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())
55 , tolb_(tol0_ * tol2_)
56 , xthresh_(1000 * tol2_)
58 , _f(f <= 1 ? f : 1/f)
61 , _ep2(_e2 /
Math::sq(_f1))
65 Math::eatanhe(real(1), (_f < 0 ? -1 : 1) * sqrt(abs(_e2))) / _e2)
77 , _etol2(0.1 * tol2_ /
78 sqrt( max(real(0.001), abs(_f)) * min(real(1), 1 - _f/2) / 2 ))
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
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);
138 real& s12, real& azi1, real& azi2,
139 real& m12, real& M12, real& M21, real& S12)
148 int lonsign = lon12 >= 0 ? 1 : -1;
154 int swapp = abs(lat1) >= abs(lat2) ? 1 : -1;
160 int latsign = lat1 < 0 ? 1 : -1;
175 real sbet1, cbet1, sbet2, cbet2, s12x, m12x;
180 Math::norm(sbet1, cbet1); cbet1 = max(tiny_, cbet1);
184 Math::norm(sbet2, cbet2); cbet2 = max(tiny_, cbet2);
194 if (cbet1 < -sbet1) {
196 sbet2 = sbet2 < 0 ? sbet1 : -sbet1;
198 if (abs(sbet2) == -sbet1)
203 dn1 = sqrt(1 + _ep2 *
Math::sq(sbet1)),
204 dn2 = sqrt(1 + _ep2 *
Math::sq(sbet2));
211 real a12, sig12, calp1, salp1, calp2 = 0, salp2 = 0;
215 bool meridian = lat1 == -90 || slam12 == 0;
222 calp1 = clam12; salp1 = slam12;
223 calp2 = 1; salp2 = 0;
227 ssig1 = sbet1, csig1 = calp1 * cbet1,
228 ssig2 = sbet2, csig2 = calp2 * cbet2;
231 sig12 = atan2(max(csig1 * ssig2 - ssig1 * csig2, real(0)),
232 csig1 * csig2 + ssig1 * ssig2);
235 Lengths(_n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2,
237 s12x, m12x, dummy, M12, M21, Ca);
246 if (sig12 < 1 || m12x >= 0) {
248 if (sig12 < 3 * tiny_)
249 sig12 = m12x = s12x = 0;
265 calp1 = calp2 = 0; salp1 = salp2 = 1;
267 sig12 = omg12 = lam12 / _f1;
268 m12x = _b * sin(sig12);
270 M12 = M21 = cos(sig12);
273 }
else if (!meridian) {
280 sig12 = InverseStart(sbet1, cbet1, dn1, sbet2, cbet2, dn2,
282 salp1, calp1, salp2, calp2, dnm,
287 s12x = sig12 * _b * dnm;
288 m12x =
Math::sq(dnm) * _b * sin(sig12 / dnm);
290 M12 = M21 = cos(sig12 / dnm);
292 omg12 = lam12 / (_f1 * dnm);
308 real ssig1 = 0, csig1 = 0, ssig2 = 0, csig2 = 0, eps = 0;
311 real salp1a = tiny_, calp1a = 1, salp1b = tiny_, calp1b = -1;
312 for (
bool tripn =
false, tripb =
false;
318 real v = Lambda12(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1,
319 salp2, calp2, sig12, ssig1, csig1, ssig2, csig2,
320 eps, omg12, numit < maxit1_, dv, Ca)
324 if (tripb || !(abs(v) >= (tripn ? 8 : 2) * tol0_))
break;
326 if (v > 0 && (numit > maxit1_ || calp1/salp1 > calp1b/salp1b))
327 { salp1b = salp1; calp1b = calp1; }
328 else if (v < 0 && (numit > maxit1_ || calp1/salp1 < calp1a/salp1a))
329 { salp1a = salp1; calp1a = calp1; }
330 if (numit < maxit1_ && dv > 0) {
334 sdalp1 = sin(dalp1), cdalp1 = cos(dalp1),
335 nsalp1 = salp1 * cdalp1 + calp1 * sdalp1;
336 if (nsalp1 > 0 && abs(dalp1) <
Math::pi()) {
337 calp1 = calp1 * cdalp1 - salp1 * sdalp1;
343 tripn = abs(v) <= 16 * tol0_;
355 salp1 = (salp1a + salp1b)/2;
356 calp1 = (calp1a + calp1b)/2;
359 tripb = (abs(salp1a - salp1) + (calp1a - calp1) < tolb_ ||
360 abs(salp1 - salp1b) + (calp1 - calp1b) < tolb_);
