34# pragma warning (disable: 4701)
42 : maxit2_(maxit1_ +
Math::digits() + 10)
46 , tiny_(sqrt(numeric_limits<real>::min()))
47 , tol0_(numeric_limits<real>::epsilon())
54 , xthresh_(1000 * tol2_)
60 , _ep2(_e2 /
Math::sq(_f1))
65 Math::eatanhe(real(1), (_f < 0 ? -1 : 1) * sqrt(fabs(_e2))) / _e2))
77 , _etol2(real(0.1) * tol2_ /
78 sqrt( fmax(real(0.001), fabs(_f)) * fmin(real(1), 1 - _f/2) / 2 ))
84 if (!(isfinite(_a) && _a > 0))
85 throw GeographicErr(
"Equatorial radius is not positive");
86 if (!(isfinite(_b) && _b > 0))
87 throw GeographicErr(
"Polar semi-axis is not positive");
101 const real c[],
int n) {
109 ar = 2 * (cosx - sinx) * (cosx + sinx),
110 y0 = n & 1 ? *--c : 0, y1 = 0;
115 y1 = ar * y0 - y1 + *--c;
116 y0 = ar * y1 - y0 + *--c;
119 ? 2 * sinx * cosx * y0
124 unsigned caps)
const {
129 bool arcmode, real s12_a12,
unsigned outmask,
130 real& lat2, real& lon2, real& azi2,
131 real& s12, real& m12, real& M12, real& M21,
134 return _geodexact.GenDirect(lat1, lon1, azi1, arcmode, s12_a12, outmask,
136 s12, m12, M12, M21, S12);
141 GenPosition(arcmode, s12_a12, outmask,
142 lat2, lon2, azi2, s12, m12, M12, M21, S12);
146 bool arcmode, real s12_a12,
147 unsigned caps)
const {
154 return GeodesicLine(*
this, lat1, lon1, azi1, salp1, calp1,
155 caps, arcmode, s12_a12);
159 unsigned caps)
const {
164 real a12,
unsigned caps)
const {
169 unsigned outmask,
real& s12,
175 return _geodexact.GenInverse(lat1, lon1, lat2, lon2,
177 salp1, calp1, salp2, calp2,
183 int lonsign = signbit(lon12) ? -1 : 1;
184 lon12 *= lonsign; lon12s *= lonsign;
191 lon12s = (
Math::hd - lon12) - lon12s;
198 int swapp = fabs(lat1) < fabs(lat2) || isnan(lat2) ? -1 : 1;
204 int latsign = signbit(lat1) ? 1 : -1;
224 Math::norm(sbet1, cbet1); cbet1 = fmax(tiny_, cbet1);
228 Math::norm(sbet2, cbet2); cbet2 = fmax(tiny_, cbet2);
238 if (cbet1 < -sbet1) {
240 sbet2 = copysign(sbet1, sbet2);
242 if (fabs(sbet2) == -sbet1)
247 dn1 = sqrt(1 + _ep2 *
Math::sq(sbet1)),
248 dn2 = sqrt(1 + _ep2 *
Math::sq(sbet2));
254 bool meridian = lat1 == -
Math::qd || slam12 == 0;
261 calp1 = clam12; salp1 = slam12;
262 calp2 = 1; salp2 = 0;
266 ssig1 = sbet1, csig1 = calp1 * cbet1,
267 ssig2 = sbet2, csig2 = calp2 * cbet2;
270 sig12 = atan2(fmax(
real(0), csig1 * ssig2 - ssig1 * csig2) +
real(0),
271 csig1 * csig2 + ssig1 * ssig2);
274 Lengths(_n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2,
276 s12x, m12x, dummy, M12, M21, Ca);
282 if (sig12 < tol2_ || m12x >= 0) {
284 if (sig12 < 3 * tiny_ ||
286 (sig12 < tol0_ && (s12x < 0 || m12x < 0)))
287 sig12 = m12x = s12x = 0;
297 real omg12 = 0, somg12 = 2, comg12 = 0;
300 (_f <= 0 || lon12s >= _f *
Math::hd)) {
