35 # pragma warning (disable: 4701 4127 5055 5054)
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) {
369 sdalp1 = sin(dalp1), cdalp1 = cos(dalp1),
370 nsalp1 = salp1 * cdalp1 + calp1 * sdalp1;
372 calp1 = calp1 * cdalp1 - salp1 * sdalp1;
378 tripn = fabs(v) <= 16 * tol0_;
391 salp1 = (salp1a + salp1b)/2;
392 calp1 = (calp1a + calp1b)/2;
395 tripb = (fabs(salp1a - salp1) + (calp1a - calp1) < tolb_ ||
396 fabs(salp1 - salp1b) + (calp1 - calp1b) < tolb_);
402 unsigned lengthmask = outmask |
404 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
405 cbet1, cbet2, lengthmask, s12x, m12x, dummy, M12, M21, Ca);
410 if (outmask &
AREA) {
412 real sdomg12 = sin(domg12), cdomg12 = cos(domg12);
413 somg12 = slam12 * cdomg12 - clam12 * sdomg12;
414 comg12 = clam12 * cdomg12 + slam12 * sdomg12;
420 s12 =
real(0) + s12x;
423 m12 =
real(0) + m12x;
425 if (outmask &
AREA) {
428 salp0 = salp1 * cbet1,
429 calp0 = hypot(calp1, salp1 * sbet1);
431 if (calp0 != 0 && salp0 != 0) {
434 ssig1 = sbet1, csig1 = calp1 * cbet1,
435 ssig2 = sbet2, csig2 = calp2 * cbet2,
437 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2),
439 A4 =
Math::sq(_a) * calp0 * salp0 * _e2;
444 B41 = SinCosSeries(
false, ssig1, csig1, Ca, nC4_),
445 B42 = SinCosSeries(
false, ssig2, csig2, Ca, nC4_);
446 S12 = A4 * (B42 - B41);
450 if (!meridian && somg12 == 2) {
451 somg12 = sin(omg12); comg12 = cos(omg12);
456 comg12 > -
real(0.7071) &&
457 sbet2 - sbet1 <
real(1.75)) {
461 real domg12 = 1 + comg12, dbet1 = 1 + cbet1, dbet2 = 1 + cbet2;
462 alp12 = 2 * atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
463 domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) );
467 salp12 = salp2 * calp1 - calp2 * salp1,
468 calp12 = calp2 * calp1 + salp2 * salp1;
473 if (salp12 == 0 && calp12 < 0) {
474 salp12 = tiny_ * calp1;
477 alp12 = atan2(salp12, calp12);
480 S12 *= swapp * lonsign * latsign;
493 salp1 *= swapp * lonsign; calp1 *= swapp * latsign;
494 salp2 *= swapp * lonsign; calp2 *= swapp * latsign;
499 Math::real Geodesic::GenInverse(real lat1, real lon1, real lat2, real lon2,
501 real& s12, real& azi1, real& azi2,
502 real& m12, real& M12, real& M21,
505 real salp1, calp1, salp2, calp2,
506 a12 = GenInverse(lat1, lon1, lat2, lon2,
507 outmask, s12, salp1, calp1, salp2, calp2,
517 real lat2, real lon2,
518 unsigned caps)
const {
519 real t, salp1, calp1, salp2, calp2,
520 a12 = GenInverse(lat1, lon1, lat2, lon2,
522 0u, t, salp1, calp1, salp2, calp2,
528 GeodesicLine(*
this, lat1, lon1, azi1, salp1, calp1, caps,
true, a12);
531 void Geodesic::Lengths(
real eps,
real sig12,
534 real cbet1,
real cbet2,
unsigned outmask,
547 real m0x = 0, J12 = 0, A1 = 0, A2 = 0;
561 real B1 = SinCosSeries(
true, ssig2, csig2, Ca, nC1_) -
562 SinCosSeries(
true, ssig1, csig1, Ca, nC1_);
564 s12b = A1 * (sig12 + B1);
566 real B2 = SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
567 SinCosSeries(
true, ssig1, csig1, Cb, nC2_);
568 J12 = m0x * sig12 + (A1 * B1 - A2 * B2);
572 for (
int l = 1; l <= nC2_; ++l)
573 Cb[l] = A1 * Ca[l] - A2 * Cb[l];