366 unsigned lengthmask = outmask |
368 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
369 cbet1, cbet2, lengthmask, s12x, m12x, dummy, M12, M21, Ca);
374 omg12 = lam12 - omg12;
384 if (outmask &
AREA) {
387 salp0 = salp1 * cbet1,
390 if (calp0 != 0 && salp0 != 0) {
393 ssig1 = sbet1, csig1 = calp1 * cbet1,
394 ssig2 = sbet2, csig2 = calp2 * cbet2,
396 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2),
398 A4 =
Math::sq(_a) * calp0 * salp0 * _e2;
403 B41 = SinCosSeries(
false, ssig1, csig1, Ca, nC4_),
404 B42 = SinCosSeries(
false, ssig2, csig2, Ca, nC4_);
405 S12 = A4 * (B42 - B41);
412 sbet2 - sbet1 < real(1.75)) {
417 somg12 = sin(omg12), domg12 = 1 + cos(omg12),
418 dbet1 = 1 + cbet1, dbet2 = 1 + cbet2;
419 alp12 = 2 * atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
420 domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) );
424 salp12 = salp2 * calp1 - calp2 * salp1,
425 calp12 = calp2 * calp1 + salp2 * salp1;
430 if (salp12 == 0 && calp12 < 0) {
431 salp12 = tiny_ * calp1;
434 alp12 = atan2(salp12, calp12);
437 S12 *= swapp * lonsign * latsign;
450 salp1 *= swapp * lonsign; calp1 *= swapp * latsign;
451 salp2 *= swapp * lonsign; calp2 *= swapp * latsign;
462 void Geodesic::Lengths(
real eps,
real sig12,
465 real cbet1,
real cbet2,
unsigned outmask,
477 real m0x = 0, J12 = 0, A1 = 0, A2 = 0;
491 real B1 = SinCosSeries(
true, ssig2, csig2, Ca, nC1_) -
492 SinCosSeries(
true, ssig1, csig1, Ca, nC1_);
494 s12b = A1 * (sig12 + B1);
496 real B2 = SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
497 SinCosSeries(
true, ssig1, csig1, Cb, nC2_);
498 J12 = m0x * sig12 + (A1 * B1 - A2 * B2);
502 for (
int l = 1; l <= nC2_; ++l)
503 Cb[l] = A1 * Ca[l] - A2 * Cb[l];
504 J12 = m0x * sig12 + (SinCosSeries(
true, ssig2, csig2, Cb, nC2_) -
505 SinCosSeries(
true, ssig1, csig1, Cb, nC2_));
512 m12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
516 real csig12 = csig1 * csig2 + ssig1 * ssig2;
517 real t = _ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2);
518 M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
519 M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
531 if ( !(q == 0 && r <= 0) ) {
540 disc = S * (S + 2 * r3);
547 T3 += T3 < 0 ? -sqrt(disc) : sqrt(disc);
551 u += T + (T ? r2 / T : 0);
554 real ang = atan2(sqrt(-disc), -(S + r3));
557 u += 2 * r * cos(ang / 3);
562 uv = u < 0 ? q / (v - u) : u + v,
563 w = (uv - q) / (2 * v);
566 k = uv / (sqrt(uv +
Math::sq(w)) + w);
591 sbet12 = sbet2 * cbet1 - cbet2 * sbet1,
592 cbet12 = cbet2 * cbet1 + sbet2 * sbet1;
593 #if defined(__GNUC__) && __GNUC__ == 4 && \
594 (__GNUC_MINOR__ < 6 || defined(__MINGW32__))
608 real sbet12a = sbet2 * cbet1 + cbet2 * sbet1;
610 bool shortline = cbet12 >= 0 && sbet12 <
real(0.5) &&
611 cbet2 * lam12 <
real(0.5);
617 sbetm2 /= sbetm2 +
Math::sq(cbet1 + cbet2);
618 dnm = sqrt(1 + _ep2 * sbetm2);
621 real somg12 = sin(omg12), comg12 = cos(omg12);
623 salp1 = cbet2 * somg12;
624 calp1 = comg12 >= 0 ?
