31#if !defined(__cplusplus)
35#define GEOGRAPHICLIB_GEODESIC_ORDER 6
36#define nA1 GEOGRAPHICLIB_GEODESIC_ORDER
37#define nC1 GEOGRAPHICLIB_GEODESIC_ORDER
38#define nC1p GEOGRAPHICLIB_GEODESIC_ORDER
39#define nA2 GEOGRAPHICLIB_GEODESIC_ORDER
40#define nC2 GEOGRAPHICLIB_GEODESIC_ORDER
41#define nA3 GEOGRAPHICLIB_GEODESIC_ORDER
43#define nC3 GEOGRAPHICLIB_GEODESIC_ORDER
44#define nC3x ((nC3 * (nC3 - 1)) / 2)
45#define nC4 GEOGRAPHICLIB_GEODESIC_ORDER
46#define nC4x ((nC4 * (nC4 + 1)) / 2)
47#define nC (GEOGRAPHICLIB_GEODESIC_ORDER + 1)
52static unsigned init = 0;
53static const int FALSE = 0;
54static const int TRUE = 1;
55static unsigned digits, maxit1, maxit2;
56static real epsilon, realmin, pi, degree, NaN,
57 tiny, tol0, tol1, tol2, tolb, xthresh;
59static void Init(
void) {
61 digits = DBL_MANT_DIG;
62 epsilon = DBL_EPSILON;
67 pi = atan2(0.0, -1.0);
70 maxit2 = maxit1 + digits + 10;
80 xthresh = 1000 * tol2;
98static real sq(
real x) {
return x * x; }
101 volatile real s = u + v;
102 volatile real up = s - v;
103 volatile real vpp = s - up;
106 if (t) *t = -(up + vpp);
114 real y = N < 0 ? 0 : *p++;
115 while (--N >= 0) y = y * x + *p++;
121{
return (b < a) ? b : a; }
124{
return (a < b) ? b : a; }
127{
real t = *x; *x = *y; *y = t; }
129static void norm2(
real* sinx,
real* cosx) {
130#if defined(_MSC_VER) && defined(_M_IX86)
139 real r = sqrt(*sinx * *sinx + *cosx * *cosx);
141 real r = hypot(*sinx, *cosx);
148 x = remainder(x, (
real)(360));
149 return x != -180 ? x : 180;
153{
return fabs(x) > 90 ? NaN : x; }
156 real t, d = AngNormalize(sumx(AngNormalize(-x), AngNormalize(y), &t));
163 return sumx(d == 180 && t > 0 ? -180 : d, t, e);
169 if (x == 0)
return 0;
172 y = y < z ? z - (z - y) : y;
173 return x < 0 ? -y : y;
179 real r, s, c;
int q = 0;
180 r = remquo(x, (
real)(90), &q);
184 s = sin(r); c = cos(r);
185 switch ((
unsigned)q & 3U) {
186 case 0U: *sinx = s; *cosx = c;
break;
187 case 1U: *sinx = c; *cosx = -s;
break;
188 case 2U: *sinx = -s; *cosx = -c;
break;
189 default: *sinx = -c; *cosx = s;
break;
191 if (x != 0) { *sinx += (
real)(0); *cosx += (
real)(0); }
200 if (fabs(y) > fabs(x)) { swapx(&x, &y); q = 2; }
201 if (x < 0) { x = -x; ++q; }
203 ang = atan2(y, x) / degree;
210 case 1: ang = (y >= 0 ? 180 : -180) - ang;
break;
211 case 2: ang = 90 - ang;
break;
212 case 3: ang = -90 + ang;
break;
221static real SinCosSeries(boolx sinp,
223 const real c[],
int n);
256 boolx diffp,
real* pdlam12,
264static void C1pf(
real eps,
real c[]);
267static int transit(
real lon1,
real lon2);
268static int transitdirect(
real lon1,
real lon2);
269static void accini(
real s[]);
270static void acccopy(
const real s[],
real t[]);
271static void accadd(
real s[],
real y);
273static void accneg(
real s[]);
274static void accrem(
real s[],
real y);
276 int crossings, boolx reverse, boolx sign);
278 int crossings, boolx reverse, boolx sign);
285 g->e2 = g->
f * (2 - g->
f);
286 g->ep2 = g->e2 / sq(g->f1);
287 g->n = g->
f / ( 2 - g->
f);