574 J12 = m0x * sig12 + (SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
575 SinCosSeries(
true, ssig1, csig1, Cb, nC2_));
582 m12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
586 real csig12 = csig1 * csig2 + ssig1 * ssig2;
587 real t = _ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2);
588 M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
589 M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
601 if ( !(q == 0 && r <= 0) ) {
610 disc = S * (S + 2 * r3);
617 T3 += T3 < 0 ? -sqrt(disc) : sqrt(disc);
621 u += T + (T != 0 ? r2 / T : 0);
624 real ang = atan2(sqrt(-disc), -(S + r3));
627 u += 2 * r * cos(ang / 3);
632 uv = u < 0 ? q / (v - u) : u + v,
633 w = (uv - q) / (2 * v);
636 k = uv / (sqrt(uv +
Math::sq(w)) + w);
661 sbet12 = sbet2 * cbet1 - cbet2 * sbet1,
662 cbet12 = cbet2 * cbet1 + sbet2 * sbet1;
663 real sbet12a = sbet2 * cbet1 + cbet2 * sbet1;
664 bool shortline = cbet12 >= 0 && sbet12 <
real(0.5) &&
665 cbet2 * lam12 <
real(0.5);
671 sbetm2 /= sbetm2 +
Math::sq(cbet1 + cbet2);
672 dnm = sqrt(1 + _ep2 * sbetm2);
673 real omg12 = lam12 / (_f1 * dnm);
674 somg12 = sin(omg12); comg12 = cos(omg12);
676 somg12 = slam12; comg12 = clam12;
679 salp1 = cbet2 * somg12;
680 calp1 = comg12 >= 0 ?
681 sbet12 + cbet2 * sbet1 *
Math::sq(somg12) / (1 + comg12) :
682 sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
685 ssig12 = hypot(salp1, calp1),
686 csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12;
688 if (shortline && ssig12 < _etol2) {
690 salp2 = cbet1 * somg12;
691 calp2 = sbet12 - cbet1 * sbet2 *
692 (comg12 >= 0 ?
Math::sq(somg12) / (1 + comg12) : 1 - comg12);
695 sig12 = atan2(ssig12, csig12);
696 }
else if (fabs(_n) >
real(0.1) ||
703 real x, y, lamscale, betscale;
704 real lam12x = atan2(-slam12, -clam12);
710 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
711 lamscale = _f * cbet1 * A3f(eps) *
Math::pi();
713 betscale = lamscale * cbet1;
715 x = lam12x / lamscale;
716 y = sbet12a / betscale;
720 cbet12a = cbet2 * cbet1 - sbet2 * sbet1,
721 bet12a = atan2(sbet12a, cbet12a);
722 real m12b, m0, dummy;
726 sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
729 x = -1 + m12b / (cbet1 * cbet2 * m0 *
Math::pi());
730 betscale = x < -
real(0.01) ? sbet12a / x :
732 lamscale = betscale / cbet1;
733 y = lam12x / lamscale;
736 if (y > -tol1_ && x > -1 - xthresh_) {
740 salp1 = fmin(
real(1), -x); calp1 = - sqrt(1 -
Math::sq(salp1));
742 calp1 = fmax(
real(x > -tol1_ ? 0 : -1), x);
780 real k = Astroid(x, y);
782 omg12a = lamscale * ( _f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k );
783 somg12 = sin(omg12a); comg12 = -cos(omg12a);
785 salp1 = cbet2 * somg12;
786 calp1 = sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
793 salp1 = 1; calp1 = 0;
807 bool diffp,
real& dlam12,
811 if (sbet1 == 0 && calp1 == 0)
818 salp0 = salp1 * cbet1,
819 calp0 = hypot(calp1, salp1 * sbet1);
821 real somg1, comg1, somg2, comg2, somg12, comg12, lam12;
824 ssig1 = sbet1; somg1 = salp0 * sbet1;
825 csig1 = comg1 = calp1 * cbet1;
833 salp2 = cbet2 != cbet1 ? salp0 / cbet2 : salp1;
838 calp2 = cbet2 != cbet1 || fabs(sbet2) != -sbet1 ?