303 calp1 = calp2 = 0; salp1 = salp2 = 1;
305 sig12 = omg12 = lam12 / _f1;
306 m12x = _b * sin(sig12);
308 M12 = M21 = cos(sig12);
311 }
else if (!meridian) {
318 sig12 = InverseStart(sbet1, cbet1, dn1, sbet2, cbet2, dn2,
319 lam12, slam12, clam12,
320 salp1, calp1, salp2, calp2, dnm,
325 s12x = sig12 * _b * dnm;
326 m12x =
Math::sq(dnm) * _b * sin(sig12 / dnm);
328 M12 = M21 = cos(sig12 / dnm);
330 omg12 = lam12 / (_f1 * dnm);
346 real ssig1 = 0, csig1 = 0, ssig2 = 0, csig2 = 0, eps = 0, domg12 = 0;
349 real salp1a = tiny_, calp1a = 1, salp1b = tiny_, calp1b = -1;
350 for (
bool tripn =
false, tripb =
false;; ++numit) {
354 real v = Lambda12(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1,
356 salp2, calp2, sig12, ssig1, csig1, ssig2, csig2,
357 eps, domg12, numit < maxit1_, dv, Ca);
360 !(fabs(v) >= (tripn ? 8 : 1) * tol0_) ||
365 if (v > 0 && (numit > maxit1_ || calp1/salp1 > calp1b/salp1b))
366 { salp1b = salp1; calp1b = calp1; }
367 else if (v < 0 && (numit > maxit1_ || calp1/salp1 < calp1a/salp1a))
368 { salp1a = salp1; calp1a = calp1; }
369 if (numit < maxit1_ && dv > 0) {
377 sdalp1 = sin(dalp1), cdalp1 = cos(dalp1),
378 nsalp1 = salp1 * cdalp1 + calp1 * sdalp1;
380 calp1 = calp1 * cdalp1 - salp1 * sdalp1;
386 tripn = fabs(v) <= 16 * tol0_;
399 salp1 = (salp1a + salp1b)/2;
400 calp1 = (calp1a + calp1b)/2;
403 tripb = (fabs(salp1a - salp1) + (calp1a - calp1) < tolb_ ||
404 fabs(salp1 - salp1b) + (calp1 - calp1b) < tolb_);
410 unsigned lengthmask = outmask |
412 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
413 cbet1, cbet2, lengthmask, s12x, m12x, dummy, M12, M21, Ca);
418 if (outmask &
AREA) {
420 real sdomg12 = sin(domg12), cdomg12 = cos(domg12);
421 somg12 = slam12 * cdomg12 - clam12 * sdomg12;
422 comg12 = clam12 * cdomg12 + slam12 * sdomg12;
428 s12 =
real(0) + s12x;
431 m12 =
real(0) + m12x;
433 if (outmask &
AREA) {
436 salp0 = salp1 * cbet1,
437 calp0 = hypot(calp1, salp1 * sbet1);
439 if (calp0 != 0 && salp0 != 0) {
442 ssig1 = sbet1, csig1 = calp1 * cbet1,
443 ssig2 = sbet2, csig2 = calp2 * cbet2,
445 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2),
447 A4 =
Math::sq(_a) * calp0 * salp0 * _e2;
452 B41 = SinCosSeries(
false, ssig1, csig1, Ca, nC4_),
453 B42 = SinCosSeries(
false, ssig2, csig2, Ca, nC4_);
454 S12 = A4 * (B42 - B41);
458 if (!meridian && somg12 == 2) {
459 somg12 = sin(omg12); comg12 = cos(omg12);
464 comg12 > -
real(0.7071) &&
465 sbet2 - sbet1 <
real(1.75)) {
469 real domg12 = 1 + comg12, dbet1 = 1 + cbet1, dbet2 = 1 + cbet2;
470 alp12 = 2 * atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
471 domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) );
