henry/SimCore
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

ADD: new track message, Entity class and Position class

Browse Source
This commit is contained in:
Henry Winkel
2022-12-20 17:20:35 +01:00
parent 469ecfb099
commit 98ebb563a8
2114 changed files with 482360 additions and 24 deletions
Download Patch File Download Diff File Expand all files Collapse all files

387
libs/geographiclib/src/Rhumb.cpp Normal file
View File

@@ -0,0 +1,387 @@
/**
* \file Rhumb.cpp
* \brief Implementation for GeographicLib::Rhumb and GeographicLib::RhumbLine
* classes
*
* Copyright (c) Charles Karney (2014-2022) <charles@karney.com> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#include <algorithm>
#include <GeographicLib/Rhumb.hpp>
#if defined(_MSC_VER)
// Squelch warnings about enum-float expressions
# pragma warning (disable: 5055)
#endif
namespace GeographicLib {
using namespace std;
Rhumb::Rhumb(real a, real f, bool exact)
: _ell(a, f)
, _exact(exact)
, _c2(_ell.Area() / (2 * Math::td))
{
// Generated by Maxima on 2015-05-15 08:24:04-04:00
#if GEOGRAPHICLIB_RHUMBAREA_ORDER == 4
static const real coeff[] = {
// R[0]/n^0, polynomial in n of order 4
691, 7860, -20160, 18900, 0, 56700,
// R[1]/n^1, polynomial in n of order 3
1772, -5340, 6930, -4725, 14175,
// R[2]/n^2, polynomial in n of order 2
-1747, 1590, -630, 4725,
// R[3]/n^3, polynomial in n of order 1
104, -31, 315,
// R[4]/n^4, polynomial in n of order 0
-41, 420,
}; // count = 20
#elif GEOGRAPHICLIB_RHUMBAREA_ORDER == 5
static const real coeff[] = {
// R[0]/n^0, polynomial in n of order 5
-79036, 22803, 259380, -665280, 623700, 0, 1871100,
// R[1]/n^1, polynomial in n of order 4
41662, 58476, -176220, 228690, -155925, 467775,
// R[2]/n^2, polynomial in n of order 3
18118, -57651, 52470, -20790, 155925,
// R[3]/n^3, polynomial in n of order 2
-23011, 17160, -5115, 51975,
// R[4]/n^4, polynomial in n of order 1
5480, -1353, 13860,
// R[5]/n^5, polynomial in n of order 0
-668, 5775,
}; // count = 27
#elif GEOGRAPHICLIB_RHUMBAREA_ORDER == 6
static const real coeff[] = {
// R[0]/n^0, polynomial in n of order 6
128346268, -107884140, 31126095, 354053700, -908107200, 851350500, 0,
2554051500LL,
// R[1]/n^1, polynomial in n of order 5
-114456994, 56868630, 79819740, -240540300, 312161850, -212837625,
638512875,
// R[2]/n^2, polynomial in n of order 4
51304574, 24731070, -78693615, 71621550, -28378350, 212837625,
// R[3]/n^3, polynomial in n of order 3
1554472, -6282003, 4684680, -1396395, 14189175,
// R[4]/n^4, polynomial in n of order 2
-4913956, 3205800, -791505, 8108100,
// R[5]/n^5, polynomial in n of order 1
1092376, -234468, 2027025,
// R[6]/n^6, polynomial in n of order 0
-313076, 2027025,
}; // count = 35
#elif GEOGRAPHICLIB_RHUMBAREA_ORDER == 7
static const real coeff[] = {
// R[0]/n^0, polynomial in n of order 7
-317195588, 385038804, -323652420, 93378285, 1062161100, -2724321600LL,
2554051500LL, 0, 7662154500LL,
// R[1]/n^1, polynomial in n of order 6
258618446, -343370982, 170605890, 239459220, -721620900, 936485550,
-638512875, 1915538625,
// R[2]/n^2, polynomial in n of order 5
-248174686, 153913722, 74193210, -236080845, 214864650, -85135050,
638512875,
// R[3]/n^3, polynomial in n of order 4
114450437, 23317080, -94230045, 70270200, -20945925, 212837625,
