35 # pragma warning (disable: 4701 4127)
43 : maxit2_(maxit1_ +
Math::digits() + 10)
47 , tiny_(sqrt(numeric_limits<real>::min()))
48 , tol0_(numeric_limits<real>::epsilon())
54 , tolb_(tol0_ * tol2_)
55 , 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 ))
80 if (!(isfinite(_a) && _a > 0))
82 if (!(isfinite(_b) && _b > 0))
96 const real c[],
int n) {
104 ar = 2 * (cosx - sinx) * (cosx + sinx),
105 y0 = n & 1 ? *--c : 0, y1 = 0;
110 y1 = ar * y0 - y1 + *--c;
111 y0 = ar * y1 - y0 + *--c;
114 ? 2 * sinx * cosx * y0
119 unsigned caps)
const {
124 bool arcmode, real s12_a12,
unsigned outmask,
125 real& lat2, real& lon2, real& azi2,
126 real& s12, real& m12, real& M12, real& M21,
132 GenPosition(arcmode, s12_a12, outmask,
133 lat2, lon2, azi2, s12, m12, M12, M21, S12);
137 bool arcmode, real s12_a12,
138 unsigned caps)
const {
145 return GeodesicLine(*
this, lat1, lon1, azi1, salp1, calp1,
146 caps, arcmode, s12_a12);
150 unsigned caps)
const {
155 real a12,
unsigned caps)
const {
160 unsigned outmask,
real& s12,
169 int lonsign = signbit(lon12) ? -1 : 1;
170 lon12 *= lonsign; lon12s *= lonsign;
177 lon12s = (
Math::hd - lon12) - lon12s;
184 int swapp = fabs(lat1) < fabs(lat2) || isnan(lat2) ? -1 : 1;
190 int latsign = signbit(lat1) ? 1 : -1;
205 real sbet1, cbet1, sbet2, cbet2, s12x, m12x;
210 Math::norm(sbet1, cbet1); cbet1 = fmax(tiny_, cbet1);
214 Math::norm(sbet2, cbet2); cbet2 = fmax(tiny_, cbet2);
224 if (cbet1 < -sbet1) {
226 sbet2 = copysign(sbet1, sbet2);
228 if (fabs(sbet2) == -sbet1)
233 dn1 = sqrt(1 + _ep2 *
Math::sq(sbet1)),
234 dn2 = sqrt(1 + _ep2 *
Math::sq(sbet2));
240 bool meridian = lat1 == -
Math::qd || slam12 == 0;
247 calp1 = clam12; salp1 = slam12;
248 calp2 = 1; salp2 = 0;
252 ssig1 = sbet1, csig1 = calp1 * cbet1,
253 ssig2 = sbet2, csig2 = calp2 * cbet2;
256 sig12 = atan2(fmax(
real(0), csig1 * ssig2 - ssig1 * csig2) +
real(0),
257 csig1 * csig2 + ssig1 * ssig2);
260 Lengths(_n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2,
262 s12x, m12x, dummy, M12, M21, Ca);
276 if (sig12 < 1 || m12x >= 0) {
278 if (sig12 < 3 * tiny_ ||
280 (sig12 < tol0_ && (s12x < 0 || m12x < 0)))
281 sig12 = m12x = s12x = 0;
291 real omg12 = 0, somg12 = 2, comg12 = 0;
294 (_f <= 0 || lon12s >= _f *
Math::hd)) {
297 calp1 = calp2 = 0; salp1 = salp2 = 1;
299 sig12 = omg12 = lam12 / _f1;
300 m12x = _b * sin(sig12);
302 M12 = M21 = cos(sig12);
305 }
else if (!meridian) {
312 sig12 = InverseStart(sbet1, cbet1, dn1, sbet2, cbet2, dn2,
313 lam12, slam12, clam12,
314 salp1, calp1, salp2, calp2, dnm,
319 s12x = sig12 * _b * dnm;
320 m12x =
Math::sq(dnm) * _b * sin(sig12 / dnm);
322 M12 = M21 = cos(sig12 / dnm);