841 (cbet2 - cbet1) * (cbet1 + cbet2) :
842 (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 :
846 ssig2 = sbet2; somg2 = salp0 * sbet2;
847 csig2 = comg2 = calp2 * cbet2;
852 sig12 = atan2(fmax(
real(0), csig1 * ssig2 - ssig1 * csig2) +
real(0),
853 csig1 * csig2 + ssig1 * ssig2);
856 somg12 = fmax(
real(0), comg1 * somg2 - somg1 * comg2) +
real(0);
857 comg12 = comg1 * comg2 + somg1 * somg2;
859 real eta = atan2(somg12 * clam120 - comg12 * slam120,
860 comg12 * clam120 + somg12 * slam120);
863 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
865 B312 = (SinCosSeries(
true, ssig2, csig2, Ca, nC3_-1) -
866 SinCosSeries(
true, ssig1, csig1, Ca, nC3_-1));
867 domg12 = -_f * A3f(eps) * salp0 * (sig12 + B312);
868 lam12 = eta + domg12;
872 dlam12 = - 2 * _f1 * dn1 / sbet1;
875 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
877 dummy, dlam12, dummy, dummy, dummy, Ca);
878 dlam12 *= _f1 / (calp2 * cbet2);
890 void Geodesic::C3f(
real eps,
real c[])
const {
895 for (
int l = 1; l < nC3_; ++l) {
896 int m = nC3_ - l - 1;
904 void Geodesic::C4f(
real eps,
real c[])
const {
909 for (
int l = 0; l < nC4_; ++l) {
910 int m = nC4_ - l - 1;
944 #if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
945 static const real coeff[] = {
949 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
950 static const real coeff[] = {
954 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
955 static const real coeff[] = {
959 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
960 static const real coeff[] = {
962 25, 64, 256, 4096, 0, 16384,
965 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
967 static_assert(
sizeof(coeff) /
sizeof(
real) == nA1_/2 + 2,
968 "Coefficient array size mismatch in A1m1f");
971 return (t + eps) / (1 - eps);
975 void Geodesic::C1f(
real eps,
real c[]) {
977 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
978 static const real coeff[] = {
986 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
987 static const real coeff[] = {
997 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
998 static const real coeff[] = {
1010 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1011 static const real coeff[] = {
1025 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1026 static const real coeff[] = {
1028 19, -64, 384, -1024, 2048,
1042 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1043 static const real coeff[] = {
1045 19, -64, 384, -1024, 2048,
1047 7, -18, 128, -256, 4096,
1051 -11, 96, -160, 16384,
1062 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1064 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1065 (nC1_*nC1_ + 7*nC1_ - 2*(nC1_/2)) / 4,
1066 "Coefficient array size mismatch in C1f");
1071 for (
int l = 1; l <= nC1_; ++l) {
1072 int m = (nC1_ - l) / 2;
1073 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1081 void Geodesic::C1pf(
real eps,
real c[]) {
1083 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1084 static const real coeff[] = {
1092 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1093 static const real coeff[] = {
1103 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1104 static const real coeff[] = {
1106 205, -432, 768, 1536,
1116 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1117 static const real coeff[] = {
1119 205, -432, 768, 1536,
1121 4005, -4736, 3840, 12288,
1131 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1132 static const real coeff[] = {
1134 -4879, 9840, -20736, 36864, 73728,
1136 4005, -4736, 3840, 12288,
1138 8703, -7200, 3712, 12288,
1142 -141115, 41604, 92160,
1148 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1149 static const real coeff[] = {
1151 -4879, 9840, -20736, 36864, 73728,
1153 -86171, 120150, -142080, 115200, 368640,