// R[4]/n^4, polynomial in n of order 3
15445736, -103193076, 67321800, -16621605, 170270100,
// R[5]/n^5, polynomial in n of order 2
-27766753, 16385640, -3517020, 30405375,
// R[6]/n^6, polynomial in n of order 1
4892722, -939228, 6081075,
// R[7]/n^7, polynomial in n of order 0
-3189007, 14189175,
}; // count = 44
#elif GEOGRAPHICLIB_RHUMBAREA_ORDER == 8
static const real coeff[] = {
// R[0]/n^0, polynomial in n of order 8
71374704821LL, -161769749880LL, 196369790040LL, -165062734200LL,
47622925350LL, 541702161000LL, -1389404016000LL, 1302566265000LL, 0,
3907698795000LL,
// R[1]/n^1, polynomial in n of order 7
-13691187484LL, 65947703730LL, -87559600410LL, 43504501950LL,
61062101100LL, -184013329500LL, 238803815250LL, -162820783125LL,
488462349375LL,
// R[2]/n^2, polynomial in n of order 6
30802104839LL, -63284544930LL, 39247999110LL, 18919268550LL,
-60200615475LL, 54790485750LL, -21709437750LL, 162820783125LL,
// R[3]/n^3, polynomial in n of order 5
-8934064508LL, 5836972287LL, 1189171080, -4805732295LL, 3583780200LL,
-1068242175, 10854718875LL,
// R[4]/n^4, polynomial in n of order 4
50072287748LL, 3938662680LL, -26314234380LL, 17167059000LL,
-4238509275LL, 43418875500LL,
// R[5]/n^5, polynomial in n of order 3
359094172, -9912730821LL, 5849673480LL, -1255576140, 10854718875LL,
// R[6]/n^6, polynomial in n of order 2
-16053944387LL, 8733508770LL, -1676521980, 10854718875LL,
// R[7]/n^7, polynomial in n of order 1
930092876, -162639357, 723647925,
// R[8]/n^8, polynomial in n of order 0
-673429061, 1929727800,
}; // count = 54
#else
#error "Bad value for GEOGRAPHICLIB_RHUMBAREA_ORDER"
#endif
static_assert(sizeof(coeff) / sizeof(real) ==
((maxpow_ + 1) * (maxpow_ + 4))/2,
"Coefficient array size mismatch for Rhumb");
real d = 1;
int o = 0;
for (int l = 0; l <= maxpow_; ++l) {
int m = maxpow_ - l;
// R[0] is just an integration constant so it cancels when evaluating a
// definite integral. So don't bother computing it. It won't be used
// when invoking SinCosSeries.
if (l)
_rR[l] = d * Math::polyval(m, coeff + o, _ell._n) / coeff[o + m + 1];
o += m + 2;
d *= _ell._n;
}
// Post condition: o == sizeof(alpcoeff) / sizeof(real)
}
const Rhumb& Rhumb::WGS84() {
static const Rhumb
wgs84(Constants::WGS84_a(), Constants::WGS84_f(), false);
return wgs84;
}
void Rhumb::GenInverse(real lat1, real lon1, real lat2, real lon2,
unsigned outmask,
real& s12, real& azi12, real& S12) const {
real
lon12 = Math::AngDiff(lon1, lon2),
psi1 = _ell.IsometricLatitude(lat1),
psi2 = _ell.IsometricLatitude(lat2),
psi12 = psi2 - psi1,
h = hypot(lon12, psi12);
if (outmask & AZIMUTH)
azi12 = Math::atan2d(lon12, psi12);
if (outmask & DISTANCE) {
real dmudpsi = DIsometricToRectifying(psi2, psi1);
s12 = h * dmudpsi * _ell.QuarterMeridian() / Math::qd;
}
if (outmask & AREA)
S12 = _c2 * lon12 *
MeanSinXi(psi2 * Math::degree(), psi1 * Math::degree());
}
RhumbLine Rhumb::Line(real lat1, real lon1, real azi12) const
{ return RhumbLine(*this, lat1, lon1, azi12); }
void Rhumb::GenDirect(real lat1, real lon1, real azi12, real s12,
unsigned outmask,
real& lat2, real& lon2, real& S12) const
{ Line(lat1, lon1, azi12).GenPosition(s12, outmask, lat2, lon2, S12); }
Math::real Rhumb::DE(real x, real y) const {
const EllipticFunction& ei = _ell._ell;