625 sbet12 + cbet2 * sbet1 *
Math::sq(somg12) / (1 + comg12) :
626 sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
630 csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12;
632 if (shortline && ssig12 < _etol2) {
634 salp2 = cbet1 * somg12;
635 calp2 = sbet12 - cbet1 * sbet2 *
636 (comg12 >= 0 ?
Math::sq(somg12) / (1 + comg12) : 1 - comg12);
639 sig12 = atan2(ssig12, csig12);
640 }
else if (abs(_n) >
real(0.1) ||
647 real y, lamscale, betscale;
657 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
658 lamscale = _f * cbet1 * A3f(eps) *
Math::pi();
660 betscale = lamscale * cbet1;
662 x = (lam12 -
Math::pi()) / lamscale;
663 y = sbet12a / betscale;
667 cbet12a = cbet2 * cbet1 - sbet2 * sbet1,
668 bet12a = atan2(sbet12a, cbet12a);
669 real m12b, m0, dummy;
673 sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
674 cbet1, cbet2, REDUCEDLENGTH, dummy, m12b, m0, dummy, dummy, Ca);
675 x = -1 + m12b / (cbet1 * cbet2 * m0 *
Math::pi());
676 betscale = x < -
real(0.01) ? sbet12a / x :
678 lamscale = betscale / cbet1;
679 y = (lam12 -
Math::pi()) / lamscale;
682 if (y > -tol1_ && x > -1 - xthresh_) {
688 calp1 = max(
real(x > -tol1_ ? 0 : -1),
real(x));
726 real k = Astroid(x, y);
728 omg12a = lamscale * ( _f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k );
729 somg12 = sin(omg12a); comg12 = -cos(omg12a);
731 salp1 = cbet2 * somg12;
732 calp1 = sbet12a - cbet2 * sbet1 *
Math::sq(somg12) / (1 - comg12);
739 salp1 = 1; calp1 = 0;
752 bool diffp,
real& dlam12,
756 if (sbet1 == 0 && calp1 == 0)
763 salp0 = salp1 * cbet1,
766 real somg1, comg1, somg2, comg2, omg12, lam12;
769 ssig1 = sbet1; somg1 = salp0 * sbet1;
770 csig1 = comg1 = calp1 * cbet1;
778 salp2 = cbet2 != cbet1 ? salp0 / cbet2 : salp1;
783 calp2 = cbet2 != cbet1 || abs(sbet2) != -sbet1 ?