289 g->c2 = (sq(g->
a) + sq(g->b) *
291 (g->e2 > 0 ? atanh(sqrt(g->e2)) : atan(sqrt(-g->e2))) /
292 sqrt(fabs(g->e2))))/2;
302 g->etol2 = 0.1 * tol2 /
303 sqrt( maxx((
real)(0.001), fabs(g->
f)) * minx((
real)(1), 1 - g->
f/2) / 2 );
315 real cbet1, sbet1, eps;
326 l->
lat1 = LatFix(lat1);
332 sincosdx(AngRound(l->
lat1), &sbet1, &cbet1); sbet1 *= l->f1;
334 norm2(&sbet1, &cbet1); cbet1 = maxx(tiny, cbet1);
335 l->dn1 = sqrt(1 + g->ep2 * sq(sbet1));
338 l->salp0 = l->
salp1 * cbet1;
351 l->ssig1 = sbet1; l->somg1 = l->salp0 * sbet1;
352 l->csig1 = l->comg1 = sbet1 != 0 || l->
calp1 != 0 ? cbet1 * l->
calp1 : 1;
353 norm2(&l->ssig1, &l->csig1);
356 l->k2 = sq(l->calp0) * g->ep2;
357 eps = l->k2 / (2 * (1 + sqrt(1 + l->k2)) + l->k2);
359 if (l->
caps & CAP_C1) {
361 l->A1m1 = A1m1f(eps);
363 l->B11 = SinCosSeries(TRUE, l->ssig1, l->csig1, l->C1a, nC1);
364 s = sin(l->B11); c = cos(l->B11);
366 l->stau1 = l->ssig1 * c + l->csig1 * s;
367 l->ctau1 = l->csig1 * c - l->ssig1 * s;
372 if (l->
caps & CAP_C1p)
375 if (l->
caps & CAP_C2) {
376 l->A2m1 = A2m1f(eps);
378 l->B21 = SinCosSeries(TRUE, l->ssig1, l->csig1, l->C2a, nC2);
381 if (l->
caps & CAP_C3) {
383 l->A3c = -l->
f * l->salp0 * A3f(g, eps);
384 l->B31 = SinCosSeries(TRUE, l->ssig1, l->csig1, l->C3a, nC3-1);
387 if (l->
caps & CAP_C4) {
390 l->A4 = sq(l->
a) * l->calp0 * l->salp0 * g->e2;
391 l->B41 = SinCosSeries(FALSE, l->ssig1, l->csig1, l->C4a, nC4);
401 azi1 = AngNormalize(azi1);
403 sincosdx(AngRound(azi1), &salp1, &calp1);
404 geod_lineinit_int(l, g, lat1, lon1, azi1, salp1, calp1, caps);
410 unsigned flags,
real s12_a12,
419 real s12,
unsigned caps) {
424 unsigned flags,
real s12_a12,
429 real lat2 = 0, lon2 = 0, azi2 = 0, s12 = 0,
430 m12 = 0, M12 = 0, M21 = 0, S12 = 0;
432 real sig12, ssig12, csig12, B12 = 0, AB1 = 0;
433 real omg12, lam12, lon12;
434 real ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2, dn2;
444 outmask &= l->
caps & OUT_ALL;
451 sig12 = s12_a12 * degree;
452 sincosdx(s12_a12, &ssig12, &csig12);
456 tau12 = s12_a12 / (l->b * (1 + l->A1m1)),
460 B12 = - SinCosSeries(TRUE,
461 l->stau1 * c + l->ctau1 * s,
462 l->ctau1 * c - l->stau1 * s,
464 sig12 = tau12 - (B12 - l->B11);
465 ssig12 = sin(sig12); csig12 = cos(sig12);
466 if (fabs(l->
f) > 0.01) {
489 ssig2 = l->ssig1 * csig12 + l->csig1 * ssig12;
490 csig2 = l->csig1 * csig12 - l->ssig1 * ssig12;
491 B12 = SinCosSeries(TRUE, ssig2, csig2, l->C1a, nC1);
492 serr = (1 + l->A1m1) * (sig12 + (B12 - l->B11)) - s12_a12 / l->b;
493 sig12 = sig12 - serr / sqrt(1 + l->k2 * sq(ssig2));
494 ssig12 = sin(sig12); csig12 = cos(sig12);
500 ssig2 = l->ssig1 * csig12 + l->csig1 * ssig12;
501 csig2 = l->csig1 * csig12 - l->ssig1 * ssig12;
502 dn2 = sqrt(1 + l->k2 * sq(ssig2));
505 B12 = SinCosSeries(TRUE, ssig2, csig2, l->C1a, nC1);
506 AB1 = (1 + l->A1m1) * (B12 - l->B11);
509 sbet2 = l->calp0 * ssig2;
511 cbet2 = hypot(l->salp0, l->calp0 * csig2);
514 cbet2 = csig2 = tiny;
516 salp2 = l->salp0; calp2 = l->calp0 * csig2;
