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GravityModel.cpp
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/**
* \file GravityModel.cpp
* \brief Implementation for GeographicLib::GravityModel class
*
* Copyright (c) Charles Karney (2011-2023) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#include <GeographicLib/GravityModel.hpp>
#include <fstream>
#include <limits>
#include <GeographicLib/SphericalEngine.hpp>
#include <GeographicLib/GravityCircle.hpp>
#include <GeographicLib/Utility.hpp>
#if !defined(GEOGRAPHICLIB_DATA)
# if defined(_WIN32)
# define GEOGRAPHICLIB_DATA "C:/ProgramData/GeographicLib"
# else
# define GEOGRAPHICLIB_DATA "/usr/local/share/GeographicLib"
# endif
#endif
#if !defined(GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME)
# define GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME "egm96"
#endif
#if defined(_MSC_VER)
// Squelch warnings about unsafe use of getenv
# pragma warning (disable: 4996)
#endif
namespace GeographicLib {
using namespace std;
GravityModel::GravityModel(const std::string& name, const std::string& path,
int Nmax, int Mmax)
: _name(name)
, _dir(path)
, _description("NONE")
, _date("UNKNOWN")
, _amodel(Math::NaN())
, _gGMmodel(Math::NaN())
, _zeta0(0)
, _corrmult(1)
, _nmx(-1)
, _mmx(-1)
, _norm(SphericalHarmonic::FULL)
{
if (_dir.empty())
_dir = DefaultGravityPath();
bool truncate = Nmax >= 0 || Mmax >= 0;
if (truncate) {
if (Nmax >= 0 && Mmax < 0) Mmax = Nmax;
if (Nmax < 0) Nmax = numeric_limits<int>::max();
if (Mmax < 0) Mmax = numeric_limits<int>::max();
}
ReadMetadata(_name);
{
string coeff = _filename + ".cof";
ifstream coeffstr(coeff.c_str(), ios::binary);
if (!coeffstr.good())
throw GeographicErr("Error opening " + coeff);
char id[idlength_ + 1];
coeffstr.read(id, idlength_);
if (!coeffstr.good())
throw GeographicErr("No header in " + coeff);
id[idlength_] = '\0';
if (_id != string(id))
throw GeographicErr("ID mismatch: " + _id + " vs " + id);
int N, M;
if (truncate) { N = Nmax; M = Mmax; }
SphericalEngine::coeff::readcoeffs(coeffstr, N, M, _cCx, _sSx, truncate);
if (!(N >= 0 && M >= 0))
throw GeographicErr("Degree and order must be at least 0");
if (_cCx[0] != 0)
throw GeographicErr("The degree 0 term should be zero");
_cCx[0] = 1; // Include the 1/r term in the sum
_gravitational = SphericalHarmonic(_cCx, _sSx, N, N, M, _amodel, _norm);
if (truncate) { N = Nmax; M = Mmax; }
SphericalEngine::coeff::readcoeffs(coeffstr, N, M, _cCC, _cCS, truncate);
if (N < 0) {
N = M = 0;
_cCC.resize(1, real(0));
}
_cCC[0] += _zeta0 / _corrmult;
_correction = SphericalHarmonic(_cCC, _cCS, N, N, M, real(1), _norm);
int pos = int(coeffstr.tellg());
coeffstr.seekg(0, ios::end);
if (pos != coeffstr.tellg())
throw GeographicErr("Extra data in " + coeff);
}
int nmx = _gravitational.Coefficients().nmx();
_nmx = max(nmx, _correction.Coefficients().nmx());
_mmx = max(_gravitational.Coefficients().mmx(),
_correction.Coefficients().mmx());
// Adjust the normalization of the normal potential to match the model.
real mult = _earth._gGM / _gGMmodel;
real amult = Math::sq(_earth._a / _amodel);
// The 0th term in _zonal should be is 1 + _dzonal0. Instead set it to 1
// to give exact cancellation with the (0,0) term in the model and account
// for _dzonal0 separately.