475 salp12 = salp2 * calp1 - calp2 * salp1,
476 calp12 = calp2 * calp1 + salp2 * salp1;
481 if (salp12 == 0 && calp12 < 0) {
482 salp12 = tiny_ * calp1;
485 alp12 = atan2(salp12, calp12);
488 S12 *= swapp * lonsign * latsign;
501 salp1 *= swapp * lonsign; calp1 *= swapp * latsign;
502 salp2 *= swapp * lonsign; calp2 *= swapp * latsign;
507 Math::real Geodesic::GenInverse(real lat1, real lon1, real lat2, real lon2,
509 real& s12, real& azi1, real& azi2,
510 real& m12, real& M12, real& M21,
513 real salp1, calp1, salp2, calp2,
514 a12 = GenInverse(lat1, lon1, lat2, lon2,
515 outmask, s12, salp1, calp1, salp2, calp2,
525 real lat2, real lon2,
526 unsigned caps)
const {
527 real t, salp1, calp1, salp2, calp2,
528 a12 = GenInverse(lat1, lon1, lat2, lon2,
530 0u, t, salp1, calp1, salp2, calp2,
536 GeodesicLine(*
this, lat1, lon1, azi1, salp1, calp1, caps,
true, a12);
539 void Geodesic::Lengths(
real eps,
real sig12,
542 real cbet1,
real cbet2,
unsigned outmask,
555 real m0x = 0, J12 = 0, A1 = 0, A2 = 0;
569 real B1 = SinCosSeries(
true, ssig2, csig2, Ca, nC1_) -
570 SinCosSeries(
true, ssig1, csig1, Ca, nC1_);
572 s12b = A1 * (sig12 + B1);
574 real B2 = SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
575 SinCosSeries(
true, ssig1, csig1, Cb, nC2_);
576 J12 = m0x * sig12 + (A1 * B1 - A2 * B2);
580 for (
int l = 1; l <= nC2_; ++l)
581 Cb[l] = A1 * Ca[l] - A2 * Cb[l];
582 J12 = m0x * sig12 + (SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
583 SinCosSeries(
true, ssig1, csig1, Cb, nC2_));
590 m12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
594 real csig12 = csig1 * csig2 + ssig1 * ssig2;
595 real t = _ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2);
596 M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
597 M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
609 if ( !(q == 0 && r <= 0) ) {
618 disc = S * (S + 2 * r3);
625 T3 += T3 < 0 ? -sqrt(disc) : sqrt(disc);
629 u += T + (T != 0 ? r2 / T : 0);
632 real ang = atan2(sqrt(-disc), -(S + r3));
635 u += 2 * r * cos(ang / 3);
640 uv = u < 0 ? q / (v - u) : u + v,
641 w = (uv - q) / (2 * v);
644 k = uv / (sqrt(uv +
Math::sq(w)) + w);
669 sbet12 = sbet2 * cbet1 - cbet2 * sbet1,
670 cbet12 = cbet2 * cbet1 + sbet2 * sbet1;
671 real sbet12a = sbet2 * cbet1 + cbet2 * sbet1;
672 bool shortline = cbet12 >= 0 && sbet12 <
real(0.5) &&
673 cbet2 * lam12 <
real(0.5);
676 real sbetm2 =
Math::sq(sbet1 + sbet2);
679 sbetm2 /= sbetm2 +
Math::sq(cbet1 + cbet2);
680 dnm = sqrt(1 + _ep2 * sbetm2);
681 real omg12 = lam12 / (_f1 * dnm);
682 somg12 = sin(omg12); comg12 = cos(omg12);
684 somg12 = slam12; comg12 = clam12;
687 salp1 = cbet2 * somg12;
688 calp1 = comg12 >= 0 ?