real d = x - y;
if (x * y <= 0)
return d != 0 ? (ei.E(x) - ei.E(y)) / d : 1;
// See DLMF: Eqs (19.11.2) and (19.11.4) letting
// theta -> x, phi -> -y, psi -> z
//
// (E(x) - E(y)) / d = E(z)/d - k2 * sin(x) * sin(y) * sin(z)/d
//
// tan(z/2) = (sin(x)*Delta(y) - sin(y)*Delta(x)) / (cos(x) + cos(y))
// = d * Dsin(x,y) * (sin(x) + sin(y))/(cos(x) + cos(y)) /
// (sin(x)*Delta(y) + sin(y)*Delta(x))
// = t = d * Dt
// sin(z) = 2*t/(1+t^2); cos(z) = (1-t^2)/(1+t^2)
// Alt (this only works for |z| <= pi/2 -- however, this conditions holds
// if x*y > 0):
// sin(z) = d * Dsin(x,y) * (sin(x) + sin(y))/
// (sin(x)*cos(y)*Delta(y) + sin(y)*cos(x)*Delta(x))
// cos(z) = sqrt((1-sin(z))*(1+sin(z)))
real sx = sin(x), sy = sin(y), cx = cos(x), cy = cos(y);
real Dt = Dsin(x, y) * (sx + sy) /
((cx + cy) * (sx * ei.Delta(sy, cy) + sy * ei.Delta(sx, cx))),
t = d * Dt, Dsz = 2 * Dt / (1 + t*t),
sz = d * Dsz, cz = (1 - t) * (1 + t) / (1 + t*t);
return ((sz != 0 ? ei.E(sz, cz, ei.Delta(sz, cz)) / sz : 1)
- ei.k2() * sx * sy) * Dsz;
}
Math::real Rhumb::DRectifying(real latx, real laty) const {
real
tbetx = _ell._f1 * Math::tand(latx),
tbety = _ell._f1 * Math::tand(laty);
return (Math::pi()/2) * _ell._b * _ell._f1 * DE(atan(tbetx), atan(tbety))
* Dtan(latx, laty) * Datan(tbetx, tbety) / _ell.QuarterMeridian();
}
Math::real Rhumb::DIsometric(real latx, real laty) const {
real
phix = latx * Math::degree(), tx = Math::tand(latx),
phiy = laty * Math::degree(), ty = Math::tand(laty);
return Dasinh(tx, ty) * Dtan(latx, laty)
- Deatanhe(sin(phix), sin(phiy)) * Dsin(phix, phiy);
}
Math::real Rhumb::SinCosSeries(bool sinp,
real x, real y, const real c[], int n) {
// N.B. n >= 0 and c[] has n+1 elements 0..n, of which c[0] is ignored.
//
// Use Clenshaw summation to evaluate
// m = (g(x) + g(y)) / 2 -- mean value
// s = (g(x) - g(y)) / (x - y) -- average slope
// where
// g(x) = sum(c[j]*SC(2*j*x), j = 1..n)
// SC = sinp ? sin : cos
// CS = sinp ? cos : sin
//
// This function returns only s; m is discarded.
//
// Write
// t = [m; s]
// t = sum(c[j] * f[j](x,y), j = 1..n)
// where
// f[j](x,y) = [ (SC(2*j*x)+SC(2*j*y))/2 ]
// [ (SC(2*j*x)-SC(2*j*y))/d ]
//
// = [ cos(j*d)*SC(j*p) ]
// [ +/-(2/d)*sin(j*d)*CS(j*p) ]
// (+/- = sinp ? + : -) and
// p = x+y, d = x-y
//
// f[j+1](x,y) = A * f[j](x,y) - f[j-1](x,y)
//
// A = [ 2*cos(p)*cos(d) -sin(p)*sin(d)*d]
// [ -4*sin(p)*sin(d)/d 2*cos(p)*cos(d) ]
//
// Let b[n+1] = b[n+2] = [0 0; 0 0]
// b[j] = A * b[j+1] - b[j+2] + c[j] * I for j = n..1
// t = (c[0] * I - b[2]) * f[0](x,y) + b[1] * f[1](x,y)
// c[0] is not accessed for s = t[2]
real p = x + y, d = x - y,
cp = cos(p), cd = cos(d),
sp = sin(p), sd = d != 0 ? sin(d)/d : 1,
m = 2 * cp * cd, s = sp * sd;
// 2x2 matrices stored in row-major order
const real a[4] = {m, -s * d * d, -4 * s, m};
real ba[4] = {0, 0, 0, 0};
real bb[4] = {0, 0, 0, 0};
real* b1 = ba;
real* b2 = bb;
if (n > 0) b1[0] = b1[3] = c[n];
for (int j = n - 1; j > 0; --j) { // j = n-1 .. 1
swap(b1, b2);
// b1 = A * b2 - b1 + c[j] * I
b1[0] = a[0] * b2[0] + a[1] * b2[2] - b1[0] + c[j];
b1[1] = a[0] * b2[1] + a[1] * b2[3] - b1[1];
b1[2] = a[2] * b2[0] + a[3] * b2[2] - b1[2];
b1[3] = a[2] * b2[1] + a[3] * b2[3] - b1[3] + c[j];
}
// Here are the full expressions for m and s