_zonal.clear(); _zonal.push_back(1);
_dzonal0 = (_earth.MassConstant() - _gGMmodel) / _gGMmodel;
for (int n = 2; n <= nmx; n += 2) {
// Only include as many normal zonal terms as matter. Figuring the limit
// in this way works because the coefficients of the normal potential
// (which is smooth) decay much more rapidly that the corresponding
// coefficient of the model potential (which is bumpy). Typically this
// goes out to n = 18.
mult *= amult;
real
r = _cCx[n], // the model term
s = - mult * _earth.Jn(n) / sqrt(real(2 * n + 1)), // the normal term
t = r - s; // the difference
if (t == r) // the normal term is negligible
break;
_zonal.push_back(0); // index = n - 1; the odd terms are 0
_zonal.push_back(s);
}
int nmx1 = int(_zonal.size()) - 1;
_disturbing = SphericalHarmonic1(_cCx, _sSx,
_gravitational.Coefficients().N(),
nmx, _gravitational.Coefficients().mmx(),
_zonal,
_zonal, // This is not accessed!
nmx1, nmx1, 0,
_amodel,
SphericalHarmonic1::normalization(_norm));
}
void GravityModel::ReadMetadata(const string& name) {
const char* spaces = " \t\n\v\f\r";
_filename = _dir + "/" + name + ".egm";
ifstream metastr(_filename.c_str());
if (!metastr.good())
throw GeographicErr("Cannot open " + _filename);
string line;
getline(metastr, line);
if (!(line.size() >= 6 && line.substr(0,5) == "EGMF-"))
throw GeographicErr(_filename + " does not contain EGMF-n signature");
string::size_type n = line.find_first_of(spaces, 5);
if (n != string::npos)
n -= 5;
string version(line, 5, n);
if (version != "1")
throw GeographicErr("Unknown version in " + _filename + ": " + version);
string key, val;
real a = Math::NaN(), GM = a, omega = a, f = a, J2 = a;
while (getline(metastr, line)) {
if (!Utility::ParseLine(line, key, val))
continue;
// Process key words
if (key == "Name")
_name = val;
else if (key == "Description")
_description = val;
else if (key == "ReleaseDate")
_date = val;
else if (key == "ModelRadius")
_amodel = Utility::val<real>(val);
else if (key == "ModelMass")
_gGMmodel = Utility::val<real>(val);
else if (key == "AngularVelocity")
omega = Utility::val<real>(val);
else if (key == "ReferenceRadius")
a = Utility::val<real>(val);
else if (key == "ReferenceMass")
GM = Utility::val<real>(val);
else if (key == "Flattening")
f = Utility::fract<real>(val);
else if (key == "DynamicalFormFactor")
J2 = Utility::fract<real>(val);
else if (key == "HeightOffset")
_zeta0 = Utility::fract<real>(val);
else if (key == "CorrectionMultiplier")
_corrmult = Utility::fract<real>(val);
else if (key == "Normalization") {
if (val == "FULL" || val == "Full" || val == "full")
_norm = SphericalHarmonic::FULL;
else if (val == "SCHMIDT" || val == "Schmidt" || val == "schmidt")
_norm = SphericalHarmonic::SCHMIDT;
else
throw GeographicErr("Unknown normalization " + val);
} else if (key == "ByteOrder") {
if (val == "Big" || val == "big")
throw GeographicErr("Only little-endian ordering is supported");
else if (!(val == "Little" || val == "little"))
throw GeographicErr("Unknown byte ordering " + val);
} else if (key == "ID")
_id = val;
// else unrecognized keywords are skipped
}
// Check values
if (!(isfinite(_amodel) && _amodel > 0))
throw GeographicErr("Model radius must be positive");
if (!(isfinite(_gGMmodel) && _gGMmodel > 0))
throw GeographicErr("Model mass constant must be positive");
if (!(isfinite(_corrmult) && _corrmult > 0))
throw GeographicErr("Correction multiplier must be positive");
if (!(isfinite(_zeta0)))
throw GeographicErr("Height offset must be finite");
if (int(_id.size()) != idlength_)
throw GeographicErr("Invalid ID");
if (isfinite(f) && isfinite(J2))
throw GeographicErr("Cannot specify both f and J2");
_earth = NormalGravity(a, GM, omega,
isfinite(f) ? f : J2, isfinite(f));
}
Math::real GravityModel::InternalT(real X, real Y, real Z,
real& deltaX, real& deltaY, real& deltaZ,
bool gradp, bool correct) const {
// If correct, then produce the correct T = W - U. Otherwise, neglect the
// n = 0 term (which is proportial to the difference in the model and
// reference values of GM).