324 omg12 = lam12 / (_f1 * dnm);
340 real ssig1 = 0, csig1 = 0, ssig2 = 0, csig2 = 0, eps = 0, domg12 = 0;
343 real salp1a = tiny_, calp1a = 1, salp1b = tiny_, calp1b = -1;
344 for (
bool tripn =
false, tripb =
false;
350 real v = Lambda12(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1,
352 salp2, calp2, sig12, ssig1, csig1, ssig2, csig2,
353 eps, domg12, numit < maxit1_, dv, Ca);
355 if (tripb || !(fabs(v) >= (tripn ? 8 : 1) * tol0_))
break;
357 if (v > 0 && (numit > maxit1_ || calp1/salp1 > calp1b/salp1b))
358 { salp1b = salp1; calp1b = calp1; }
359 else if (v < 0 && (numit > maxit1_ || calp1/salp1 < calp1a/salp1a))
360 { salp1a = salp1; calp1a = calp1; }
361 if (numit < maxit1_ && dv > 0) {
365 sdalp1 = sin(dalp1), cdalp1 = cos(dalp1),
366 nsalp1 = salp1 * cdalp1 + calp1 * sdalp1;
367 if (nsalp1 > 0 && fabs(dalp1) <
Math::pi()) {
368 calp1 = calp1 * cdalp1 - salp1 * sdalp1;
374 tripn = fabs(v) <= 16 * tol0_;
386 salp1 = (salp1a + salp1b)/2;
387 calp1 = (calp1a + calp1b)/2;
390 tripb = (fabs(salp1a - salp1) + (calp1a - calp1) < tolb_ ||
391 fabs(salp1 - salp1b) + (calp1 - calp1b) < tolb_);
397 unsigned lengthmask = outmask |
399 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
400 cbet1, cbet2, lengthmask, s12x, m12x, dummy, M12, M21, Ca);
405 if (outmask &
AREA) {
407 real sdomg12 = sin(domg12), cdomg12 = cos(domg12);
408 somg12 = slam12 * cdomg12 - clam12 * sdomg12;
409 comg12 = clam12 * cdomg12 + slam12 * sdomg12;
415 s12 =
real(0) + s12x;
418 m12 =
real(0) + m12x;
420 if (outmask &
AREA) {
423 salp0 = salp1 * cbet1,
424 calp0 = hypot(calp1, salp1 * sbet1);
426 if (calp0 != 0 && salp0 != 0) {
429 ssig1 = sbet1, csig1 = calp1 * cbet1,
430 ssig2 = sbet2, csig2 = calp2 * cbet2,
432 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2),
434 A4 =
Math::sq(_a) * calp0 * salp0 * _e2;
439 B41 = SinCosSeries(
false, ssig1, csig1, Ca, nC4_),
440 B42 = SinCosSeries(
false, ssig2, csig2, Ca, nC4_);
441 S12 = A4 * (B42 - B41);
445 if (!meridian && somg12 == 2) {
446 somg12 = sin(omg12); comg12 = cos(omg12);
451 comg12 > -
real(0.7071) &&
452 sbet2 - sbet1 <
real(1.75)) {
456 real domg12 = 1 + comg12, dbet1 = 1 + cbet1, dbet2 = 1 + cbet2;
457 alp12 = 2 * atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
458 domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) );
462 salp12 = salp2 * calp1 - calp2 * salp1,
463 calp12 = calp2 * calp1 + salp2 * salp1;
468 if (salp12 == 0 && calp12 < 0) {
469 salp12 = tiny_ * calp1;
472 alp12 = atan2(salp12, calp12);
475 S12 *= swapp * lonsign * latsign;
488 salp1 *= swapp * lonsign; calp1 *= swapp * latsign;
489 salp2 *= swapp * lonsign; calp2 *= swapp * latsign;
