// Boost.Geometry
// This file is manually converted from PROJ4
// This file was modified by Oracle on 2017.
// Modifications copyright (c) 2017, Oracle and/or its affiliates.
// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
// Use, modification and distribution is subject to the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// This file is converted from PROJ4, http://trac.osgeo.org/proj
// PROJ4 is originally written by Gerald Evenden (then of the USGS)
// PROJ4 is maintained by Frank Warmerdam
// This file was converted to Geometry Library by Adam Wulkiewicz
// Original copyright notice:
/***************************************************************************/
/* RSC IDENTIFIER: GEOCENTRIC
*
* ABSTRACT
*
* This component provides conversions between Geodetic coordinates (latitude,
* longitude in radians and height in meters) and Geocentric coordinates
* (X, Y, Z) in meters.
*
* ERROR HANDLING
*
* This component checks parameters for valid values. If an invalid value
* is found, the error code is combined with the current error code using
* the bitwise or. This combining allows multiple error codes to be
* returned. The possible error codes are:
*
* GEOCENT_NO_ERROR : No errors occurred in function
* GEOCENT_LAT_ERROR : Latitude out of valid range
* (-90 to 90 degrees)
* GEOCENT_LON_ERROR : Longitude out of valid range
* (-180 to 360 degrees)
* GEOCENT_A_ERROR : Semi-major axis lessthan or equal to zero
* GEOCENT_B_ERROR : Semi-minor axis lessthan or equal to zero
* GEOCENT_A_LESS_B_ERROR : Semi-major axis less than semi-minor axis
*
*
* REUSE NOTES
*
* GEOCENTRIC is intended for reuse by any application that performs
* coordinate conversions between geodetic coordinates and geocentric
* coordinates.
*
*
* REFERENCES
*
* An Improved Algorithm for Geocentric to Geodetic Coordinate Conversion,
* Ralph Toms, February 1996 UCRL-JC-123138.
*
* Further information on GEOCENTRIC can be found in the Reuse Manual.
*
* GEOCENTRIC originated from : U.S. Army Topographic Engineering Center
* Geospatial Information Division
* 7701 Telegraph Road
* Alexandria, VA 22310-3864
*
* LICENSES
*
* None apply to this component.
*
* RESTRICTIONS
*
* GEOCENTRIC has no restrictions.
*
* ENVIRONMENT
*
* GEOCENTRIC was tested and certified in the following environments:
*
* 1. Solaris 2.5 with GCC version 2.8.1
* 2. Windows 95 with MS Visual C++ version 6
*
* MODIFICATIONS
*
* Date Description
* ---- -----------
* 25-02-97 Original Code
*
*/
#ifndef BOOST_GEOMETRY_SRS_PROJECTIONS_IMPL_GEOCENT_HPP
#define BOOST_GEOMETRY_SRS_PROJECTIONS_IMPL_GEOCENT_HPP
#include <boost/geometry/util/math.hpp>
namespace boost { namespace geometry { namespace projections
{
namespace detail
{
/***************************************************************************/
/*
* DEFINES
*/
static const long GEOCENT_NO_ERROR = 0x0000;
static const long GEOCENT_LAT_ERROR = 0x0001;
static const long GEOCENT_LON_ERROR = 0x0002;
static const long GEOCENT_A_ERROR = 0x0004;
static const long GEOCENT_B_ERROR = 0x0008;
static const long GEOCENT_A_LESS_B_ERROR = 0x0010;
template <typename T>
struct GeocentricInfo
{
T Geocent_a; /* Semi-major axis of ellipsoid in meters */
T Geocent_b; /* Semi-minor axis of ellipsoid */
T Geocent_a2; /* Square of semi-major axis */
T Geocent_b2; /* Square of semi-minor axis */
T Geocent_e2; /* Eccentricity squared */
T Geocent_ep2; /* 2nd eccentricity squared */
};
template <typename T>
inline T COS_67P5()
{
/*return 0.38268343236508977*/;
return cos(T(67.5) * math::d2r<T>()); /* cosine of 67.5 degrees */
}
template <typename T>
inline T AD_C()
{
return 1.0026000; /* Toms region 1 constant */
}
/***************************************************************************/
/*
* FUNCTIONS
*/
template <typename T>
inline long pj_Set_Geocentric_Parameters (GeocentricInfo<T> & gi, T const& a, T const& b)
{ /* BEGIN Set_Geocentric_Parameters */
/*
* The function Set_Geocentric_Parameters receives the ellipsoid parameters
* as inputs and sets the corresponding state variables.