786 (cbet2 - cbet1) * (cbet1 + cbet2) :
787 (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 :
791 ssig2 = sbet2; somg2 = salp0 * sbet2;
792 csig2 = comg2 = calp2 * cbet2;
797 sig12 = atan2(max(csig1 * ssig2 - ssig1 * csig2,
real(0)),
798 csig1 * csig2 + ssig1 * ssig2);
801 omg12 = atan2(max(comg1 * somg2 - somg1 * comg2,
real(0)),
802 comg1 * comg2 + somg1 * somg2);
805 eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2);
807 B312 = (SinCosSeries(
true, ssig2, csig2, Ca, nC3_-1) -
808 SinCosSeries(
true, ssig1, csig1, Ca, nC3_-1));
810 domg12 = salp0 * h0 * (sig12 + B312);
811 lam12 = omg12 + domg12;
815 dlam12 = - 2 * _f1 * dn1 / sbet1;
818 Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
819 cbet1, cbet2, REDUCEDLENGTH,
820 dummy, dlam12, dummy, dummy, dummy, Ca);
821 dlam12 *= _f1 / (calp2 * cbet2);
833 void Geodesic::C3f(
real eps,
real c[])
const {
838 for (
int l = 1; l < nC3_; ++l) {
839 int m = nC3_ - l - 1;
847 void Geodesic::C4f(
real eps,
real c[])
const {
852 for (
int l = 0; l < nC4_; ++l) {
853 int m = nC4_ - l - 1;
887 #if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
888 static const real coeff[] = {
892 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
893 static const real coeff[] = {
897 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
898 static const real coeff[] = {
902 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
903 static const real coeff[] = {
905 25, 64, 256, 4096, 0, 16384,
908 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
910 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) == nA1_/2 + 2,
911 "Coefficient array size mismatch in A1m1f");
914 return (t + eps) / (1 - eps);
918 void Geodesic::C1f(
real eps,
real c[]) {
920 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
921 static const real coeff[] = {
929 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
930 static const real coeff[] = {
940 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
941 static const real coeff[] = {
953 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
954 static const real coeff[] = {
968 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
969 static const real coeff[] = {
971 19, -64, 384, -1024, 2048,
985 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
986 static const real coeff[] = {
988 19, -64, 384, -1024, 2048,
990 7, -18, 128, -256, 4096,
994 -11, 96, -160, 16384,
1005 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1007 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) ==
1008 (nC1_*nC1_ + 7*nC1_ - 2*(nC1_/2)) / 4,
1009 "Coefficient array size mismatch in C1f");
1014 for (
int l = 1; l <= nC1_; ++l) {
1015 int m = (nC1_ - l) / 2;
1016 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1024 void Geodesic::C1pf(
real eps,
real c[]) {
1026 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1027 static const real coeff[] = {
1035 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1036 static const real coeff[] = {
1046 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1047 static const real coeff[] = {
1049 205, -432, 768, 1536,
1059 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1060 static const real coeff[] = {
1062 205, -432, 768, 1536,
1064 4005, -4736, 3840, 12288,
1074 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1075 static const real coeff[] = {
1077 -4879, 9840, -20736, 36864, 73728,
1079 4005, -4736, 3840, 12288,
1081 8703, -7200, 3712, 12288,
1085 -141115, 41604, 92160,
1091 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1092 static const real coeff[] = {
1094 -4879, 9840, -20736, 36864, 73728,
1096 -86171, 120150, -142080, 115200, 368640,
1098 8703, -7200, 3712, 12288,
1100 1082857, -688608, 258720, 737280,
1102 -141115, 41604, 92160,
1104 -2200311, 533134, 860160,
1108 109167851, 82575360,
1111 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1113 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) ==
1114 (nC1p_*nC1p_ + 7*nC1p_ - 2*(nC1p_/2)) / 4,