494 Math::real Geodesic::GenInverse(real lat1, real lon1, real lat2, real lon2,
496 real& s12, real& azi1, real& azi2,
497 real& m12, real& M12, real& M21,
500 real salp1, calp1, salp2, calp2,
501 a12 = GenInverse(lat1, lon1, lat2, lon2,
502 outmask, s12, salp1, calp1, salp2, calp2,
512 real lat2, real lon2,
513 unsigned caps)
const {
514 real t, salp1, calp1, salp2, calp2,
515 a12 = GenInverse(lat1, lon1, lat2, lon2,
517 0u, t, salp1, calp1, salp2, calp2,
523 GeodesicLine(*
this, lat1, lon1, azi1, salp1, calp1, caps,
true, a12);
526 void Geodesic::Lengths(
real eps,
real sig12,
529 real cbet1,
real cbet2,
unsigned outmask,
542 real m0x = 0, J12 = 0, A1 = 0, A2 = 0;
556 real B1 = SinCosSeries(
true, ssig2, csig2, Ca, nC1_) -
557 SinCosSeries(
true, ssig1, csig1, Ca, nC1_);
559 s12b = A1 * (sig12 + B1);
561 real B2 = SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
562 SinCosSeries(
true, ssig1, csig1, Cb, nC2_);
563 J12 = m0x * sig12 + (A1 * B1 - A2 * B2);
567 for (
int l = 1; l <= nC2_; ++l)
568 Cb[l] = A1 * Ca[l] - A2 * Cb[l];
569 J12 = m0x * sig12 + (SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
570 SinCosSeries(
true, ssig1, csig1, Cb, nC2_));
577 m12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
581 real csig12 = csig1 * csig2 + ssig1 * ssig2;
582 real t = _ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2);
583 M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
584 M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
596 if ( !(q == 0 && r <= 0) ) {
605 disc = S * (S + 2 * r3);
612 T3 += T3 < 0 ? -sqrt(disc) : sqrt(disc);
616 u += T + (T != 0 ? r2 / T : 0);
619 real ang = atan2(sqrt(-disc), -(S + r3));
622 u += 2 * r * cos(ang / 3);
627 uv = u < 0 ? q / (v - u) : u + v,
628 w = (uv - q) / (2 * v);
631 k = uv / (sqrt(uv +
Math::sq(w)) + w);
656 sbet12 = sbet2 * cbet1 - cbet2 * sbet1,
657 cbet12 = cbet2 * cbet1 + sbet2 * sbet1;
658 real sbet12a = sbet2 * cbet1 + cbet2 * sbet1;
659 bool shortline = cbet12 >= 0 && sbet12 <
real(0.5) &&
660 cbet2 * lam12 <
real(0.5);
666 sbetm2 /= sbetm2 +
Math::sq(cbet1 + cbet2);
667 dnm = sqrt(1 + _ep2 * sbetm2);
668 real omg12 = lam12 / (_f1 * dnm);
669 somg12 = sin(omg12); comg12 = cos(omg12);
671 somg12 = slam12; comg12 = clam12;
674 salp1 = cbet2 * somg12;
675 calp1 = comg12 >= 0 ?
676 sbet12 + cbet2 * sbet1 *
Math::sq(somg12) / (1 + comg12) :
677 sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
680 ssig12 = hypot(salp1, calp1),
681 csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12;
683 if (shortline && ssig12 < _etol2) {
685 salp2 = cbet1 * somg12;
686 calp2 = sbet12 - cbet1 * sbet2 *
687 (comg12 >= 0 ?