520 l->b * ((1 + l->A1m1) * sig12 + AB1) :
524 real E = copysign(1, l->salp0);
526 somg2 = l->salp0 * ssig2; comg2 = csig2;
530 - (atan2( ssig2, csig2) - atan2( l->ssig1, l->csig1))
531 + (atan2(E * somg2, comg2) - atan2(E * l->somg1, l->comg1)))
532 : atan2(somg2 * l->comg1 - comg2 * l->somg1,
533 comg2 * l->comg1 + somg2 * l->somg1);
534 lam12 = omg12 + l->A3c *
535 ( sig12 + (SinCosSeries(TRUE, ssig2, csig2, l->C3a, nC3-1)
537 lon12 = lam12 / degree;
539 AngNormalize(AngNormalize(l->
lon1) + AngNormalize(lon12));
543 lat2 = atan2dx(sbet2, l->f1 * cbet2);
546 azi2 = atan2dx(salp2, calp2);
550 B22 = SinCosSeries(TRUE, ssig2, csig2, l->C2a, nC2),
551 AB2 = (1 + l->A2m1) * (B22 - l->B21),
552 J12 = (l->A1m1 - l->A2m1) * sig12 + (AB1 - AB2);
556 m12 = l->b * ((dn2 * (l->csig1 * ssig2) - l->dn1 * (l->ssig1 * csig2))
557 - l->csig1 * csig2 * J12);
559 real t = l->k2 * (ssig2 - l->ssig1) * (ssig2 + l->ssig1) /
561 M12 = csig12 + (t * ssig2 - csig2 * J12) * l->ssig1 / l->dn1;
562 M21 = csig12 - (t * l->ssig1 - l->csig1 * J12) * ssig2 / dn2;
568 B42 = SinCosSeries(FALSE, ssig2, csig2, l->C4a, nC4);
570 if (l->calp0 == 0 || l->salp0 == 0) {
583 salp12 = l->calp0 * l->salp0 *
584 (csig12 <= 0 ? l->csig1 * (1 - csig12) + ssig12 * l->ssig1 :
585 ssig12 * (l->csig1 * ssig12 / (1 + csig12) + l->ssig1));
586 calp12 = sq(l->salp0) + sq(l->calp0) * l->csig1 * csig2;
588 S12 = l->c2 * atan2(salp12, calp12) + l->A4 * (B42 - l->B41);
610 if (pM12) *pM12 = M12;
611 if (pM21) *pM21 = M21;
616 return (flags &
GEOD_ARCMODE) ? s12_a12 : sig12 / degree;
622 nullptr,
nullptr,
nullptr,
nullptr,
nullptr);
626 l->
a13 = a13; l->
s13 = NaN;
628 nullptr,
nullptr,
nullptr,
nullptr);
632 unsigned flags,
real s13_a13) {
634 geod_setarc(l, s13_a13) :
641 nullptr,
nullptr,
nullptr,
nullptr,
nullptr);
646 unsigned flags,
real s12_a12,
665 plat2, plon2, pazi2, ps12, pm12, pM12, pM21, pS12);
673 nullptr,
nullptr,
nullptr,
nullptr,
nullptr);
683 real s12 = 0, m12 = 0, M12 = 0, M21 = 0, S12 = 0;
685 int latsign, lonsign, swapp;
686 real sbet1, cbet1, sbet2, cbet2, s12x = 0, m12x = 0;
687 real dn1, dn2, lam12, slam12, clam12;
692 real omg12 = 0, somg12 = 2, comg12 = 0;
704 lon12 = AngDiff(
lon1, lon2, &lon12s);
706 lonsign = lon12 >= 0 ? 1 : -1;
708 lon12 = lonsign * AngRound(lon12);
709 lon12s = AngRound((180 - lon12) - lonsign * lon12s);
710 lam12 = lon12 * degree;
712 sincosdx(lon12s, &slam12, &clam12);
715 sincosdx(lon12, &slam12, &clam12);
719 lat2 = AngRound(LatFix(lat2));
722 swapp = fabs(
lat1) < fabs(lat2) ? -1 : 1;
728 latsign =
lat1 < 0 ? 1 : -1;
743 sincosdx(
lat1, &sbet1, &cbet1); sbet1 *= g->f1;
745 norm2(&sbet1, &cbet1); cbet1 = maxx(tiny, cbet1);
747 sincosdx(lat2, &sbet2, &cbet2); sbet2 *= g->f1;
749 norm2(&sbet2, &cbet2); cbet2 = maxx(tiny, cbet2);
759 if (cbet1 < -sbet1) {
761 sbet2 = sbet2 < 0 ? sbet1 : -sbet1;
763 if (fabs(sbet2) == -sbet1)
767 dn1 = sqrt(1 + g->ep2 * sq(sbet1));
768 dn2 = sqrt(1 + g->ep2 * sq(sbet2));
770 meridian =
lat1 == -90 || slam12 == 0;