if (_dzonal0 == 0)
// No need to do the correction
correct = false;
real T, invR = correct ? 1 / hypot(hypot(X, Y), Z) : 1;
if (gradp) {
// initial values to suppress warnings
deltaX = deltaY = deltaZ = 0;
T = _disturbing(-1, X, Y, Z, deltaX, deltaY, deltaZ);
real f = _gGMmodel / _amodel;
deltaX *= f;
deltaY *= f;
deltaZ *= f;
if (correct) {
invR = _gGMmodel * _dzonal0 * invR * invR * invR;
deltaX += X * invR;
deltaY += Y * invR;
deltaZ += Z * invR;
}
} else
T = _disturbing(-1, X, Y, Z);
T = (T / _amodel - (correct ? _dzonal0 : 0) * invR) * _gGMmodel;
return T;
}
Math::real GravityModel::V(real X, real Y, real Z,
real& GX, real& GY, real& GZ) const {
real
Vres = _gravitational(X, Y, Z, GX, GY, GZ),
f = _gGMmodel / _amodel;
Vres *= f;
GX *= f;
GY *= f;
GZ *= f;
return Vres;
}
Math::real GravityModel::W(real X, real Y, real Z,
real& gX, real& gY, real& gZ) const {
real fX, fY,
Wres = V(X, Y, Z, gX, gY, gZ) + _earth.Phi(X, Y, fX, fY);
gX += fX;
gY += fY;
return Wres;
}
void GravityModel::SphericalAnomaly(real lat, real lon, real h,
real& Dg01, real& xi, real& eta) const {
real X, Y, Z, M[Geocentric::dim2_];
_earth.Earth().IntForward(lat, lon, h, X, Y, Z, M);
real
deltax, deltay, deltaz,
T = InternalT(X, Y, Z, deltax, deltay, deltaz, true, false),
clam = M[3], slam = -M[0],
P = hypot(X, Y),
R = hypot(P, Z),
// theta is geocentric latitude
ctheta = R != 0 ? P / R : M[7],
stheta = R != 0 ? Z / R : M[8];
// Rotate cartesian into spherical coordinates
real MC[Geocentric::dim2_];
Geocentric::Rotation(stheta, ctheta, slam, clam, MC);
Geocentric::Unrotate(MC, deltax, deltay, deltaz, deltax, deltay, deltaz);
// H+M, Eq 2-151c
Dg01 = - deltaz - 2 * T / R;
real gammaX, gammaY, gammaZ;
_earth.U(X, Y, Z, gammaX, gammaY, gammaZ);
real gamma = hypot( hypot(gammaX, gammaY), gammaZ);
xi = -(deltay/gamma) / Math::degree();
eta = -(deltax/gamma) / Math::degree();
}
Math::real GravityModel::GeoidHeight(real lat, real lon) const
{
real X, Y, Z;
_earth.Earth().IntForward(lat, lon, 0, X, Y, Z, NULL);
real
gamma0 = _earth.SurfaceGravity(lat),
dummy,
T = InternalT(X, Y, Z, dummy, dummy, dummy, false, false),
invR = 1 / hypot(hypot(X, Y), Z),
correction = _corrmult * _correction(invR * X, invR * Y, invR * Z);
// _zeta0 has been included in _correction
return T/gamma0 + correction;
}
Math::real GravityModel::Gravity(real lat, real lon, real h,
real& gx, real& gy, real& gz) const {
real X, Y, Z, M[Geocentric::dim2_];
_earth.Earth().IntForward(lat, lon, h, X, Y, Z, M);
real Wres = W(X, Y, Z, gx, gy, gz);
Geocentric::Unrotate(M, gx, gy, gz, gx, gy, gz);
return Wres;
}
Math::real GravityModel::Disturbance(real lat, real lon, real h,
real& deltax, real& deltay,
real& deltaz) const {
real X, Y, Z, M[Geocentric::dim2_];
_earth.Earth().IntForward(lat, lon, h, X, Y, Z, M);
real Tres = InternalT(X, Y, Z, deltax, deltay, deltaz, true, true);
Geocentric::Unrotate(M, deltax, deltay, deltaz, deltax, deltay, deltaz);
return Tres;
}
GravityCircle GravityModel::Circle(real lat, real h, unsigned caps) const {
if (h != 0)
// Disallow invoking GeoidHeight unless h is zero.