689 sbet12 + cbet2 * sbet1 *
Math::sq(somg12) / (1 + comg12) :
690 sbet12a - cbet2 * sbet1 * Math::sq(somg12) / (1 - comg12);
693 ssig12 = hypot(salp1, calp1),
694 csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12;
696 if (shortline && ssig12 < _etol2) {
698 salp2 = cbet1 * somg12;
699 calp2 = sbet12 - cbet1 * sbet2 *
700 (comg12 >= 0 ?
Math::sq(somg12) / (1 + comg12) : 1 - comg12);
703 sig12 = atan2(ssig12, csig12);
704 }
else if (fabs(_n) >
real(0.1) ||
711 real x, y, lamscale, betscale;
712 real lam12x = atan2(-slam12, -clam12);
718 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
719 lamscale = _f * cbet1 * A3f(eps) *
Math::pi();
721 betscale = lamscale * cbet1;
723 x = lam12x / lamscale;
724 y = sbet12a / betscale;
728 cbet12a = cbet2 * cbet1 - sbet2 * sbet1,
729 bet12a = atan2(sbet12a, cbet12a);
730 real m12b, m0, dummy;
734 sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
737 x = -1 + m12b / (cbet1 * cbet2 * m0 *
Math::pi());
738 betscale = x < -
real(0.01) ? sbet12a / x :
740 lamscale = betscale / cbet1;
741 y = lam12x / lamscale;
744 if (y > -tol1_ && x > -1 - xthresh_) {
748 salp1 = fmin(
real(1), -x); calp1 = - sqrt(1 -
Math::sq(salp1));
750 calp1 = fmax(
real(x > -tol1_ ? 0 : -1), x);
788 real k = Astroid(x, y);
790 omg12a = lamscale * ( _f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k );
791 somg12 = sin(omg12a); comg12 = -cos(omg12a);
793 salp1 = cbet2 * somg12;
794 calp1 = sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
801 salp1 = 1; calp1 = 0;
815 bool diffp,
real& dlam12,
819 if (sbet1 == 0 && calp1 == 0)
826 salp0 = salp1 * cbet1,
827 calp0 = hypot(calp1, salp1 * sbet1);
829 real somg1, comg1, somg2, comg2, somg12, comg12, lam12;
832 ssig1 = sbet1; somg1 = salp0 * sbet1;
833 csig1 = comg1 = calp1 * cbet1;
841 salp2 = cbet2 != cbet1 ? salp0 / cbet2 : salp1;
846 calp2 = cbet2 != cbet1 || fabs(sbet2) != -sbet1 ?
849 (cbet2 - cbet1) * (cbet1 + cbet2) :
850 (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 :
854 ssig2 = sbet2; somg2 = salp0 * sbet2;
855 csig2 = comg2 = calp2 * cbet2;
860 sig12 = atan2(fmax(
real(0), csig1 * ssig2 - ssig1 * csig2) +
real(0),
861 csig1 * csig2 + ssig1 * ssig2);
864 somg12 = fmax(
real(0), comg1 * somg2 - somg1 * comg2) +
real(0);
865 comg12 = comg1 * comg2 + somg1 * somg2;
867 real eta = atan2(somg12 * clam120 - comg12 * slam120,
868 comg12 * clam120 + somg12 * slam120);
871 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
873 B312 = (SinCosSeries(
true, ssig2, csig2, Ca, nC3_-1) -
874 SinCosSeries(
true, ssig1, csig1, Ca, nC3_-1));
875 domg12 = -_f * A3f(eps) * salp0 * (sig12 + B312);
876 lam12 = eta + domg12;
880 dlam12 = - 2 * _f1 * dn1 / sbet1;
883 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
885 dummy, dlam12, dummy, dummy, dummy, Ca);
886 dlam12 *= _f1 / (calp2 * cbet2);
898 void Geodesic::C3f(
real eps,
real c[])
const {
903 for (
int l = 1; l < nC3_; ++l) {
904 int m = nC3_ - l - 1;
912 void Geodesic::C4f(
real eps,
real c[])
const {
917 for (
int l = 0; l < nC4_; ++l) {
918 int m = nC4_ - l - 1;
952#if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
953 static const real coeff[] = {
957#elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
958 static const real coeff[] = {
962#elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
963 static const real coeff[] = {
967#elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
968 static const real coeff[] = {
970 25, 64, 256, 4096, 0, 16384,
973#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
975 static_assert(
sizeof(coeff) /
sizeof(real) == nA1_/2 + 2,
976 "Coefficient array size mismatch in A1m1f");