Math::sq(somg12) / (1 + comg12) : 1 - comg12);
690 sig12 = atan2(ssig12, csig12);
691 }
else if (fabs(_n) >
real(0.1) ||
698 real x, y, lamscale, betscale;
699 real lam12x = atan2(-slam12, -clam12);
705 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
706 lamscale = _f * cbet1 * A3f(eps) *
Math::pi();
708 betscale = lamscale * cbet1;
710 x = lam12x / lamscale;
711 y = sbet12a / betscale;
715 cbet12a = cbet2 * cbet1 - sbet2 * sbet1,
716 bet12a = atan2(sbet12a, cbet12a);
717 real m12b, m0, dummy;
721 sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
724 x = -1 + m12b / (cbet1 * cbet2 * m0 *
Math::pi());
725 betscale = x < -
real(0.01) ? sbet12a / x :
727 lamscale = betscale / cbet1;
728 y = lam12x / lamscale;
731 if (y > -tol1_ && x > -1 - xthresh_) {
735 salp1 = fmin(
real(1), -x); calp1 = - sqrt(1 -
Math::sq(salp1));
737 calp1 = fmax(
real(x > -tol1_ ? 0 : -1), x);
775 real k = Astroid(x, y);
777 omg12a = lamscale * ( _f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k );
778 somg12 = sin(omg12a); comg12 = -cos(omg12a);
780 salp1 = cbet2 * somg12;
781 calp1 = sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
788 salp1 = 1; calp1 = 0;
802 bool diffp,
real& dlam12,
806 if (sbet1 == 0 && calp1 == 0)
813 salp0 = salp1 * cbet1,
814 calp0 = hypot(calp1, salp1 * sbet1);
816 real somg1, comg1, somg2, comg2, somg12, comg12, lam12;
819 ssig1 = sbet1; somg1 = salp0 * sbet1;
820 csig1 = comg1 = calp1 * cbet1;
828 salp2 = cbet2 != cbet1 ? salp0 / cbet2 : salp1;
833 calp2 = cbet2 != cbet1 || fabs(sbet2) != -sbet1 ?
836 (cbet2 - cbet1) * (cbet1 + cbet2) :
837 (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 :
841 ssig2 = sbet2; somg2 = salp0 * sbet2;
842 csig2 = comg2 = calp2 * cbet2;
847 sig12 = atan2(fmax(
real(0), csig1 * ssig2 - ssig1 * csig2) +
real(0),
848 csig1 * csig2 + ssig1 * ssig2);
851 somg12 = fmax(
real(0), comg1 * somg2 - somg1 * comg2) +
real(0);
852 comg12 = comg1 * comg2 + somg1 * somg2;
854 real eta = atan2(somg12 * clam120 - comg12 * slam120,
855 comg12 * clam120 + somg12 * slam120);
858 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
860 B312 = (SinCosSeries(
true, ssig2, csig2, Ca, nC3_-1) -
861 SinCosSeries(
true, ssig1, csig1, Ca, nC3_-1));
862 domg12 = -_f * A3f(eps) * salp0 * (sig12 + B312);
863 lam12 = eta + domg12;
867 dlam12 = - 2 * _f1 * dn1 / sbet1;
870 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
872 dummy, dlam12, dummy, dummy, dummy, Ca);
873 dlam12 *= _f1 / (calp2 * cbet2);
885 void Geodesic::C3f(
real eps,
real c[])
const {
890 for (
int l = 1; l < nC3_; ++l) {
891 int m = nC3_ - l - 1;
899 void Geodesic::C4f(
real eps,
real c[])
const {
904 for (
int l = 0; l < nC4_; ++l) {
905 int m = nC4_ - l - 1;
939 #if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
940 static const real coeff[] = {
944 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
945 static const real coeff[] = {
949 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
950 static const real coeff[] = {
954 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
955 static const real coeff[] = {
957 25, 64, 256, 4096, 0, 16384,
960 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
962 static_assert(
sizeof(coeff) /
sizeof(
real) == nA1_/2 + 2,
963 "Coefficient array size mismatch in A1m1f");
966 return (t + eps) / (1 - eps);
970 void Geodesic::C1f(
real eps,
real c[]) {
972 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
973 static const real coeff[] = {
981 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
982 static const real coeff[] = {
992 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
993 static const real coeff[] = {
1005 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1006 static const real coeff[] = {
1020 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1021 static const real coeff[] = {
1023 19, -64, 384, -1024, 2048,
1037 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1038 static const real coeff[] = {
1040 19, -64, 384, -1024, 2048,
1042 7, -18, 128, -256, 4096,
1046 -11, 96, -160, 16384,
1057 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1059 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1060 (nC1_*nC1_ + 7*nC1_ - 2*(nC1_/2)) / 4,
1061 "Coefficient array size mismatch in C1f");
1066 for (
int l = 1; l <= nC1_; ++l) {
1067 int m = (nC1_ - l) / 2;
1068 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1076 void Geodesic::C1pf(