1155 8703, -7200, 3712, 12288,
1157 1082857, -688608, 258720, 737280,
1159 -141115, 41604, 92160,
1161 -2200311, 533134, 860160,
1165 109167851, 82575360,
1168 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1170 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1171 (nC1p_*nC1p_ + 7*nC1p_ - 2*(nC1p_/2)) / 4,
1172 "Coefficient array size mismatch in C1pf");
1177 for (
int l = 1; l <= nC1p_; ++l) {
1178 int m = (nC1p_ - l) / 2;
1179 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1189 #if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
1190 static const real coeff[] = {
1194 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
1195 static const real coeff[] = {
1199 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
1200 static const real coeff[] = {
1202 -11, -28, -192, 0, 256,
1204 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
1205 static const real coeff[] = {
1207 -375, -704, -1792, -12288, 0, 16384,
1210 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1212 static_assert(
sizeof(coeff) /
sizeof(
real) == nA2_/2 + 2,
1213 "Coefficient array size mismatch in A2m1f");
1216 return (t - eps) / (1 + eps);
1220 void Geodesic::C2f(
real eps,
real c[]) {
1222 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1223 static const real coeff[] = {
1231 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1232 static const real coeff[] = {
1242 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1243 static const real coeff[] = {
1255 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1256 static const real coeff[] = {
1270 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1271 static const real coeff[] = {
1273 41, 64, 128, 1024, 2048,
1287 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1288 static const real coeff[] = {
1290 41, 64, 128, 1024, 2048,
1292 47, 70, 128, 768, 4096,
1296 133, 224, 1120, 16384,
1307 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1309 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1310 (nC2_*nC2_ + 7*nC2_ - 2*(nC2_/2)) / 4,
1311 "Coefficient array size mismatch in C2f");
1316 for (
int l = 1; l <= nC2_; ++l) {
1317 int m = (nC2_ - l) / 2;
1318 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1326 void Geodesic::A3coeff() {
1328 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1329 static const real coeff[] = {
1337 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1338 static const real coeff[] = {
1348 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1349 static const real coeff[] = {
1361 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1362 static const real coeff[] = {
1376 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1377 static const real coeff[] = {
1393 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1394 static const real coeff[] = {
1402 -5, -20, -4, -6, 128,
1413 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1415 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1416 (nA3_*nA3_ + 7*nA3_ - 2*(nA3_/2)) / 4,
1417 "Coefficient array size mismatch in A3f");
1419 for (
int j = nA3_ - 1; j >= 0; --j) {
1420 int m = min(nA3_ - j - 1, j);
1421 _aA3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1428 void Geodesic::C3coeff() {
1430 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1431 static const real coeff[] = {
1439 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1440 static const real coeff[] = {
1456 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1457 static const real coeff[] = {
1479 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1480 static const real coeff[] = {
1512 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1513 static const real coeff[] = {
1557 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1558 static const real coeff[] = {