777 real ssig1, csig1, ssig2, csig2;
779 calp2 = 1; salp2 = 0;
782 ssig1 = sbet1; csig1 =
calp1 * cbet1;
783 ssig2 = sbet2; csig2 = calp2 * cbet2;
786 sig12 = atan2(maxx((
real)(0), csig1 * ssig2 - ssig1 * csig2),
787 csig1 * csig2 + ssig1 * ssig2);
788 Lengths(g, g->n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
789 cbet1, cbet2, &s12x, &m12x,
nullptr,
800 if (sig12 < 1 || m12x >= 0) {
802 if (sig12 < 3 * tiny ||
804 (sig12 < tol0 && (s12x < 0 || m12x < 0)))
805 sig12 = m12x = s12x = 0;
808 a12 = sig12 / degree;
817 (g->
f <= 0 || lon12s >= g->
f * 180)) {
822 sig12 = omg12 = lam12 / g->f1;
823 m12x = g->b * sin(sig12);
825 M12 = M21 = cos(sig12);
828 }
else if (!meridian) {
835 sig12 = InverseStart(g, sbet1, cbet1, dn1, sbet2, cbet2, dn2,
836 lam12, slam12, clam12,
842 s12x = sig12 * g->b * dnm;
843 m12x = sq(dnm) * g->b * sin(sig12 / dnm);
845 M12 = M21 = cos(sig12 / dnm);
846 a12 = sig12 / degree;
847 omg12 = lam12 / (g->f1 * dnm);
861 real ssig1 = 0, csig1 = 0, ssig2 = 0, csig2 = 0, eps = 0, domg12 = 0;
864 real salp1a = tiny, calp1a = 1, salp1b = tiny, calp1b = -1;
867 for (; numit < maxit2; ++numit) {
871 v = Lambda12(g, sbet1, cbet1, dn1, sbet2, cbet2, dn2,
salp1,
calp1,
873 &salp2, &calp2, &sig12, &ssig1, &csig1, &ssig2, &csig2,
874 &eps, &domg12, numit < maxit1, &dv, Ca);
876 if (tripb || !(fabs(v) >= (tripn ? 8 : 1) * tol0))
break;
878 if (v > 0 && (numit > maxit1 ||
calp1/
salp1 > calp1b/salp1b))
880 else if (v < 0 && (numit > maxit1 ||
calp1/
salp1 < calp1a/salp1a))
882 if (numit < maxit1 && dv > 0) {
886 sdalp1 = sin(dalp1), cdalp1 = cos(dalp1),
888 if (nsalp1 > 0 && fabs(dalp1) < pi) {
895 tripn = fabs(v) <= 16 * tol0;
907 salp1 = (salp1a + salp1b)/2;
908 calp1 = (calp1a + calp1b)/2;
911 tripb = (fabs(salp1a -
salp1) + (calp1a -
calp1) < tolb ||
912 fabs(
salp1 - salp1b) + (
calp1 - calp1b) < tolb);
914 Lengths(g, eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
915 cbet1, cbet2, &s12x, &m12x,
nullptr,
920 a12 = sig12 / degree;
923 real sdomg12 = sin(domg12), cdomg12 = cos(domg12);
924 somg12 = slam12 * cdomg12 - clam12 * sdomg12;
925 comg12 = clam12 * cdomg12 + slam12 * sdomg12;
939 salp0 =
salp1 * cbet1,
942 if (calp0 != 0 && salp0 != 0) {
945 ssig1 = sbet1, csig1 =
calp1 * cbet1,
946 ssig2 = sbet2, csig2 = calp2 * cbet2,
947 k2 = sq(calp0) * g->ep2,
948 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2),
950 A4 = sq(g->
a) * calp0 * salp0 * g->e2;
952 norm2(&ssig1, &csig1);
953 norm2(&ssig2, &csig2);
955 B41 = SinCosSeries(FALSE, ssig1, csig1, Ca, nC4);
956 B42 = SinCosSeries(FALSE, ssig2, csig2, Ca, nC4);
957 S12 = A4 * (B42 - B41);
962 if (!meridian && somg12 > 1) {
963 somg12 = sin(omg12); comg12 = cos(omg12);
968 comg12 > -(
real)(0.7071) &&
969 sbet2 - sbet1 < (
real)(1.75)) {
974 domg12 = 1 + comg12, dbet1 = 1 + cbet1, dbet2 = 1 + cbet2;
975 alp12 = 2 * atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
976 domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) );
986 if (salp12 == 0 && calp12 < 0) {