real eps,
real c[]) {
1078 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1079 static const real coeff[] = {
1087 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1088 static const real coeff[] = {
1098 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1099 static const real coeff[] = {
1101 205, -432, 768, 1536,
1111 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1112 static const real coeff[] = {
1114 205, -432, 768, 1536,
1116 4005, -4736, 3840, 12288,
1126 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1127 static const real coeff[] = {
1129 -4879, 9840, -20736, 36864, 73728,
1131 4005, -4736, 3840, 12288,
1133 8703, -7200, 3712, 12288,
1137 -141115, 41604, 92160,
1143 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1144 static const real coeff[] = {
1146 -4879, 9840, -20736, 36864, 73728,
1148 -86171, 120150, -142080, 115200, 368640,
1150 8703, -7200, 3712, 12288,
1152 1082857, -688608, 258720, 737280,
1154 -141115, 41604, 92160,
1156 -2200311, 533134, 860160,
1160 109167851, 82575360,
1163 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1165 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1166 (nC1p_*nC1p_ + 7*nC1p_ - 2*(nC1p_/2)) / 4,
1167 "Coefficient array size mismatch in C1pf");
1172 for (
int l = 1; l <= nC1p_; ++l) {
1173 int m = (nC1p_ - l) / 2;
1174 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1184 #if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
1185 static const real coeff[] = {
1189 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
1190 static const real coeff[] = {
1194 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
1195 static const real coeff[] = {
1197 -11, -28, -192, 0, 256,
1199 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
1200 static const real coeff[] = {
1202 -375, -704, -1792, -12288, 0, 16384,
1205 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1207 static_assert(
sizeof(coeff) /
sizeof(
real) == nA2_/2 + 2,
1208 "Coefficient array size mismatch in A2m1f");
1211 return (t - eps) / (1 + eps);
1215 void Geodesic::C2f(
real eps,
real c[]) {
1217 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1218 static const real coeff[] = {
1226 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1227 static const real coeff[] = {
1237 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1238 static const real coeff[] = {
1250 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1251 static const real coeff[] = {
1265 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1266 static const real coeff[] = {
1268 41, 64, 128, 1024, 2048,
1282 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1283 static const real coeff[] = {
1285 41, 64, 128, 1024, 2048,
1287 47, 70, 128, 768, 4096,
1291 133, 224, 1120, 16384,
1302 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1304 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1305 (nC2_*nC2_ + 7*nC2_ - 2*(nC2_/2)) / 4,
1306 "Coefficient array size mismatch in C2f");
1311 for (
int l = 1; l <= nC2_; ++l) {
1312 int m = (nC2_ - l) / 2;
1313 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1321 void Geodesic::A3coeff() {
1323 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1324 static const real coeff[] = {
1332 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1333 static const real coeff[] = {
1343 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1344 static const real coeff[] = {
1356 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1357 static const real coeff[] = {
1371 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1372 static const real coeff[] = {
1388 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1389 static const real coeff[] = {
1397 -5, -20, -4, -6, 128,
1408 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1410 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1411 (nA3_*nA3_ + 7*nA3_ - 2*(nA3_/2)) / 4,
1412 "Coefficient array size mismatch in A3f");
1414 for (
int j = nA3_ - 1; j >= 0; --j) {
1415 int m = min(nA3_ - j - 1, j);
1416 _aA3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1423 void Geodesic::C3coeff() {
1425 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1426 static const real coeff[] = {
1434 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1435 static const real coeff[] = {
1451 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1452 static const real coeff[] = {
