add GeographicLib
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Sven Czarnian
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external/include/GeographicLib/TransverseMercator.hpp
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external/include/GeographicLib/TransverseMercator.hpp
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/**
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* \file TransverseMercator.hpp
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* \brief Header for GeographicLib::TransverseMercator class
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*
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* Copyright (c) Charles Karney (2008-2020) <charles@karney.com> and licensed
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* under the MIT/X11 License. For more information, see
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* https://geographiclib.sourceforge.io/
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**********************************************************************/
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#if !defined(GEOGRAPHICLIB_TRANSVERSEMERCATOR_HPP)
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#define GEOGRAPHICLIB_TRANSVERSEMERCATOR_HPP 1
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#include <GeographicLib/Constants.hpp>
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#if !defined(GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER)
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/**
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* The order of the series approximation used in TransverseMercator.
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* GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER can be set to any integer in [4, 8].
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**********************************************************************/
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# define GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER \
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(GEOGRAPHICLIB_PRECISION == 2 ? 6 : \
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(GEOGRAPHICLIB_PRECISION == 1 ? 4 : 8))
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#endif
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namespace GeographicLib {
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/**
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* \brief Transverse Mercator projection
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*
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* This uses Krüger's method which evaluates the projection and its
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* inverse in terms of a series. See
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* - L. Krüger,
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* <a href="https://doi.org/10.2312/GFZ.b103-krueger28"> Konforme
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* Abbildung des Erdellipsoids in der Ebene</a> (Conformal mapping of the
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* ellipsoidal earth to the plane), Royal Prussian Geodetic Institute, New
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* Series 52, 172 pp. (1912).
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* - C. F. F. Karney,
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* <a href="https://doi.org/10.1007/s00190-011-0445-3">
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* Transverse Mercator with an accuracy of a few nanometers,</a>
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* J. Geodesy 85(8), 475--485 (Aug. 2011);
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* preprint
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* <a href="https://arxiv.org/abs/1002.1417">arXiv:1002.1417</a>.
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*
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* Krüger's method has been extended from 4th to 6th order. The maximum
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* error is 5 nm (5 nanometers), ground distance, for all positions within 35
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* degrees of the central meridian. The error in the convergence is 2
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* × 10<sup>−15</sup>" and the relative error in the scale
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* is 6 × 10<sup>−12</sup>%%. See Sec. 4 of
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* <a href="https://arxiv.org/abs/1002.1417">arXiv:1002.1417</a> for details.
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* The speed penalty in going to 6th order is only about 1%.
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*
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* There's a singularity in the projection at φ = 0°, λ
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* − λ<sub>0</sub> = ±(1 − \e e)90° (≈
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* ±82.6° for the WGS84 ellipsoid), where \e e is the
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* eccentricity. Beyond this point, the series ceases to converge and the
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* results from this method will be garbage. To be on the safe side, don't
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* use this method if the angular distance from the central meridian exceeds
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* (1 − 2e)90° (≈ 75° for the WGS84 ellipsoid)
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*
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* TransverseMercatorExact is an alternative implementation of the projection
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* using exact formulas which yield accurate (to 8 nm) results over the
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* entire ellipsoid.
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*
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* The ellipsoid parameters and the central scale are set in the constructor.
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* The central meridian (which is a trivial shift of the longitude) is
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* specified as the \e lon0 argument of the TransverseMercator::Forward and
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* TransverseMercator::Reverse functions. The latitude of origin is taken to
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* be the equator. There is no provision in this class for specifying a
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* false easting or false northing or a different latitude of origin.
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* However these are can be simply included by the calling function. For
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* example, the UTMUPS class applies the false easting and false northing for
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* the UTM projections. A more complicated example is the British National
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* Grid (<a href="https://www.spatialreference.org/ref/epsg/7405/">
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* EPSG:7405</a>) which requires the use of a latitude of origin. This is
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* implemented by the GeographicLib::OSGB class.
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*
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* This class also returns the meridian convergence \e gamma and scale \e k.
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* The meridian convergence is the bearing of grid north (the \e y axis)
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* measured clockwise from true north.
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*
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* See TransverseMercator.cpp for more information on the implementation.
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*
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* See \ref transversemercator for a discussion of this projection.