987 salp12 = tiny *
calp1;
990 alp12 = atan2(salp12, calp12);
992 S12 += g->c2 * alp12;
993 S12 *= swapp * lonsign * latsign;
1000 swapx(&
salp1, &salp2);
1001 swapx(&
calp1, &calp2);
1006 salp1 *= swapp * lonsign;
calp1 *= swapp * latsign;
1007 salp2 *= swapp * lonsign; calp2 *= swapp * latsign;
1009 if (psalp1) *psalp1 =
salp1;
1010 if (pcalp1) *pcalp1 =
calp1;
1011 if (psalp2) *psalp2 = salp2;
1012 if (pcalp2) *pcalp2 = calp2;
1019 if (pM12) *pM12 = M12;
1020 if (pM21) *pM21 = M21;
1034 a12 = geod_geninverse_int(g,
lat1,
lon1, lat2, lon2, ps12,
1036 pm12, pM12, pM21, pS12);
1038 if (pazi2) *pazi2 = atan2dx(salp2, calp2);
1047 a12 = geod_geninverse_int(g,
lat1,
lon1, lat2, lon2,
nullptr,
1049 nullptr,
nullptr,
nullptr,
nullptr),
1055 geod_setarc(l, a12);
1062 nullptr,
nullptr,
nullptr,
nullptr);
1065real SinCosSeries(boolx sinp,
real sinx,
real cosx,
const real c[],
int n) {
1073 ar = 2 * (cosx - sinx) * (cosx + sinx);
1074 y0 = (n & 1) ? *--c : 0; y1 = 0;
1079 y1 = ar * y0 - y1 + *--c;
1080 y0 = ar * y1 - y0 + *--c;
1083 ? 2 * sinx * cosx * y0
1096 real m0 = 0, J12 = 0, A1 = 0, A2 = 0;
1101 boolx redlp = pm12b || pm0 || pM12 || pM21;
1102 if (ps12b || redlp) {
1114 real B1 = SinCosSeries(TRUE, ssig2, csig2, Ca, nC1) -
1115 SinCosSeries(TRUE, ssig1, csig1, Ca, nC1);
1117 *ps12b = A1 * (sig12 + B1);
1119 real B2 = SinCosSeries(TRUE, ssig2, csig2, Cb, nC2) -
1120 SinCosSeries(TRUE, ssig1, csig1, Cb, nC2);
1121 J12 = m0 * sig12 + (A1 * B1 - A2 * B2);
1126 for (l = 1; l <= nC2; ++l)
1127 Cb[l] = A1 * Ca[l] - A2 * Cb[l];
1128 J12 = m0 * sig12 + (SinCosSeries(TRUE, ssig2, csig2, Cb, nC2) -
1129 SinCosSeries(TRUE, ssig1, csig1, Cb, nC2));
1136 *pm12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
1137 csig1 * csig2 * J12;
1139 real csig12 = csig1 * csig2 + ssig1 * ssig2;
1140 real t = g->ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2);
1142 *pM12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
1144 *pM21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
1155 r = (p + q - 1) / 6;
1156 if ( !(q == 0 && r <= 0) ) {
1165 disc = S * (S + 2 * r3);
1169 real T3 = S + r3, T;
1173 T3 += T3 < 0 ? -sqrt(disc) : sqrt(disc);
1177 u += T + (T != 0 ? r2 / T : 0);
1180 real ang = atan2(sqrt(-disc), -(S + r3));
1183 u += 2 * r * cos(ang / 3);
1185 v = sqrt(sq(u) + q);
1187 uv = u < 0 ? q / (v - u) : u + v;
1188 w = (uv - q) / (2 * v);
1191 k = uv / (sqrt(uv + sq(w)) + w);
1219 sbet12 = sbet2 * cbet1 - cbet2 * sbet1,
1220 cbet12 = cbet2 * cbet1 + sbet2 * sbet1;
1222 boolx shortline = cbet12 >= 0 && sbet12 < (
real)(0.5) &&
1223 cbet2 * lam12 < (
real)(0.5);
1224 real somg12, comg12, ssig12, csig12;
1225 sbet12a = sbet2 * cbet1 + cbet2 * sbet1;
1227 real sbetm2 = sq(sbet1 + sbet2), omg12;
1230 sbetm2 /= sbetm2 + sq(cbet1 + cbet2);
1231 dnm = sqrt(1 + g->ep2 * sbetm2);
1232 omg12 = lam12 / (g->f1 * dnm);
1233 somg12 = sin(omg12); comg12 = cos(omg12);
1235 somg12 = slam12; comg12 = clam12;
1238 salp1 = cbet2 * somg12;
1239 calp1 = comg12 >= 0 ?
