298, 0.005694926133132, 0.004599755803491},
      {0.257664213026852, 0.029160544117579, 0.010104842876312},
      {0.218780231495104, 0.068044525649326, 0.014254616512793},
      {0.169719176965060, 0.117105580179370, 0.016480104312102},
      {0.117105580179370, 0.169719176965060, 0.016480104312102},
      {0.068044525649326, 0.218780231495104, 0.014254616512793},
      {0.029160544117579, 0.257664213026852, 0.010104842876312},
      {0.005694926133132, 0.281129831011298, 0.004599755803491},
      {0.445782964189930, 0.009030351006644, 0.008017259531392},
      {0.408573918447520, 0.046239396749053, 0.017612488863395},
      {0.346916226396932, 0.107897088799642, 0.024845440711608},
      {0.269120916535959, 0.185692398660614, 0.028724410385925},
      {0.185692398660614, 0.269120916535959, 0.028724410385925},
      {0.107897088799642, 0.346916226396932, 0.024845440711608},
      {0.046239396749053, 0.408573918447521, 0.017612488863395},
      {0.009030351006644, 0.445782964189930, 0.008017259531392},
      {0.615597503479888, 0.012470331936840, 0.010735018973159},
      {0.564214212717487, 0.063853622699241, 0.023582921492411},
      {0.479068919277106, 0.148998916139621, 0.033267761432852},
      {0.371638617134706, 0.256429218282022, 0.038461657537508},
      {0.256429218282022, 0.371638617134706, 0.038461657537508},
      {0.148998916139621, 0.479068919277106, 0.033267761432852},
      {0.063853622699241, 0.564214212717487, 0.023582921492411},
      {0.012470331936840, 0.615597503479888, 0.010735018973159},
      {0.770091559088435, 0.015599961515934, 0.011388797404617},
      {0.705812808329004, 0.079878712275365, 0.025019156068340},
      {0.599298939439204, 0.186392581165165, 0.035293816993822},
      {0.464907281899148, 0.320784238705222, 0.040804029004109},
      {0.320784238705222, 0.464907281899148, 0.040804029004109},
      {0.186392581165165, 0.599298939439204, 0.035293816993822},
      {0.079878712275365, 0.705812808329004, 0.025019156068340},
      {0.015599961515934, 0.770091559088435, 0.011388797404617},
      {0.890634557136406, 0.018041834963800, 0.009223845390918},
      {0.816294206251800, 0.092382185848406, 0.020263142734638},
      {0.693107643137351, 0.215568748962855, 0.028584643280635},
      {0.537679560614672, 0.370996831485534, 0.033047392230182},
      {0.370996831485534, 0.537679560614672, 0.033047392230182},
      {0.215568748962855, 0.693107643137351, 0.028584643280635},
      {0.092382185848406, 0.816294206251800, 0.020263142734638},
      {0.018041834963800, 0.890634557136406, 0.009223845390918},
      {0.962718034592387, 0.019502050260250, 0.004509812716079},
      {0.882360949948550, 0.099859134904086, 0.009907253959653},
      {0.749204286556732, 0.233015798295905, 0.013975883407426},
      {0.581196637484813, 0.401023447367823, 0.016157854278398},
      {0.401023447367823, 0.581196637484814, 0.016157854278398},
      {0.233015798295905, 0.749204286556732, 0.013975883407426},
      {0.099859134904086, 0.882360949948550, 0.009907253959653},
      {0.019502050260250, 0.962718034592387, 0.004509812716079}};

int triquad_int(int n, double x1, double y1,
                       double x2, double y2,
                       double x3, double y3,
                       double X[], double Y[], double W[])
{
  int i, nn;
  double a, area;
  typedef double pt[3];
  pt *tqd;
  
  a = x1*y2 - x2*y1 + x2*y3 - x3*y2 + x3*y1 - x1*y3;
  area = abs(a)/2.0;
  nn = n*n;
  
  if(n<1 || n>8) return 0;
  if(n==1) tqd = (pt *)&tq1[0][0];
  if(n==2) tqd = (pt *)&tq2[0][0];
  if(n==3) tqd = (pt *)&tq3[0][0];
  if(n==4) tqd = (pt *)&tq4[0][0];
  if(n==5) tqd = (pt *)&tq5[0][0];
  if(n==6) tqd = (pt *)&tq6[0][0];
  if(n==7) tqd = (pt *)&tq7[0][0];
  if(n==8) tqd = (pt *)&tq8[0][0];

  for(i=0; i<nn; i++) /* map onto callers triangle */
  {
    X[i] = x1 + (x2-x1)*tqd[i][0] + (x3-x1)*tqd[i][1];
    Y[i] = y1 + (y2-y1)*tqd[i][0] + (y3-y1)*tqd[i][1];
    W[i] = tqd[i][2]*area; 
  }
  return nn;
} /* end triquad_int.c */