/usr/include/GeographicLib/PolarStereographic.hpp is in libgeographiclib-dev 1.21-1ubuntu1.
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* \file PolarStereographic.hpp
* \brief Header for GeographicLib::PolarStereographic class
*
* Copyright (c) Charles Karney (2008-2011) <charles@karney.com> and licensed
* under the MIT/X11 License. For more information, see
* http://geographiclib.sourceforge.net/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_POLARSTEREOGRAPHIC_HPP)
#define GEOGRAPHICLIB_POLARSTEREOGRAPHIC_HPP \
"$Id: 07add8492c46e42012007a8738060abc902a5504 $"
#include <GeographicLib/Constants.hpp>
namespace GeographicLib {
/**
* \brief Polar Stereographic Projection
*
* Implementation taken from the report,
* - J. P. Snyder,
* <a href="http://pubs.er.usgs.gov/usgspubs/pp/pp1395"> Map Projections: A
* Working Manual</a>, USGS Professional Paper 1395 (1987),
* pp. 160–163.
*
* This is a straightforward implementation of the equations in Snyder except
* that Newton's method is used to invert the projection.
*
* Example of use:
* \include example-PolarStereographic.cpp
**********************************************************************/
class GEOGRAPHIC_EXPORT PolarStereographic {
private:
typedef Math::real real;
// _Cx used to be _C but g++ 3.4 has a macro of that name
real _a, _f, _e2, _e, _e2m, _Cx, _c;
real _k0;
static const real tol_;
static const real overflow_;
static const int numit_ = 5;
// tan(x) for x in [-pi/2, pi/2] ensuring that the sign is right
static inline real tanx(real x) throw() {
real t = std::tan(x);
// Write the tests this way to ensure that tanx(NaN()) is NaN()
return x >= 0 ? (!(t < 0) ? t : overflow_) : (!(t >= 0) ? t : -overflow_);
}
// Return e * atanh(e * x) for f >= 0, else return
// - sqrt(-e2) * atan( sqrt(-e2) * x) for f < 0
inline real eatanhe(real x) const throw() {
return _f >= 0 ? _e * Math::atanh(_e * x) : - _e * std::atan(_e * x);
}
public:
/**
* Constructor for a ellipsoid with
*
* @param[in] a equatorial radius (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid. If \e f > 1, set flattening
* to 1/\e f.
* @param[in] k0 central scale factor.
*
* An exception is thrown if either of the axes of the ellipsoid is
* not positive \e a or if \e k0 is not positive.
**********************************************************************/
PolarStereographic(real a, real f, real k0);
/**
* Set the scale for the projection.
*
* @param[in] lat (degrees) assuming \e northp = true.
* @param[in] k scale at latitude \e lat (default 1).
*
* This allows a "latitude of true scale" to be specified. An exception is
* thrown if \e k is not positive or if \e lat is not in the range (-90,
* 90].
**********************************************************************/
void SetScale(real lat, real k = real(1));
/**
* Forward projection, from geographic to polar stereographic.
*
* @param[in] northp the pole which is the center of projection (true means
* north, false means south).
* @param[in] lat latitude of point (degrees).
* @param[in] lon longitude of point (degrees).
* @param[out] x easting of point (meters).
* @param[out] y northing of point (meters).
* @param[out] gamma meridian convergence at point (degrees).
* @param[out] k scale of projection at point.
*
* No false easting or northing is added. \e lat should be in the range
* (-90, 90] for \e northp = true and in the range [-90, 90) for \e northp
* = false; \e lon should be in the range [-180, 360].
**********************************************************************/
void Forward(bool northp, real lat, real lon,
real& x, real& y, real& gamma, real& k) const throw();
/**
* Reverse projection, from polar stereographic to geographic.
*
* @param[in] northp the pole which is the center of projection (true means
* north, false means south).
* @param[in] x easting of point (meters).
* @param[in] y northing of point (meters).
* @param[out] lat latitude of point (degrees).
* @param[out] lon longitude of point (degrees).
* @param[out] gamma meridian convergence at point (degrees).
* @param[out] k scale of projection at point.
*
* No false easting or northing is added. The value of \e lon returned is
* in the range [-180, 180).
**********************************************************************/
void Reverse(bool northp, real x, real y,
real& lat, real& lon, real& gamma, real& k) const throw();
/**
* PolarStereographic::Forward without returning the convergence and scale.
**********************************************************************/
void Forward(bool northp, real lat, real lon,
real& x, real& y) const throw() {
real gamma, k;
Forward(northp, lat, lon, x, y, gamma, k);
}
/**
* PolarStereographic::Reverse without returning the convergence and scale.
**********************************************************************/
void Reverse(bool northp, real x, real y,
real& lat, real& lon) const throw() {
real gamma, k;
Reverse(northp, x, y, lat, lon, gamma, k);
}
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value used in the constructor.
**********************************************************************/
Math::real MajorRadius() const throw() { return _a; }
/**
* @return \e f the flattening of the ellipsoid. This is the value used in
* the constructor.
**********************************************************************/
Math::real Flattening() const throw() { return _f; }
/// \cond SKIP
/**
* <b>DEPRECATED</b>
* @return \e r the inverse flattening of the ellipsoid.
**********************************************************************/
Math::real InverseFlattening() const throw() { return 1/_f; }
/// \endcond
/**
* The central scale for the projection. This is the value of \e k0 used
* in the constructor and is the scale at the pole unless overridden by
* PolarStereographic::SetScale.
**********************************************************************/
Math::real CentralScale() const throw() { return _k0; }
///@}
/**
* A global instantiation of PolarStereographic with the WGS84 ellipsoid
* and the UPS scale factor. However, unlike UPS, no false easting or
* northing is added.
**********************************************************************/
static const PolarStereographic UPS;
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_POLARSTEREOGRAPHIC_HPP
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