1240 sbet12 + cbet2 * sbet1 * sq(somg12) / (1 + comg12) :
1241 sbet12a - cbet2 * sbet1 * sq(somg12) / (1 - comg12);
1244 csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12;
1246 if (shortline && ssig12 < g->etol2) {
1248 salp2 = cbet1 * somg12;
1249 calp2 = sbet12 - cbet1 * sbet2 *
1250 (comg12 >= 0 ? sq(somg12) / (1 + comg12) : 1 - comg12);
1251 norm2(&salp2, &calp2);
1253 sig12 = atan2(ssig12, csig12);
1254 }
else if (fabs(g->n) > (
real)(0.1) ||
1256 ssig12 >= 6 * fabs(g->n) * pi * sq(cbet1)) {
1261 real y, lamscale, betscale;
1266 real lam12x = atan2(-slam12, -clam12);
1271 k2 = sq(sbet1) * g->ep2,
1272 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
1273 lamscale = g->
f * cbet1 * A3f(g, eps) * pi;
1275 betscale = lamscale * cbet1;
1277 x = lam12x / lamscale;
1278 y = sbet12a / betscale;
1282 cbet12a = cbet2 * cbet1 - sbet2 * sbet1,
1283 bet12a = atan2(sbet12a, cbet12a);
1287 Lengths(g, g->n, pi + bet12a,
1288 sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
1289 cbet1, cbet2,
nullptr, &m12b, &m0,
nullptr,
nullptr, Ca);
1290 x = -1 + m12b / (cbet1 * cbet2 * m0 * pi);
1291 betscale = x < -(
real)(0.01) ? sbet12a / x :
1292 -g->
f * sq(cbet1) * pi;
1293 lamscale = betscale / cbet1;
1294 y = lam12x / lamscale;
1297 if (y > -tol1 && x > -1 - xthresh) {
1340 real k = Astroid(x, y);
1342 omg12a = lamscale * ( g->
f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k );
1343 somg12 = sin(omg12a); comg12 = -cos(omg12a);
1345 salp1 = cbet2 * somg12;
1346 calp1 = sbet12a - cbet2 * sbet1 * sq(somg12) / (1 - comg12);
1378 boolx diffp,
real* pdlam12,
1381 real salp2 = 0, calp2 = 0, sig12 = 0,
1382 ssig1 = 0, csig1 = 0, ssig2 = 0, csig2 = 0, eps = 0,
1383 domg12 = 0, dlam12 = 0;
1385 real somg1, comg1, somg2, comg2, somg12, comg12, lam12;
1388 if (sbet1 == 0 &&
calp1 == 0)
1394 salp0 =
salp1 * cbet1;
1399 ssig1 = sbet1; somg1 = salp0 * sbet1;
1400 csig1 = comg1 =
calp1 * cbet1;
1401 norm2(&ssig1, &csig1);
1408 salp2 = cbet2 != cbet1 ? salp0 / cbet2 :
salp1;
1413 calp2 = cbet2 != cbet1 || fabs(sbet2) != -sbet1 ?
1414 sqrt(sq(
calp1 * cbet1) +
1416 (cbet2 - cbet1) * (cbet1 + cbet2) :
1417 (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 :
1421 ssig2 = sbet2; somg2 = salp0 * sbet2;
1422 csig2 = comg2 = calp2 * cbet2;
1423 norm2(&ssig2, &csig2);
1427 sig12 = atan2(maxx((
real)(0), csig1 * ssig2 - ssig1 * csig2),
1428 csig1 * csig2 + ssig1 * ssig2);
1431 somg12 = maxx((
real)(0), comg1 * somg2 - somg1 * comg2);
1432 comg12 = comg1 * comg2 + somg1 * somg2;
1434 eta = atan2(somg12 * clam120 - comg12 * slam120,
1435 comg12 * clam120 + somg12 * slam120);
1436 k2 = sq(calp0) * g->ep2;
1437 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
1439 B312 = (SinCosSeries(TRUE, ssig2, csig2, Ca, nC3-1) -
1440 SinCosSeries(TRUE, ssig1, csig1, Ca, nC3-1));
1441 domg12 = -g->
f * A3f(g, eps) * salp0 * (sig12 + B312);
1442 lam12 = eta + domg12;
1446 dlam12 = - 2 * g->f1 * dn1 / sbet1;
1448 Lengths(g, eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
1449 cbet1, cbet2,
nullptr, &dlam12,
nullptr,
nullptr,
nullptr, Ca);
1450 dlam12 *= g->f1 / (calp2 * cbet2);
1471 return polyval(nA3 - 1, g->A3x, eps);
1479 for (l = 1; l < nC3; ++l) {
1480 int m = nC3 - l - 1;
1482 c[l] = mult * polyval(m, g->C3x + o, eps);
1492 for (l = 0; l < nC4; ++l) {
1493 int m = nC4 - l - 1;
1494 c[l] = mult * polyval(m, g->C4x + o, eps);
1502 static const real coeff[] = {
1507 real t = polyval(m, coeff, sq(eps)) / coeff[m + 1];
1508 return (t + eps) / (1 - eps);
1513 static const real coeff[] = {
1531 for (l = 1; l <= nC1; ++l) {
1532 int m = (nC1 - l) / 2;