*
* a : Semi-major axis, in meters. (input)
* b : Semi-minor axis, in meters. (input)
*/
long Error_Code = GEOCENT_NO_ERROR;
if (a <= 0.0)
Error_Code |= GEOCENT_A_ERROR;
if (b <= 0.0)
Error_Code |= GEOCENT_B_ERROR;
if (a < b)
Error_Code |= GEOCENT_A_LESS_B_ERROR;
if (!Error_Code)
{
gi.Geocent_a = a;
gi.Geocent_b = b;
gi.Geocent_a2 = a * a;
gi.Geocent_b2 = b * b;
gi.Geocent_e2 = (gi.Geocent_a2 - gi.Geocent_b2) / gi.Geocent_a2;
gi.Geocent_ep2 = (gi.Geocent_a2 - gi.Geocent_b2) / gi.Geocent_b2;
}
return (Error_Code);
} /* END OF Set_Geocentric_Parameters */
template <typename T>
inline void pj_Get_Geocentric_Parameters (GeocentricInfo<T> const& gi,
T & a,
T & b)
{ /* BEGIN Get_Geocentric_Parameters */
/*
* The function Get_Geocentric_Parameters returns the ellipsoid parameters
* to be used in geocentric coordinate conversions.
*
* a : Semi-major axis, in meters. (output)
* b : Semi-minor axis, in meters. (output)
*/
a = gi.Geocent_a;
b = gi.Geocent_b;
} /* END OF Get_Geocentric_Parameters */
template <typename T>
inline long pj_Convert_Geodetic_To_Geocentric (GeocentricInfo<T> const& gi,
T Longitude, T Latitude, T Height,
T & X, T & Y, T & Z)
{ /* BEGIN Convert_Geodetic_To_Geocentric */
/*
* The function Convert_Geodetic_To_Geocentric converts geodetic coordinates
* (latitude, longitude, and height) to geocentric coordinates (X, Y, Z),
* according to the current ellipsoid parameters.
*
* Latitude : Geodetic latitude in radians (input)
* Longitude : Geodetic longitude in radians (input)
* Height : Geodetic height, in meters (input)
* X : Calculated Geocentric X coordinate, in meters (output)
* Y : Calculated Geocentric Y coordinate, in meters (output)
* Z : Calculated Geocentric Z coordinate, in meters (output)
*
*/
long Error_Code = GEOCENT_NO_ERROR;
T Rn; /* Earth radius at location */
T Sin_Lat; /* sin(Latitude) */
T Sin2_Lat; /* Square of sin(Latitude) */
T Cos_Lat; /* cos(Latitude) */
static const T PI = math::pi<T>();
static const T PI_OVER_2 = math::half_pi<T>();
/*
** Don't blow up if Latitude is just a little out of the value
** range as it may just be a rounding issue. Also removed longitude
** test, it should be wrapped by cos() and sin(). NFW for PROJ.4, Sep/2001.
*/
if( Latitude < -PI_OVER_2 && Latitude > -1.001 * PI_OVER_2 )
Latitude = -PI_OVER_2;
else if( Latitude > PI_OVER_2 && Latitude < 1.001 * PI_OVER_2 )
Latitude = PI_OVER_2;
else if ((Latitude < -PI_OVER_2) || (Latitude > PI_OVER_2))
{ /* Latitude out of range */
Error_Code |= GEOCENT_LAT_ERROR;
}
if (!Error_Code)
{ /* no errors */
if (Longitude > PI)
Longitude -= (2*PI);
Sin_Lat = sin(Latitude);
Cos_Lat = cos(Latitude);
Sin2_Lat = Sin_Lat * Sin_Lat;
Rn = gi.Geocent_a / (sqrt(1.0e0 - gi.Geocent_e2 * Sin2_Lat));
X = (Rn + Height) * Cos_Lat * cos(Longitude);
Y = (Rn + Height) * Cos_Lat * sin(Longitude);
Z = ((Rn * (1 - gi.Geocent_e2)) + Height) * Sin_Lat;
}
return (Error_Code);
} /* END OF Convert_Geodetic_To_Geocentric */
/*
* The function Convert_Geocentric_To_Geodetic converts geocentric
* coordinates (X, Y, Z) to geodetic coordinates (latitude, longitude,
* and height), according to the current ellipsoid parameters.