979 return (t + eps) / (1 - eps);
983 void Geodesic::C1f(
real eps,
real c[]) {
985#if GEOGRAPHICLIB_GEODESIC_ORDER == 3
986 static const real coeff[] = {
994#elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
995 static const real coeff[] = {
1005#elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1006 static const real coeff[] = {
1018#elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1019 static const real coeff[] = {
1033#elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1034 static const real coeff[] = {
1036 19, -64, 384, -1024, 2048,
1050#elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1051 static const real coeff[] = {
1053 19, -64, 384, -1024, 2048,
1055 7, -18, 128, -256, 4096,
1059 -11, 96, -160, 16384,
1070#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1072 static_assert(
sizeof(coeff) /
sizeof(real) ==
1073 (nC1_*nC1_ + 7*nC1_ - 2*(nC1_/2)) / 4,
1074 "Coefficient array size mismatch in C1f");
1079 for (
int l = 1; l <= nC1_; ++l) {
1080 int m = (nC1_ - l) / 2;
1081 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1089 void Geodesic::C1pf(
real eps,
real c[]) {
1091#if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1092 static const real coeff[] = {
1100#elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1101 static const real coeff[] = {
1111#elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1112 static const real coeff[] = {
1114 205, -432, 768, 1536,
1124#elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1125 static const real coeff[] = {
1127 205, -432, 768, 1536,
1129 4005, -4736, 3840, 12288,
1139#elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1140 static const real coeff[] = {
1142 -4879, 9840, -20736, 36864, 73728,
1144 4005, -4736, 3840, 12288,
1146 8703, -7200, 3712, 12288,
1150 -141115, 41604, 92160,
1156#elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1157 static const real coeff[] = {
1159 -4879, 9840, -20736, 36864, 73728,
1161 -86171, 120150, -142080, 115200, 368640,
1163 8703, -7200, 3712, 12288,
1165 1082857, -688608, 258720, 737280,
1167 -141115, 41604, 92160,
1169 -2200311, 533134, 860160,
1173 109167851, 82575360,
1176#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1178 static_assert(
sizeof(coeff) /
sizeof(real) ==
1179 (nC1p_*nC1p_ + 7*nC1p_ - 2*(nC1p_/2)) / 4,
1180 "Coefficient array size mismatch in C1pf");
1185 for (
int l = 1; l <= nC1p_; ++l) {
1186 int m = (nC1p_ - l) / 2;
1187 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1197#if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
1198 static const real coeff[] = {
1202#elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
1203 static const real coeff[] = {
1207#elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
1208 static const real coeff[] = {
1210 -11, -28, -192, 0, 256,
1212#elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
1213 static const real coeff[] = {
1215 -375, -704, -1792, -12288, 0, 16384,
1218#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1220 static_assert(
sizeof(coeff) /
sizeof(real) == nA2_/2 + 2,
1221 "Coefficient array size mismatch in A2m1f");
1224 return (t - eps) / (1 + eps);
1228 void Geodesic::C2f(
real eps,
real c[]) {
1230#if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1231 static const real coeff[] = {
1239#elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1240 static const real coeff[] = {
1250#elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1251 static const real coeff[] = {
1263#elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1264 static const real coeff[] = {