1533 c[l] = d * polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1541 static const real coeff[] = {
1543 205, -432, 768, 1536,
1545 4005, -4736, 3840, 12288,
1559 for (l = 1; l <= nC1p; ++l) {
1560 int m = (nC1p - l) / 2;
1561 c[l] = d * polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1569 static const real coeff[] = {
1571 -11, -28, -192, 0, 256,
1574 real t = polyval(m, coeff, sq(eps)) / coeff[m + 1];
1575 return (t - eps) / (1 + eps);
1580 static const real coeff[] = {
1598 for (l = 1; l <= nC2; ++l) {
1599 int m = (nC2 - l) / 2;
1600 c[l] = d * polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1608 static const real coeff[] = {
1622 int o = 0, k = 0, j;
1623 for (j = nA3 - 1; j >= 0; --j) {
1624 int m = nA3 - j - 1 < j ? nA3 - j - 1 : j;
1625 g->A3x[k++] = polyval(m, coeff + o, g->n) / coeff[o + m + 1];
1632 static const real coeff[] = {
1664 int o = 0, k = 0, l, j;
1665 for (l = 1; l < nC3; ++l) {
1666 for (j = nC3 - 1; j >= l; --j) {
1667 int m = nC3 - j - 1 < j ? nC3 - j - 1 : j;
1668 g->C3x[k++] = polyval(m, coeff + o, g->n) / coeff[o + m + 1];
1676 static const real coeff[] = {
1682 -224, -4784, 1573, 45045,
1684 -10656, 14144, -4576, -858, 45045,
1686 64, 624, -4576, 6864, -3003, 15015,
1688 100, 208, 572, 3432, -12012, 30030, 45045,
1694 5792, 1040, -1287, 135135,
1696 5952, -11648, 9152, -2574, 135135,
1698 -64, -624, 4576, -6864, 3003, 135135,
1704 -8448, 4992, -1144, 225225,
1706 -1440, 4160, -4576, 1716, 225225,
1712 3584, -3328, 1144, 315315,
1720 int o = 0, k = 0, l, j;
1721 for (l = 0; l < nC4; ++l) {
1722 for (j = nC4 - 1; j >= l; --j) {
1723 int m = nC4 - j - 1;
1724 g->C4x[k++] = polyval(m, coeff + o, g->n) / coeff[o + m + 1];
1736 lon2 = AngNormalize(lon2);
1737 lon12 = AngDiff(
lon1, lon2,
nullptr);
1738 return lon1 <= 0 && lon2 > 0 && lon12 > 0 ? 1 :
1739 (lon2 <= 0 && lon1 > 0 && lon12 < 0 ? -1 : 0);
1746 lon2 = remainder(lon2, (
real)(720));
1747 return ( (lon2 <= 0 && lon2 > -360 ? 1 : 0) -
1748 (lon1 <= 0 && lon1 > -360 ? 1 : 0) );
1751void accini(
real s[]) {
1756void acccopy(
const real s[],
real t[]) {
1758 t[0] = s[0]; t[1] = s[1];
1763 real u, z = sumx(y, s[1], &u);
1764 s[0] = sumx(z, s[0], &s[1]);
1779void accneg(
real s[]) {
1781 s[0] = -s[0]; s[1] = -s[1];
1786 s[0] = remainder(s[0], y);
1787 accadd(s, (
real)(0));
1791 p->polyline = (polylinep != 0);
1796 p->lat0 = p->lon0 = p->
lat = p->
lon = NaN;
1799 p->
num = p->crossings = 0;
1805 lon = AngNormalize(lon);
1807 p->lat0 = p->
lat = lat;
1808 p->lon0 = p->
lon = lon;
1812 &s12,
nullptr,
nullptr,
nullptr,
nullptr,
nullptr,
1813 p->polyline ?
nullptr : &S12);
1817 p->crossings += transit(p->
lon, lon);
1819 p->
lat = lat; p->
lon = lon;
1830 real lat = 0, lon = 0, S12 = 0;
1832 &lat, &lon,
nullptr,
1833 nullptr,
nullptr,
nullptr,
nullptr,
1834 p->polyline ?
nullptr : &S12);
1838 p->crossings += transitdirect(p->
lon, lon);
1840 p->
lat = lat; p->
lon = lon;
1847 boolx reverse, boolx sign,
1849 real s12, S12, t[2];
1852 if (!p->polyline && pA) *pA = 0;
1856 if (pP) *pP = p->P[0];
1860 &s12,
nullptr,
nullptr,
nullptr,
nullptr,
nullptr, &S12);
1861 if (pP) *pP = accsum(p->P, s12);
1864 if (pA) *pA = areareduceA(t, 4 * pi * g->c2,
1865 p->crossings + transit(p->
lon, p->lon0),
1873 boolx reverse, boolx sign,
1875 real perimeter, tempsum;
1877 unsigned num = p->
num + 1;
1880 if (!p->polyline && pA) *pA = 0;
1883 perimeter = p->P[0];
1884 tempsum = p->polyline ? 0 : p->A[0];
1885 crossings = p->crossings;
1886 for (i = 0; i < (p->polyline ? 1 : 2); ++i) {
1889 i == 0 ? p->
lat : lat, i == 0 ? p->
lon : lon,
1890 i != 0 ? p->lat0 : lat, i != 0 ? p->lon0 : lon,
1891 &s12,
nullptr,
nullptr,
nullptr,
nullptr,
nullptr,
1892 p->polyline ?