1474 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1475 static const real coeff[] = {
1507 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1508 static const real coeff[] = {
1552 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1553 static const real coeff[] = {
1587 10, -6, -10, 9, 384,
1597 -7, 20, -28, 14, 1024,
1612 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1614 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1615 ((nC3_-1)*(nC3_*nC3_ + 7*nC3_ - 2*(nC3_/2)))/8,
1616 "Coefficient array size mismatch in C3coeff");
1618 for (
int l = 1; l < nC3_; ++l) {
1619 for (
int j = nC3_ - 1; j >= l; --j) {
1620 int m = min(nC3_ - j - 1, j);
1621 _cC3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1628 void Geodesic::C4coeff() {
1630 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1631 static const real coeff[] = {
1645 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1646 static const real coeff[] = {
1654 4, 24, -84, 210, 315,
1668 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1669 static const real coeff[] = {
1675 1088, -352, -66, 3465,
1677 48, -352, 528, -231, 1155,
1679 16, 44, 264, -924, 2310, 3465,
1685 -896, 704, -198, 10395,
1687 -48, 352, -528, 231, 10395,
1693 320, -352, 132, 17325,
1701 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1702 static const real coeff[] = {
1708 -224, -4784, 1573, 45045,
1710 -10656, 14144, -4576, -858, 45045,
1712 64, 624, -4576, 6864, -3003, 15015,
1714 100, 208, 572, 3432, -12012, 30030, 45045,
1720 5792, 1040, -1287, 135135,
1722 5952, -11648, 9152, -2574, 135135,
1724 -64, -624, 4576, -6864, 3003, 135135,
1730 -8448, 4992, -1144, 225225,
1732 -1440, 4160, -4576, 1716, 225225,
1738 3584, -3328, 1144, 315315,
1746 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1747 static const real coeff[] = {
1753 -4480, 1088, 156, 45045,
1755 10736, -224, -4784, 1573, 45045,
1757 1664, -10656, 14144, -4576, -858, 45045,
1759 16, 64, 624, -4576, 6864, -3003, 15015,
1761 56, 100, 208, 572, 3432, -12012, 30030, 45045,
1767 3840, -2944, 468, 135135,
1769 -10704, 5792, 1040, -1287, 135135,
1771 -768, 5952, -11648, 9152, -2574, 135135,
1773 -16, -64, -624, 4576, -6864, 3003, 135135,
1779 1664, 1856, -936, 225225,
1781 6784, -8448, 4992, -1144, 225225,
1783 128, -1440, 4160, -4576, 1716, 225225,
1789 -2048, 1024, -208, 105105,
1791 -1792, 3584, -3328, 1144, 315315,
1797 3072, -2560, 832, 405405,
1805 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1806 static const real coeff[] = {
1812 20960, -7888, 4947, 765765,
1814 12480, -76160, 18496, 2652, 765765,
1816 -154048, 182512, -3808, -81328, 26741, 765765,
1818 3232, 28288, -181152, 240448, -77792, -14586, 765765,
1820 96, 272, 1088, 10608, -77792, 116688, -51051, 255255,
1822 588, 952, 1700, 3536, 9724, 58344, -204204, 510510, 765765,
1828 -39840, 1904, 255, 2297295,
1830 52608, 65280, -50048, 7956, 2297295,
1832 103744, -181968, 98464, 17680, -21879, 2297295,
1834 -1344, -13056, 101184, -198016, 155584, -43758, 2297295,
1836 -96, -272, -1088, -10608, 77792, -116688, 51051, 2297295,
1840 -928, -612, 3828825,
1842 64256, -28288, 2856, 3828825,
1844 -126528, 28288, 31552, -15912, 3828825,
1846 -41472, 115328, -143616, 84864, -19448, 3828825,
1848 160, 2176, -24480, 70720, -77792, 29172, 3828825,
1852 -16384, 1088, 5360355,
1854 -2560, 30464, -11560, 5360355,
1856 35840, -34816, 17408, -3536, 1786785,
1858 7168, -30464, 60928, -56576, 19448, 5360355,
1862 26624, -8704, 6891885,
1864 -77824, 34816, -6528, 6891885,
1866 -32256, 52224, -43520, 14144, 6891885,
1870 24576, -4352, 8423415,
1872 45056, -34816, 10880, 8423415,
1876 -28672, 8704, 9954945,
1881 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1883 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1884 (nC4_ * (nC4_ + 1) * (nC4_ + 5)) / 6,
1885 "Coefficient array size mismatch in C4coeff");
1887 for (
int l = 0; l < nC4_; ++l) {
1888 for (
int j = nC4_ - 1; j >= l; --j) {
1889 int m = nC4_ - j - 1;
1890 _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.
#define GEOGRAPHICLIB_PANIC
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
Exception handling for GeographicLib.
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 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)
@ hd
degrees per half turn
@ qd
degrees per quarter turn
Namespace for GeographicLib.
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)