1278#elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1279 static const real coeff[] = {
1281 41, 64, 128, 1024, 2048,
1295#elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1296 static const real coeff[] = {
1298 41, 64, 128, 1024, 2048,
1300 47, 70, 128, 768, 4096,
1304 133, 224, 1120, 16384,
1315#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1317 static_assert(
sizeof(coeff) /
sizeof(real) ==
1318 (nC2_*nC2_ + 7*nC2_ - 2*(nC2_/2)) / 4,
1319 "Coefficient array size mismatch in C2f");
1324 for (
int l = 1; l <= nC2_; ++l) {
1325 int m = (nC2_ - l) / 2;
1326 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1334 void Geodesic::A3coeff() {
1336#if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1337 static const real coeff[] = {
1345#elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1346 static const real coeff[] = {
1356#elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1357 static const real coeff[] = {
1369#elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1370 static const real coeff[] = {
1384#elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1385 static const real coeff[] = {
1401#elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1402 static const real coeff[] = {
1410 -5, -20, -4, -6, 128,
1421#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1423 static_assert(
sizeof(coeff) /
sizeof(real) ==
1424 (nA3_*nA3_ + 7*nA3_ - 2*(nA3_/2)) / 4,
1425 "Coefficient array size mismatch in A3f");
1427 for (
int j = nA3_ - 1; j >= 0; --j) {
1428 int m = min(nA3_ - j - 1, j);
1429 _aA3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1436 void Geodesic::C3coeff() {
1438#if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1439 static const real coeff[] = {
1447#elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1448 static const real coeff[] = {
1464#elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1465 static const real coeff[] = {
1487#elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1488 static const real coeff[] = {
1520#elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1521 static const real coeff[] = {
1565#elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1566 static const real coeff[] = {
1600 10, -6, -10, 9, 384,
1610 -7, 20, -28, 14, 1024,
1625#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1627 static_assert(
sizeof(coeff) /
sizeof(real) ==
1628 ((nC3_-1)*(nC3_*nC3_ + 7*nC3_ - 2*(nC3_/2)))/8,
1629 "Coefficient array size mismatch in C3coeff");
1631 for (
int l = 1; l < nC3_; ++l) {
1632 for (
int j = nC3_ - 1; j >= l; --j) {
1633 int m = min(nC3_ - j - 1, j);
1634 _cC3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1641 void Geodesic::C4coeff() {
1643#if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1644 static const real coeff[] = {
1658#elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1659 static const real coeff[] = {
1667 4, 24, -84, 210, 315,
1681#elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1682 static const real coeff[] = {
1688 1088, -352, -66, 3465,
1690 48, -352, 528, -231, 1155,
1692 16, 44, 264, -924, 2310, 3465,
1698 -896, 704, -198, 10395,
1700 -48, 352, -528, 231, 10395,
1706 320, -352, 132, 17325,
1714#elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1715 static const real coeff[] = {
1721 -224, -4784, 1573, 45045,
1723 -10656, 14144, -4576, -858, 45045,
1725 64, 624, -4576, 6864, -3003, 15015,
1727 100, 208, 572, 3432, -12012, 30030, 45045,
1733 5792, 1040, -1287, 135135,
1735 5952, -11648, 9152, -2574, 135135,
1737 -64, -624, 4576, -6864, 3003, 135135,
1743 -8448, 4992, -1144, 225225,
1745 -1440, 4160, -4576, 1716, 225225,
1751 3584, -3328, 1144, 315315,