nullptr : &S12);
1896 crossings += transit(i == 0 ? p->
lon : lon,
1897 i != 0 ? p->lon0 : lon);
1901 if (pP) *pP = perimeter;
1905 if (pA) *pA = areareduceB(tempsum, 4 * pi * g->c2, crossings, reverse, sign);
1912 boolx reverse, boolx sign,
1914 real perimeter, tempsum;
1916 unsigned num = p->
num + 1;
1919 if (!p->polyline && pA) *pA = NaN;
1922 perimeter = p->P[0] + s;
1924 if (pP) *pP = perimeter;
1929 crossings = p->crossings;
1933 real lat = 0, lon = 0, s12, S12 = 0;
1935 &lat, &lon,
nullptr,
1936 nullptr,
nullptr,
nullptr,
nullptr, &S12);
1938 crossings += transitdirect(p->
lon, lon);
1940 &s12,
nullptr,
nullptr,
nullptr,
nullptr,
nullptr, &S12);
1943 crossings += transit(lon, p->lon0);
1946 if (pP) *pP = perimeter;
1947 if (pA) *pA = areareduceB(tempsum, 4 * pi * g->c2, crossings, reverse, sign);
1957 for (i = 0; i < n; ++i)
1963 int crossings, boolx reverse, boolx sign) {
1964 accrem(area, area0);
1966 accadd(area, (area[0] < 0 ? 1 : -1) * area0/2);
1973 if (area[0] > area0/2)
1974 accadd(area, -area0);
1975 else if (area[0] <= -area0/2)
1976 accadd(area, +area0);
1978 if (area[0] >= area0)
1979 accadd(area, -area0);
1980 else if (area[0] < 0)
1981 accadd(area, +area0);
1987 int crossings, boolx reverse, boolx sign) {
1988 area = remainder(area, area0);
1990 area += (area < 0 ? 1 : -1) * area0/2;
1999 else if (area <= -area0/2)
GeographicLib::Math::real real
API for the geodesic routines in C.
double GEOD_DLL geod_gendirect(const struct geod_geodesic *g, double lat1, double lon1, double azi1, unsigned flags, double s12_a12, double *plat2, double *plon2, double *pazi2, double *ps12, double *pm12, double *pM12, double *pM21, double *pS12)
void GEOD_DLL geod_polygon_addedge(const struct geod_geodesic *g, struct geod_polygon *p, double azi, double s)
void GEOD_DLL geod_polygon_addpoint(const struct geod_geodesic *g, struct geod_polygon *p, double lat, double lon)
void GEOD_DLL geod_setdistance(struct geod_geodesicline *l, double s13)
void GEOD_DLL geod_gensetdistance(struct geod_geodesicline *l, unsigned flags, double s13_a13)
unsigned GEOD_DLL geod_polygon_testpoint(const struct geod_geodesic *g, const struct geod_polygon *p, double lat, double lon, int reverse, int sign, double *pA, double *pP)
void GEOD_DLL geod_polygon_clear(struct geod_polygon *p)
void GEOD_DLL geod_init(struct geod_geodesic *g, double a, double f)
void GEOD_DLL geod_directline(struct geod_geodesicline *l, const struct geod_geodesic *g, double lat1, double lon1, double azi1, double s12, unsigned caps)
void GEOD_DLL geod_inverse(const struct geod_geodesic *g, double lat1, double lon1, double lat2, double lon2, double *ps12, double *pazi1, double *pazi2)
unsigned GEOD_DLL geod_polygon_testedge(const struct geod_geodesic *g, const struct geod_polygon *p, double azi, double s, int reverse, int sign, double *pA, double *pP)
void GEOD_DLL geod_lineinit(struct geod_geodesicline *l, const struct geod_geodesic *g, double lat1, double lon1, double azi1, unsigned caps)
unsigned GEOD_DLL geod_polygon_compute(const struct geod_geodesic *g, const struct geod_polygon *p, int reverse, int sign, double *pA, double *pP)
void GEOD_DLL geod_position(const struct geod_geodesicline *l, double s12, double *plat2, double *plon2, double *pazi2)
double GEOD_DLL geod_geninverse(const struct geod_geodesic *g, double lat1, double lon1, double lat2, double lon2, double *ps12, double *pazi1, double *pazi2, double *pm12, double *pM12, double *pM21, double *pS12)
double GEOD_DLL geod_genposition(const struct geod_geodesicline *l, unsigned flags, double s12_a12, double *plat2, double *plon2, double *pazi2, double *ps12, double *pm12, double *pM12, double *pM21, double *pS12)
void GEOD_DLL geod_direct(const struct geod_geodesic *g, double lat1, double lon1, double azi1, double s12, double *plat2, double *plon2, double *pazi2)
void GEOD_DLL geod_polygonarea(const struct geod_geodesic *g, double lats[], double lons[], int n, double *pA, double *pP)
void GEOD_DLL geod_inverseline(struct geod_geodesicline *l, const struct geod_geodesic *g, double lat1, double lon1, double lat2, double lon2, unsigned caps)
void GEOD_DLL geod_gendirectline(struct geod_geodesicline *l, const struct geod_geodesic *g, double lat1, double lon1, double azi1, unsigned flags, double s12_a12, unsigned caps)
void GEOD_DLL geod_polygon_init(struct geod_polygon *p, int polylinep)