1115 "Coefficient array size mismatch in C1pf");
1120 for (
int l = 1; l <= nC1p_; ++l) {
1121 int m = (nC1p_ - l) / 2;
1122 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1132 #if GEOGRAPHICLIB_GEODESIC_ORDER/2 == 1
1133 static const real coeff[] = {
1137 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 2
1138 static const real coeff[] = {
1142 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 3
1143 static const real coeff[] = {
1145 -11, -28, -192, 0, 256,
1147 #elif GEOGRAPHICLIB_GEODESIC_ORDER/2 == 4
1148 static const real coeff[] = {
1150 -375, -704, -1792, -12288, 0, 16384,
1153 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1155 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) == nA2_/2 + 2,
1156 "Coefficient array size mismatch in A2m1f");
1159 return (t - eps) / (1 + eps);
1163 void Geodesic::C2f(
real eps,
real c[]) {
1165 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1166 static const real coeff[] = {
1174 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1175 static const real coeff[] = {
1185 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1186 static const real coeff[] = {
1198 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1199 static const real coeff[] = {
1213 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1214 static const real coeff[] = {
1216 41, 64, 128, 1024, 2048,
1230 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1231 static const real coeff[] = {
1233 41, 64, 128, 1024, 2048,
1235 47, 70, 128, 768, 4096,
1239 133, 224, 1120, 16384,
1250 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1252 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) ==
1253 (nC2_*nC2_ + 7*nC2_ - 2*(nC2_/2)) / 4,
1254 "Coefficient array size mismatch in C2f");
1259 for (
int l = 1; l <= nC2_; ++l) {
1260 int m = (nC2_ - l) / 2;
1261 c[l] = d *
Math::polyval(m, coeff + o, eps2) / coeff[o + m + 1];
1269 void Geodesic::A3coeff() {
1271 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1272 static const real coeff[] = {
1280 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1281 static const real coeff[] = {
1291 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1292 static const real coeff[] = {
1304 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1305 static const real coeff[] = {
1319 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1320 static const real coeff[] = {
1336 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1337 static const real coeff[] = {
1345 -5, -20, -4, -6, 128,
1356 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1358 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) ==
1359 (nA3_*nA3_ + 7*nA3_ - 2*(nA3_/2)) / 4,
1360 "Coefficient array size mismatch in A3f");
1362 for (
int j = nA3_ - 1; j >= 0; --j) {
1363 int m = min(nA3_ - j - 1, j);
1364 _A3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1371 void Geodesic::C3coeff() {
1373 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1374 static const real coeff[] = {
1382 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1383 static const real coeff[] = {
1399 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1400 static const real coeff[] = {
1422 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1423 static const real coeff[] = {
1455 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1456 static const real coeff[] = {
1500 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1501 static const real coeff[] = {
1535 10, -6, -10, 9, 384,
1545 -7, 20, -28, 14, 1024,
1560 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1562 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) ==
1563 ((nC3_-1)*(nC3_*nC3_ + 7*nC3_ - 2*(nC3_/2)))/8,
1564 "Coefficient array size mismatch in C3coeff");
1566 for (
int l = 1; l < nC3_; ++l) {
1567 for (
int j = nC3_ - 1; j >= l; --j) {
1568 int m = min(nC3_ - j - 1, j);
1569 _C3x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
1576 void Geodesic::C4coeff() {
1578 #if GEOGRAPHICLIB_GEODESIC_ORDER == 3
1579 static const real coeff[] = {