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*
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* Example of use:
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* \include example-TransverseMercator.cpp
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*
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* <a href="TransverseMercatorProj.1.html">TransverseMercatorProj</a> is a
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* command-line utility providing access to the functionality of
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* TransverseMercator and TransverseMercatorExact.
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**********************************************************************/
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class GEOGRAPHICLIB_EXPORT TransverseMercator {
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private:
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typedef Math::real real;
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static const int maxpow_ = GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER;
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static const int numit_ = 5;
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real _a, _f, _k0, _e2, _es, _e2m, _c, _n;
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// _alp[0] and _bet[0] unused
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real _a1, _b1, _alp[maxpow_ + 1], _bet[maxpow_ + 1];
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friend class Ellipsoid; // For access to taupf, tauf.
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public:
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/**
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* Constructor for a ellipsoid with
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*
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* @param[in] a equatorial radius (meters).
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* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
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* Negative \e f gives a prolate ellipsoid.
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* @param[in] k0 central scale factor.
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* @exception GeographicErr if \e a, (1 − \e f) \e a, or \e k0 is
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* not positive.
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**********************************************************************/
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TransverseMercator(real a, real f, real k0);
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/**
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* Forward projection, from geographic to transverse Mercator.
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*
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* @param[in] lon0 central meridian of the projection (degrees).
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* @param[in] lat latitude of point (degrees).
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* @param[in] lon longitude of point (degrees).
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* @param[out] x easting of point (meters).
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* @param[out] y northing of point (meters).
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* @param[out] gamma meridian convergence at point (degrees).
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* @param[out] k scale of projection at point.
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*
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* No false easting or northing is added. \e lat should be in the range
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* [−90°, 90°].
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**********************************************************************/
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void Forward(real lon0, real lat, real lon,
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real& x, real& y, real& gamma, real& k) const;
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/**
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* Reverse projection, from transverse Mercator to geographic.
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*
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* @param[in] lon0 central meridian of the projection (degrees).
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* @param[in] x easting of point (meters).
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* @param[in] y northing of point (meters).
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* @param[out] lat latitude of point (degrees).
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* @param[out] lon longitude of point (degrees).
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* @param[out] gamma meridian convergence at point (degrees).
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* @param[out] k scale of projection at point.
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*
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* No false easting or northing is added. The value of \e lon returned is
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* in the range [−180°, 180°].
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**********************************************************************/
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void Reverse(real lon0, real x, real y,
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real& lat, real& lon, real& gamma, real& k) const;
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/**
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* TransverseMercator::Forward without returning the convergence and scale.
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**********************************************************************/
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void Forward(real lon0, real lat, real lon,
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real& x, real& y) const {
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real gamma, k;
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Forward(lon0, lat, lon, x, y, gamma, k);
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}
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/**
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* TransverseMercator::Reverse without returning the convergence and scale.
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**********************************************************************/
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void Reverse(real lon0, real x, real y,
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real& lat, real& lon) const {
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real gamma, k;
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Reverse(lon0, x, y, lat, lon, gamma, k);
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}
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/** \name Inspector functions
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**********************************************************************/
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///@{
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/**
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* @return \e a the equatorial radius of the ellipsoid (meters). This is
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* the value used in the constructor.
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**********************************************************************/
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Math::real EquatorialRadius() const { return _a; }
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/**
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* @return \e f the flattening of the ellipsoid. This is the value used in
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* the constructor.
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**********************************************************************/
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Math::real Flattening() const { return _f; }
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/**
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* @return \e k0 central scale for the projection. This is the value of \e
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* k0 used in the constructor and is the scale on the central meridian.
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**********************************************************************/
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Math::real CentralScale() const { return _k0; }
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/**
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* \deprecated An old name for EquatorialRadius().
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**********************************************************************/
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GEOGRAPHICLIB_DEPRECATED("Use EquatorialRadius()")
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Math::real MajorRadius() const { return EquatorialRadius(); }
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///@}
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/**
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* A global instantiation of TransverseMercator with the WGS84 ellipsoid
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* and the UTM scale factor. However, unlike UTM, no false easting or
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* northing is added.
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**********************************************************************/
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static const TransverseMercator& UTM();
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};
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} // namespace GeographicLib
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#endif // GEOGRAPHICLIB_TRANSVERSEMERCATOR_HPP
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