// m = (c[0] - b2[0]) * f01 - b2[1] * f02 + b1[0] * f11 + b1[1] * f12;
// s = - b2[2] * f01 + (c[0] - b2[3]) * f02 + b1[2] * f11 + b1[3] * f12;
if (sinp) {
// real f01 = 0, f02 = 0;
real f11 = cd * sp, f12 = 2 * sd * cp;
// m = b1[0] * f11 + b1[1] * f12;
s = b1[2] * f11 + b1[3] * f12;
} else {
// real f01 = 1, f02 = 0;
real f11 = cd * cp, f12 = - 2 * sd * sp;
// m = c[0] - b2[0] + b1[0] * f11 + b1[1] * f12;
s = - b2[2] + b1[2] * f11 + b1[3] * f12;
}
return s;
}
Math::real Rhumb::DConformalToRectifying(real chix, real chiy) const {
return 1 + SinCosSeries(true, chix, chiy,
_ell.ConformalToRectifyingCoeffs(), tm_maxord);
}
Math::real Rhumb::DRectifyingToConformal(real mux, real muy) const {
return 1 - SinCosSeries(true, mux, muy,
_ell.RectifyingToConformalCoeffs(), tm_maxord);
}
Math::real Rhumb::DIsometricToRectifying(real psix, real psiy) const {
if (_exact) {
real
latx = _ell.InverseIsometricLatitude(psix),
laty = _ell.InverseIsometricLatitude(psiy);
return DRectifying(latx, laty) / DIsometric(latx, laty);
} else {
psix *= Math::degree();
psiy *= Math::degree();
return DConformalToRectifying(gd(psix), gd(psiy)) * Dgd(psix, psiy);
}
}
Math::real Rhumb::DRectifyingToIsometric(real mux, real muy) const {
real
latx = _ell.InverseRectifyingLatitude(mux/Math::degree()),
laty = _ell.InverseRectifyingLatitude(muy/Math::degree());
return _exact ?
DIsometric(latx, laty) / DRectifying(latx, laty) :
Dgdinv(Math::taupf(Math::tand(latx), _ell._es),
Math::taupf(Math::tand(laty), _ell._es)) *
DRectifyingToConformal(mux, muy);
}
Math::real Rhumb::MeanSinXi(real psix, real psiy) const {
return Dlog(cosh(psix), cosh(psiy)) * Dcosh(psix, psiy)
+ SinCosSeries(false, gd(psix), gd(psiy), _rR, maxpow_) * Dgd(psix, psiy);
}
RhumbLine::RhumbLine(const Rhumb& rh, real lat1, real lon1, real azi12)
: _rh(rh)
, _lat1(Math::LatFix(lat1))
, _lon1(lon1)
, _azi12(Math::AngNormalize(azi12))
{
real alp12 = _azi12 * Math::degree();
_salp = _azi12 == -Math::hd ? 0 : sin(alp12);
_calp = fabs(_azi12) == Math::qd ? 0 : cos(alp12);
_mu1 = _rh._ell.RectifyingLatitude(lat1);
_psi1 = _rh._ell.IsometricLatitude(lat1);
_r1 = _rh._ell.CircleRadius(lat1);
}
void RhumbLine::GenPosition(real s12, unsigned outmask,
real& lat2, real& lon2, real& S12) const {
real
mu12 = s12 * _calp * Math::qd / _rh._ell.QuarterMeridian(),
mu2 = _mu1 + mu12;
real psi2, lat2x, lon2x;
if (fabs(mu2) <= Math::qd) {
if (_calp != 0) {
lat2x = _rh._ell.InverseRectifyingLatitude(mu2);
real psi12 = _rh.DRectifyingToIsometric( mu2 * Math::degree(),
_mu1 * Math::degree()) * mu12;
lon2x = _salp * psi12 / _calp;
psi2 = _psi1 + psi12;
} else {
lat2x = _lat1;
lon2x = _salp * s12 / (_r1 * Math::degree());
psi2 = _psi1;
}
if (outmask & AREA)
S12 = _rh._c2 * lon2x *
_rh.MeanSinXi(_psi1 * Math::degree(), psi2 * Math::degree());
lon2x = outmask & LONG_UNROLL ? _lon1 + lon2x :
Math::AngNormalize(Math::AngNormalize(_lon1) + lon2x);
} else {
// Reduce to the interval [-180, 180)
mu2 = Math::AngNormalize(mu2);
// Deal with points on the anti-meridian
if (fabs(mu2) > Math::qd) mu2 = Math::AngNormalize(Math::hd - mu2);
lat2x = _rh._ell.InverseRectifyingLatitude(mu2);
lon2x = Math::NaN();
if (outmask & AREA)
S12 = Math::NaN();
}
if (outmask & LATITUDE) lat2 = lat2x;
if (outmask & LONGITUDE) lon2 = lon2x;
}
} // namespace GeographicLib