1593 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 4
1594 static const real coeff[] = {
1602 4, 24, -84, 210, 315,
1616 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 5
1617 static const real coeff[] = {
1623 1088, -352, -66, 3465,
1625 48, -352, 528, -231, 1155,
1627 16, 44, 264, -924, 2310, 3465,
1633 -896, 704, -198, 10395,
1635 -48, 352, -528, 231, 10395,
1641 320, -352, 132, 17325,
1649 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 6
1650 static const real coeff[] = {
1656 -224, -4784, 1573, 45045,
1658 -10656, 14144, -4576, -858, 45045,
1660 64, 624, -4576, 6864, -3003, 15015,
1662 100, 208, 572, 3432, -12012, 30030, 45045,
1668 5792, 1040, -1287, 135135,
1670 5952, -11648, 9152, -2574, 135135,
1672 -64, -624, 4576, -6864, 3003, 135135,
1678 -8448, 4992, -1144, 225225,
1680 -1440, 4160, -4576, 1716, 225225,
1686 3584, -3328, 1144, 315315,
1694 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 7
1695 static const real coeff[] = {
1701 -4480, 1088, 156, 45045,
1703 10736, -224, -4784, 1573, 45045,
1705 1664, -10656, 14144, -4576, -858, 45045,
1707 16, 64, 624, -4576, 6864, -3003, 15015,
1709 56, 100, 208, 572, 3432, -12012, 30030, 45045,
1715 3840, -2944, 468, 135135,
1717 -10704, 5792, 1040, -1287, 135135,
1719 -768, 5952, -11648, 9152, -2574, 135135,
1721 -16, -64, -624, 4576, -6864, 3003, 135135,
1727 1664, 1856, -936, 225225,
1729 6784, -8448, 4992, -1144, 225225,
1731 128, -1440, 4160, -4576, 1716, 225225,
1737 -2048, 1024, -208, 105105,
1739 -1792, 3584, -3328, 1144, 315315,
1745 3072, -2560, 832, 405405,
1753 #elif GEOGRAPHICLIB_GEODESIC_ORDER == 8
1754 static const real coeff[] = {
1760 20960, -7888, 4947, 765765,
1762 12480, -76160, 18496, 2652, 765765,
1764 -154048, 182512, -3808, -81328, 26741, 765765,
1766 3232, 28288, -181152, 240448, -77792, -14586, 765765,
1768 96, 272, 1088, 10608, -77792, 116688, -51051, 255255,
1770 588, 952, 1700, 3536, 9724, 58344, -204204, 510510, 765765,
1776 -39840, 1904, 255, 2297295,
1778 52608, 65280, -50048, 7956, 2297295,
1780 103744, -181968, 98464, 17680, -21879, 2297295,
1782 -1344, -13056, 101184, -198016, 155584, -43758, 2297295,
1784 -96, -272, -1088, -10608, 77792, -116688, 51051, 2297295,
1788 -928, -612, 3828825,
1790 64256, -28288, 2856, 3828825,
1792 -126528, 28288, 31552, -15912, 3828825,
1794 -41472, 115328, -143616, 84864, -19448, 3828825,
1796 160, 2176, -24480, 70720, -77792, 29172, 3828825,
1800 -16384, 1088, 5360355,
1802 -2560, 30464, -11560, 5360355,
1804 35840, -34816, 17408, -3536, 1786785,
1806 7168, -30464, 60928, -56576, 19448, 5360355,
1810 26624, -8704, 6891885,
1812 -77824, 34816, -6528, 6891885,
1814 -32256, 52224, -43520, 14144, 6891885,
1818 24576, -4352, 8423415,
1820 45056, -34816, 10880, 8423415,
1824 -28672, 8704, 9954945,
1829 #error "Bad value for GEOGRAPHICLIB_GEODESIC_ORDER"
1831 GEOGRAPHICLIB_STATIC_ASSERT(
sizeof(coeff) /
sizeof(
real) ==
1832 (nC4_ * (nC4_ + 1) * (nC4_ + 5)) / 6,
1833 "Coefficient array size mismatch in C4coeff");
1835 for (
int l = 0; l < nC4_; ++l) {
1836 for (
int j = nC4_ - 1; j >= l; --j) {
1837 int m = nC4_ - j - 1;
1838 _C4x[k++] =
Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
Header for GeographicLib::GeodesicLine class.
GeodesicLine Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
GeographicLib::Math::real real
static const Geodesic & WGS84()
Math::real GenInverse(real lat1, real lon1, real lat2, real lon2, unsigned outmask, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21, real &S12) const
static bool isfinite(T x)
Mathematical functions needed by GeographicLib.
static void sincosd(T x, T &sinx, T &cosx)
static void norm(T &x, T &y)
#define GEOGRAPHICLIB_VOLATILE
Header for GeographicLib::Geodesic class.
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
static T atan2d(T y, T x)
static T polyval(int N, const T p[], T x)
Namespace for GeographicLib.
static T AngDiff(T x, T y)
Exception handling for GeographicLib.
#define GEOGRAPHICLIB_PANIC