*
* X : Geocentric X coordinate, in meters. (input)
* Y : Geocentric Y coordinate, in meters. (input)
* Z : Geocentric Z coordinate, in meters. (input)
* Latitude : Calculated latitude value in radians. (output)
* Longitude : Calculated longitude value in radians. (output)
* Height : Calculated height value, in meters. (output)
*/
#define BOOST_GEOMETRY_PROJECTIONS_USE_ITERATIVE_METHOD
template <typename T>
inline void pj_Convert_Geocentric_To_Geodetic (GeocentricInfo<T> const& gi,
T X, T Y, T Z,
T & Longitude, T & Latitude, T & Height)
{ /* BEGIN Convert_Geocentric_To_Geodetic */
static const T PI_OVER_2 = math::half_pi<T>();
#if !defined(BOOST_GEOMETRY_PROJECTIONS_USE_ITERATIVE_METHOD)
static const T COS_67P5 = detail::COS_67P5<T>();
static const T AD_C = detail::AD_C<T>();
/*
* The method used here is derived from 'An Improved Algorithm for
* Geocentric to Geodetic Coordinate Conversion', by Ralph Toms, Feb 1996
*/
/* Note: Variable names follow the notation used in Toms, Feb 1996 */
T W; /* distance from Z axis */
T W2; /* square of distance from Z axis */
T T0; /* initial estimate of vertical component */
T T1; /* corrected estimate of vertical component */
T S0; /* initial estimate of horizontal component */
T S1; /* corrected estimate of horizontal component */
T Sin_B0; /* sin(B0), B0 is estimate of Bowring aux variable */
T Sin3_B0; /* cube of sin(B0) */
T Cos_B0; /* cos(B0) */
T Sin_p1; /* sin(phi1), phi1 is estimated latitude */
T Cos_p1; /* cos(phi1) */
T Rn; /* Earth radius at location */
T Sum; /* numerator of cos(phi1) */
bool At_Pole; /* indicates location is in polar region */
At_Pole = false;
if (X != 0.0)
{
Longitude = atan2(Y,X);
}
else
{
if (Y > 0)
{
Longitude = PI_OVER_2;
}
else if (Y < 0)
{
Longitude = -PI_OVER_2;
}
else
{
At_Pole = true;
Longitude = 0.0;
if (Z > 0.0)
{ /* north pole */
Latitude = PI_OVER_2;
}
else if (Z < 0.0)
{ /* south pole */
Latitude = -PI_OVER_2;
}
else
{ /* center of earth */
Latitude = PI_OVER_2;
Height = -Geocent_b;
return;
}
}
}
W2 = X*X + Y*Y;
W = sqrt(W2);
T0 = Z * AD_C;
S0 = sqrt(T0 * T0 + W2);
Sin_B0 = T0 / S0;
Cos_B0 = W / S0;
Sin3_B0 = Sin_B0 * Sin_B0 * Sin_B0;
T1 = Z + gi.Geocent_b * gi.Geocent_ep2 * Sin3_B0;
Sum = W - gi.Geocent_a * gi.Geocent_e2 * Cos_B0 * Cos_B0 * Cos_B0;
S1 = sqrt(T1*T1 + Sum * Sum);
Sin_p1 = T1 / S1;
Cos_p1 = Sum / S1;
Rn = gi.Geocent_a / sqrt(1.0 - gi.Geocent_e2 * Sin_p1 * Sin_p1);
if (Cos_p1 >= COS_67P5)
{
Height = W / Cos_p1 - Rn;
}
else if (Cos_p1 <= -COS_67P5)
{
Height = W / -Cos_p1 - Rn;
}
else
{
Height = Z / Sin_p1 + Rn * (gi.Geocent_e2 - 1.0);
}
if (At_Pole == false)
{
Latitude = atan(Sin_p1 / Cos_p1);
}
#else /* defined(BOOST_GEOMETRY_PROJECTIONS_USE_ITERATIVE_METHOD) */
/*
* Reference...
* ============
* Wenzel, H.-G.(1985): Hochauflösende Kugelfunktionsmodelle für
* das Gravitationspotential der Erde. Wiss. Arb. Univ. Hannover
* Nr. 137, p. 130-131.
* Programmed by GGA- Leibniz-Institute of Applied Geophysics
* Stilleweg 2
* D-30655 Hannover
* Federal Republic of Germany
* Internet: www.gga-hannover.de
*
* Hannover, March 1999, April 2004.
* see also: comments in statements
* remarks:
* Mathematically exact and because of symmetry of rotation-ellipsoid,
* each point (X,Y,Z) has at least two solutions (Latitude1,Longitude1,Height1) and
* (Latitude2,Longitude2,Height2). Is point=(0.,0.,Z) (P=0.), so you get even
* four solutions, every two symmetrical to the semi-minor axis.