1759#elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1760 static const real coeff[] = {
1766 -4480, 1088, 156, 45045,
1768 10736, -224, -4784, 1573, 45045,
1770 1664, -10656, 14144, -4576, -858, 45045,
1772 16, 64, 624, -4576, 6864, -3003, 15015,
1774 56, 100, 208, 572, 3432, -12012, 30030, 45045,
1780 3840, -2944, 468, 135135,
1782 -10704, 5792, 1040, -1287, 135135,
1784 -768, 5952, -11648, 9152, -2574, 135135,
1786 -16, -64, -624, 4576, -6864, 3003, 135135,
1792 1664, 1856, -936, 225225,
1794 6784, -8448, 4992, -1144, 225225,
1796 128, -1440, 4160, -4576, 1716, 225225,
1802 -2048, 1024, -208, 105105,
1804 -1792, 3584, -3328, 1144, 315315,
1810 3072, -2560, 832, 405405,
1818#elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1819 static const real coeff[] = {
1825 20960, -7888, 4947, 765765,
1827 12480, -76160, 18496, 2652, 765765,
1829 -154048, 182512, -3808, -81328, 26741, 765765,
1831 3232, 28288, -181152, 240448, -77792, -14586, 765765,
1833 96, 272, 1088, 10608, -77792, 116688, -51051, 255255,
1835 588, 952, 1700, 3536, 9724, 58344, -204204, 510510, 765765,
1841 -39840, 1904, 255, 2297295,
1843 52608, 65280, -50048, 7956, 2297295,
1845 103744, -181968, 98464, 17680, -21879, 2297295,
1847 -1344, -13056, 101184, -198016, 155584, -43758, 2297295,
1849 -96, -272, -1088, -10608, 77792, -116688, 51051, 2297295,
1853 -928, -612, 3828825,
1855 64256, -28288, 2856, 3828825,
1857 -126528, 28288, 31552, -15912, 3828825,
1859 -41472, 115328, -143616, 84864, -19448, 3828825,
1861 160, 2176, -24480, 70720, -77792, 29172, 3828825,
1865 -16384, 1088, 5360355,
1867 -2560, 30464, -11560, 5360355,
1869 35840, -34816, 17408, -3536, 1786785,
1871 7168, -30464, 60928, -56576, 19448, 5360355,
1875 26624, -8704, 6891885,
1877 -77824, 34816, -6528, 6891885,
1879 -32256, 52224, -43520, 14144, 6891885,
1883 24576, -4352, 8423415,
1885 45056, -34816, 10880, 8423415,
1889 -28672, 8704, 9954945,
1894#error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1896 static_assert(
sizeof(coeff) /
sizeof(real) ==
1897 (nC4_ * (nC4_ + 1) * (nC4_ + 5)) / 6,
1898 "Coefficient array size mismatch in C4coeff");
1900 for (
int l = 0; l < nC4_; ++l) {
1901 for (
int j = nC4_ - 1; j >= l; --j) {
1902 int m = nC4_ - j - 1;
1903 _cC4x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
GeographicLib::Math::real real
Header for GeographicLib::GeodesicLine class.
Header for GeographicLib::Geodesic class.
Exact geodesic calculations.
GeodesicLine InverseLine(real lat1, real lon1, real lat2, real lon2, unsigned caps=ALL) const
static const Geodesic & WGS84()
GeodesicLine ArcDirectLine(real lat1, real lon1, real azi1, real a12, unsigned caps=ALL) const
GeodesicLine Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
GeodesicLine GenDirectLine(real lat1, real lon1, real azi1, bool arcmode, real s12_a12, unsigned caps=ALL) const
friend class GeodesicLine
Math::real GenDirect(real lat1, real lon1, real azi1, bool arcmode, real s12_a12, unsigned outmask, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
GeodesicLine DirectLine(real lat1, real lon1, real azi1, real s12, unsigned caps=ALL) const
Geodesic(real a, real f, bool exact=false)
Mathematical functions needed by GeographicLib.
static void sincosd(T x, T &sinx, T &cosx)
static T atan2d(T y, T x)
static void norm(T &x, T &y)
static constexpr int qd
degrees per quarter turn
static T AngNormalize(T x)
static void sincosde(T x, T t, T &sinx, T &cosx)
static T polyval(int N, const T p[], T x)
static T AngDiff(T x, T y, T &e)
static constexpr int hd
degrees per half turn
Namespace for GeographicLib.
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)