caps &= ~(CAP_GAMMA0 | CAP_C);
real X, Y, Z, M[Geocentric::dim2_];
_earth.Earth().IntForward(lat, 0, h, X, Y, Z, M);
// Y = 0, cphi = M[7], sphi = M[8];
real
invR = 1 / hypot(X, Z),
gamma0 = (caps & CAP_GAMMA0 ?_earth.SurfaceGravity(lat)
: Math::NaN()),
fx, fy, fz, gamma;
if (caps & CAP_GAMMA) {
_earth.U(X, Y, Z, fx, fy, fz); // fy = 0
gamma = hypot(fx, fz);
} else
gamma = Math::NaN();
_earth.Phi(X, Y, fx, fy);
return GravityCircle(GravityCircle::mask(caps),
_earth._a, _earth._f, lat, h, Z, X, M[7], M[8],
_amodel, _gGMmodel, _dzonal0, _corrmult,
gamma0, gamma, fx,
caps & CAP_G ?
_gravitational.Circle(X, Z, true) :
CircularEngine(),
// N.B. If CAP_DELTA is set then CAP_T should be too.
caps & CAP_T ?
_disturbing.Circle(-1, X, Z, (caps&CAP_DELTA) != 0) :
CircularEngine(),
caps & CAP_C ?
_correction.Circle(invR * X, invR * Z, false) :
CircularEngine());
}
string GravityModel::DefaultGravityPath() {
string path;
char* gravitypath = getenv("GEOGRAPHICLIB_GRAVITY_PATH");
if (gravitypath)
path = string(gravitypath);
if (!path.empty())
return path;
char* datapath = getenv("GEOGRAPHICLIB_DATA");
if (datapath)
path = string(datapath);
return (!path.empty() ? path : string(GEOGRAPHICLIB_DATA)) + "/gravity";
}
string GravityModel::DefaultGravityName() {
string name;
char* gravityname = getenv("GEOGRAPHICLIB_GRAVITY_NAME");
if (gravityname)
name = string(gravityname);
return !name.empty() ? name : string(GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME);
}
} // namespace GeographicLib
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
GEOGRAPHICLIB_DATA
#define GEOGRAPHICLIB_DATA
Definition Geoid.cpp:19
GravityCircle.hpp
Header for GeographicLib::GravityCircle class.
GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME
#define GEOGRAPHICLIB_GRAVITY_DEFAULT_NAME
Definition GravityModel.cpp:26
GravityModel.hpp
Header for GeographicLib::GravityModel class.
SphericalEngine.hpp
Header for GeographicLib::SphericalEngine class.
Utility.hpp
Header for GeographicLib::Utility class.
GeographicLib::CircularEngine
Spherical harmonic sums for a circle.
Definition CircularEngine.hpp:52
GeographicLib::GeographicErr
Exception handling for GeographicLib.
Definition Constants.hpp:316
GeographicLib::GravityCircle
Gravity on a circle of latitude.