* Here Height1 and Height2 have at least a difference in order of
* radius of curvature (e.g. (0,0,b)=> (90.,0.,0.) or (-90.,0.,-2b);
* (a+100.)*(sqrt(2.)/2.,sqrt(2.)/2.,0.) => (0.,45.,100.) or
* (0.,225.,-(2a+100.))).
* The algorithm always computes (Latitude,Longitude) with smallest |Height|.
* For normal computations, that means |Height|<10000.m, algorithm normally
* converges after to 2-3 steps!!!
* But if |Height| has the amount of length of ellipsoid's axis
* (e.g. -6300000.m), algorithm needs about 15 steps.
*/
/* local definitions and variables */
/* end-criterium of loop, accuracy of sin(Latitude) */
static const T genau = 1.E-12;
static const T genau2 = (genau*genau);
static const int maxiter = 30;
T P; /* distance between semi-minor axis and location */
T RR; /* distance between center and location */
T CT; /* sin of geocentric latitude */
T ST; /* cos of geocentric latitude */
T RX;
T RK;
T RN; /* Earth radius at location */
T CPHI0; /* cos of start or old geodetic latitude in iterations */
T SPHI0; /* sin of start or old geodetic latitude in iterations */
T CPHI; /* cos of searched geodetic latitude */
T SPHI; /* sin of searched geodetic latitude */
T SDPHI; /* end-criterium: addition-theorem of sin(Latitude(iter)-Latitude(iter-1)) */
int iter; /* # of continuous iteration, max. 30 is always enough (s.a.) */
P = sqrt(X*X+Y*Y);
RR = sqrt(X*X+Y*Y+Z*Z);
/* special cases for latitude and longitude */
if (P/gi.Geocent_a < genau) {
/* special case, if P=0. (X=0., Y=0.) */
Longitude = 0.;
/* if (X,Y,Z)=(0.,0.,0.) then Height becomes semi-minor axis
* of ellipsoid (=center of mass), Latitude becomes PI/2 */
if (RR/gi.Geocent_a < genau) {
Latitude = PI_OVER_2;
Height = -gi.Geocent_b;
return ;
}
}
else {
/* ellipsoidal (geodetic) longitude
* interval: -PI < Longitude <= +PI */
Longitude=atan2(Y,X);
}
/* --------------------------------------------------------------
* Following iterative algorithm was developed by
* "Institut für Erdmessung", University of Hannover, July 1988.
* Internet: www.ife.uni-hannover.de
* Iterative computation of CPHI,SPHI and Height.
* Iteration of CPHI and SPHI to 10**-12 radian resp.
* 2*10**-7 arcsec.
* --------------------------------------------------------------
*/
CT = Z/RR;
ST = P/RR;
RX = 1.0/sqrt(1.0-gi.Geocent_e2*(2.0-gi.Geocent_e2)*ST*ST);
CPHI0 = ST*(1.0-gi.Geocent_e2)*RX;
SPHI0 = CT*RX;
iter = 0;
/* loop to find sin(Latitude) resp. Latitude
* until |sin(Latitude(iter)-Latitude(iter-1))| < genau */
do
{
iter++;
RN = gi.Geocent_a/sqrt(1.0-gi.Geocent_e2*SPHI0*SPHI0);
/* ellipsoidal (geodetic) height */
Height = P*CPHI0+Z*SPHI0-RN*(1.0-gi.Geocent_e2*SPHI0*SPHI0);
RK = gi.Geocent_e2*RN/(RN+Height);
RX = 1.0/sqrt(1.0-RK*(2.0-RK)*ST*ST);
CPHI = ST*(1.0-RK)*RX;
SPHI = CT*RX;
SDPHI = SPHI*CPHI0-CPHI*SPHI0;
CPHI0 = CPHI;
SPHI0 = SPHI;
}
while (SDPHI*SDPHI > genau2 && iter < maxiter);
/* ellipsoidal (geodetic) latitude */
Latitude=atan(SPHI/fabs(CPHI));
return;
#endif /* defined(BOOST_GEOMETRY_PROJECTIONS_USE_ITERATIVE_METHOD) */
} /* END OF Convert_Geocentric_To_Geodetic */
} // namespace detail
}}} // namespace boost::geometry::projections
#endif // BOOST_GEOMETRY_SRS_PROJECTIONS_IMPL_GEOCENT_HPP