1592 10, -6, -10, 9, 384,
1602 -7, 20, -28, 14, 1024,
1617 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1619 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1620 ((nC3_-1)*(nC3_*nC3_ + 7*nC3_ - 2*(nC3_/2)))/8,
1621 "Coefficient array size mismatch in C3coeff");
1623 for (
int l = 1; l < nC3_; ++l) {
1624 for (
int j = nC3_ - 1; j >= l; --j) {
1625 int m = min(nC3_ - j - 1, j);
1626 _cC3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1633 void Geodesic::C4coeff() {
1635 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1636 static const real coeff[] = {
1650 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1651 static const real coeff[] = {
1659 4, 24, -84, 210, 315,
1673 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1674 static const real coeff[] = {
1680 1088, -352, -66, 3465,
1682 48, -352, 528, -231, 1155,
1684 16, 44, 264, -924, 2310, 3465,
1690 -896, 704, -198, 10395,
1692 -48, 352, -528, 231, 10395,
1698 320, -352, 132, 17325,
1706 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1707 static const real coeff[] = {
1713 -224, -4784, 1573, 45045,
1715 -10656, 14144, -4576, -858, 45045,
1717 64, 624, -4576, 6864, -3003, 15015,
1719 100, 208, 572, 3432, -12012, 30030, 45045,
1725 5792, 1040, -1287, 135135,
1727 5952, -11648, 9152, -2574, 135135,
1729 -64, -624, 4576, -6864, 3003, 135135,
1735 -8448, 4992, -1144, 225225,
1737 -1440, 4160, -4576, 1716, 225225,
1743 3584, -3328, 1144, 315315,
1751 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1752 static const real coeff[] = {
1758 -4480, 1088, 156, 45045,
1760 10736, -224, -4784, 1573, 45045,
1762 1664, -10656, 14144, -4576, -858, 45045,
1764 16, 64, 624, -4576, 6864, -3003, 15015,
1766 56, 100, 208, 572, 3432, -12012, 30030, 45045,
1772 3840, -2944, 468, 135135,
1774 -10704, 5792, 1040, -1287, 135135,
1776 -768, 5952, -11648, 9152, -2574, 135135,
1778 -16, -64, -624, 4576, -6864, 3003, 135135,
1784 1664, 1856, -936, 225225,
1786 6784, -8448, 4992, -1144, 225225,
1788 128, -1440, 4160, -4576, 1716, 225225,
1794 -2048, 1024, -208, 105105,
1796 -1792, 3584, -3328, 1144, 315315,
1802 3072, -2560, 832, 405405,
1810 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1811 static const real coeff[] = {
1817 20960, -7888, 4947, 765765,
1819 12480, -76160, 18496, 2652, 765765,
1821 -154048, 182512, -3808, -81328, 26741, 765765,
1823 3232, 28288, -181152, 240448, -77792, -14586, 765765,
1825 96, 272, 1088, 10608, -77792, 116688, -51051, 255255,
1827 588, 952, 1700, 3536, 9724, 58344, -204204, 510510, 765765,
1833 -39840, 1904, 255, 2297295,
1835 52608, 65280, -50048, 7956, 2297295,
1837 103744, -181968, 98464, 17680, -21879, 2297295,
1839 -1344, -13056, 101184, -198016, 155584, -43758, 2297295,
1841 -96, -272, -1088, -10608, 77792, -116688, 51051, 2297295,
1845 -928, -612, 3828825,
1847 64256, -28288, 2856, 3828825,
1849 -126528, 28288, 31552, -15912, 3828825,
1851 -41472, 115328, -143616, 84864, -19448, 3828825,
1853 160, 2176, -24480, 70720, -77792, 29172, 3828825,
1857 -16384, 1088, 5360355,
1859 -2560, 30464, -11560, 5360355,
1861 35840, -34816, 17408, -3536, 1786785,
1863 7168, -30464, 60928, -56576, 19448, 5360355,
1867 26624, -8704, 6891885,
1869 -77824, 34816, -6528, 6891885,
1871 -32256, 52224, -43520, 14144, 6891885,
1875 24576, -4352, 8423415,
1877 45056, -34816, 10880, 8423415,
1881 -28672, 8704, 9954945,
1886 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1888 static_assert(
sizeof(coeff) /
sizeof(
real) ==
1889 (nC4_ * (nC4_ + 1) * (nC4_ + 5)) / 6,
1890 "Coefficient array size mismatch in C4coeff");
1892 for (
int l = 0; l < nC4_; ++l) {
1893 for (
int j = nC4_ - 1; j >= l; --j) {
1894 int m = nC4_ - j - 1;
1895 _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)