Definition GravityCircle.hpp:41
GeographicLib::GravityModel::GravityCircle
friend class GravityCircle
Definition GravityModel.hpp:86
GeographicLib::GravityModel::Disturbance
Math::real Disturbance(real lat, real lon, real h, real &deltax, real &deltay, real &deltaz) const
Definition GravityModel.cpp:312
GeographicLib::GravityModel::DefaultGravityPath
static std::string DefaultGravityPath()
Definition GravityModel.cpp:356
GeographicLib::GravityModel::SphericalAnomaly
void SphericalAnomaly(real lat, real lon, real h, real &Dg01, real &xi, real &eta) const
Definition GravityModel.cpp:264
GeographicLib::GravityModel::Circle
GravityCircle Circle(real lat, real h, unsigned caps=ALL) const
Definition GravityModel.cpp:322
GeographicLib::GravityModel::DefaultGravityName
static std::string DefaultGravityName()
Definition GravityModel.cpp:369
GeographicLib::GravityModel::GeoidHeight
Math::real GeoidHeight(real lat, real lon) const
Definition GravityModel.cpp:290
GeographicLib::GravityModel::T
Math::real T(real X, real Y, real Z, real &deltaX, real &deltaY, real &deltaZ) const
Definition GravityModel.hpp:337
GeographicLib::GravityModel::Gravity
Math::real Gravity(real lat, real lon, real h, real &gx, real &gy, real &gz) const
Definition GravityModel.cpp:304
GeographicLib::GravityModel::V
Math::real V(real X, real Y, real Z, real &GX, real &GY, real &GZ) const
Definition GravityModel.cpp:243
GeographicLib::GravityModel::W
Math::real W(real X, real Y, real Z, real &gX, real &gY, real &gZ) const
Definition GravityModel.cpp:255
GeographicLib::Math
Mathematical functions needed by GeographicLib.
Definition Math.hpp:77
GeographicLib::Math::degree
static T degree()
Definition Math.hpp:209
GeographicLib::Math::sq
static T sq(T x)
Definition Math.hpp:221
GeographicLib::Math::NaN
static T NaN()
Definition Math.cpp:277
GeographicLib::Math::real
double real
Definition Math.hpp:110
GeographicLib::NormalGravity::Earth
const Geocentric & Earth() const
Definition NormalGravity.hpp:342
GeographicLib::NormalGravity::Phi
Math::real Phi(real X, real Y, real &fX, real &fY) const
Definition NormalGravity.cpp:216
GeographicLib::NormalGravity::MassConstant
Math::real MassConstant() const
Definition NormalGravity.hpp:279
GeographicLib::NormalGravity::U
Math::real U(real X, real Y, real Z, real &gammaX, real &gammaY, real &gammaZ) const
Definition NormalGravity.cpp:223
GeographicLib::NormalGravity::SurfaceGravity
Math::real SurfaceGravity(real lat) const
Definition NormalGravity.cpp:154
GeographicLib::SphericalEngine::coeff::N
int N() const
Definition SphericalEngine.hpp:173
GeographicLib::SphericalEngine::coeff::readcoeffs
static void readcoeffs(std::istream &stream, int &N, int &M, std::vector< real > &C, std::vector< real > &S, bool truncate=false)
Definition SphericalEngine.cpp:384
GeographicLib::SphericalEngine::coeff::nmx
int nmx() const
Definition SphericalEngine.hpp:177
GeographicLib::SphericalEngine::coeff::mmx
int mmx() const
Definition SphericalEngine.hpp:181
GeographicLib::SphericalHarmonic1
Spherical harmonic series with a correction to the coefficients.
Definition SphericalHarmonic1.hpp:32
GeographicLib::SphericalHarmonic1::Circle
CircularEngine Circle(real tau, real p, real z, bool gradp) const
Definition SphericalHarmonic1.hpp:248
GeographicLib::SphericalHarmonic1::normalization
normalization
Definition SphericalHarmonic1.hpp:37
GeographicLib::SphericalHarmonic
Spherical harmonic series.
Definition SphericalHarmonic.hpp:71
GeographicLib::SphericalHarmonic::SCHMIDT
@ SCHMIDT
Definition SphericalHarmonic.hpp:120
GeographicLib::SphericalHarmonic::FULL
@ FULL
Definition SphericalHarmonic.hpp:98
GeographicLib::SphericalHarmonic::Coefficients
const SphericalEngine::coeff & Coefficients() const
Definition SphericalHarmonic.hpp:352
GeographicLib::SphericalHarmonic::Circle
CircularEngine Circle(real p, real z, bool gradp) const
Definition SphericalHarmonic.hpp:328
GeographicLib::Utility::ParseLine
static bool ParseLine(const std::string &line, std::string &key, std::string &value, char equals='\0', char comment='#')
Definition Utility.cpp:170
GeographicLib::Utility::fract
static T fract(const std::string &s)
Definition Utility.hpp:298
GeographicLib::Utility::val
static T val(const std::string &s)
Definition Utility.hpp:225
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806