ADD: new track message, Entity class and Position class
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Henry Winkel
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libs/geographiclib/examples/JacobiConformal.hpp
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176
libs/geographiclib/examples/JacobiConformal.hpp
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/**
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* \file JacobiConformal.hpp
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* \brief Header for GeographicLib::JacobiConformal class
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*
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* \note This is just sample code. It is not part of GeographicLib
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* itself.
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*
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* Copyright (c) Charles Karney (2014-2020) <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_JACOBICONFORMAL_HPP)
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#define GEOGRAPHICLIB_JACOBICONFORMAL_HPP 1
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#include <GeographicLib/EllipticFunction.hpp>
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namespace GeographicLib {
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/**
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* \brief Jacobi's conformal projection of a triaxial ellipsoid
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*
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* <b>NOTE:</b> This is just sample code. It is not part of GeographicLib
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* itself.
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*
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* This is a conformal projection of the ellipsoid to a plane in which
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* the grid lines are straight; see Jacobi,
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* <a href="https://books.google.com/books?id=ryEOAAAAQAAJ&pg=PA212">
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* Vorlesungen über Dynamik, §28</a>. The constructor takes the
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* semi-axes of the ellipsoid (which must be in order). Member functions map
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* the ellipsoidal coordinates ω and β separately to \e x and \e
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* y. Jacobi's coordinates have been multiplied by
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* (<i>a</i><sup>2</sup>−<i>c</i><sup>2</sup>)<sup>1/2</sup> /
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* (2<i>b</i>) so that the customary results are returned in the cases of
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* a sphere or an ellipsoid of revolution.
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*
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* The ellipsoid is oriented so that the large principal ellipse, \f$Z=0\f$,
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* is the equator, \f$\beta=0\f$, while the small principal ellipse,
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* \f$Y=0\f$, is the prime meridian, \f$\omega=0\f$. The four umbilic
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* points, \f$\left|\omega\right| = \left|\beta\right| = \frac12\pi\f$, lie
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* on middle principal ellipse in the plane \f$X=0\f$.
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*
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* For more information on this projection, see \ref jacobi.
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**********************************************************************/
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class JacobiConformal {
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typedef Math::real real;
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real _a, _b, _c, _ab2, _bc2, _ac2;
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EllipticFunction _ex, _ey;
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static void norm(real& x, real& y) {
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using std::hypot;
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real z = hypot(x, y); x /= z; y /= z;
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}
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public:
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/**
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* Constructor for a trixial ellipsoid with semi-axes.
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*
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* @param[in] a the largest semi-axis.
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* @param[in] b the middle semi-axis.
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* @param[in] c the smallest semi-axis.
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*
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* The semi-axes must satisfy \e a ≥ \e b ≥ \e c > 0 and \e a >
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* \e c. This form of the constructor cannot be used to specify a
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* sphere (use the next constructor).
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**********************************************************************/
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JacobiConformal(real a, real b, real c)
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: _a(a), _b(b), _c(c)
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, _ab2((_a - _b) * (_a + _b))
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, _bc2((_b - _c) * (_b + _c))
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, _ac2((_a - _c) * (_a + _c))
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, _ex(_ab2 / _ac2 * Math::sq(_c / _b), -_ab2 / Math::sq(_b),
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_bc2 / _ac2 * Math::sq(_a / _b), Math::sq(_a / _b))
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, _ey(_bc2 / _ac2 * Math::sq(_a / _b), +_bc2 / Math::sq(_b),
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_ab2 / _ac2 * Math::sq(_c / _b), Math::sq(_c / _b))
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{
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using std::isfinite;
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if (!(isfinite(_a) && _a >= _b && _b >= _c && _c > 0))
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throw GeographicErr("JacobiConformal: axes are not in order");
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if (!(_a > _c))
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throw GeographicErr
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("JacobiConformal: use alternate constructor for sphere");
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}
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/**
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* Alternate constructor for a triaxial ellipsoid.
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*
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* @param[in] a the largest semi-axis.
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* @param[in] b the middle semi-axis.
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* @param[in] c the smallest semi-axis.
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* @param[in] ab the relative magnitude of \e a − \e b.
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* @param[in] bc the relative magnitude of \e b − \e c.
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*
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* This form can be used to specify a sphere. The semi-axes must
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* satisfy \e a ≥ \e b ≥ c > 0. The ratio \e ab : \e bc must equal
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* (<i>a</i>−<i>b</i>) : (<i>b</i>−<i>c</i>) with \e ab
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* ≥ 0, \e bc ≥ 0, and \e ab + \e bc > 0.
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**********************************************************************/
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JacobiConformal(real a, real b, real c, real ab, real bc)
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: _a(a), _b(b), _c(c)
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, _ab2(ab * (_a + _b))
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, _bc2(bc * (_b + _c))
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, _ac2(_ab2 + _bc2)
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, _ex(_ab2 / _ac2 * Math::sq(_c / _b),
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-(_a - _b) * (_a + _b) / Math::sq(_b),
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_bc2 / _ac2 * Math::sq(_a / _b), Math::sq(_a / _b))
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, _ey(_bc2 / _ac2 * Math::sq(_a / _b),
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+(_b - _c) * (_b + _c) / Math::sq(_b),
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_ab2 / _ac2 * Math::sq(_c / _b), Math::sq(_c / _b))
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{
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using std::isfinite;
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if (!(isfinite(_a) && _a >= _b && _b >= _c && _c > 0 &&
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ab >= 0 && bc >= 0))
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throw GeographicErr("JacobiConformal: axes are not in order");
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if (!(ab + bc > 0 && isfinite(_ac2)))
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throw GeographicErr("JacobiConformal: ab + bc must be positive");
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}
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/**
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* @return the quadrant length in the \e x direction.
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**********************************************************************/
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Math::real x() const { return Math::sq(_a / _b) * _ex.Pi(); }
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/**
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* The \e x projection.
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*
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* @param[in] somg sin(ω).
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* @param[in] comg cos(ω).
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* @return \e x.
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**********************************************************************/
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Math::real x(real somg, real comg) const {
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real somg1 = _b * somg, comg1 = _a * comg; norm(somg1, comg1);
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return Math::sq(_a / _b)
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* _ex.Pi(somg1, comg1, _ex.Delta(somg1, comg1));
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}
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/**
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* The \e x projection.
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*
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* @param[in] omg ω (in degrees).
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* @return \e x (in degrees).
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*
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* ω must be in [−180°, 180°].
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**********************************************************************/
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Math::real x(real omg) const {
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real somg, comg;
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Math::sincosd(omg, somg, comg);
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return x(somg, comg) / Math::degree();
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}
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/**
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* @return the quadrant length in the \e y direction.
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**********************************************************************/
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Math::real y() const { return Math::sq(_c / _b) * _ey.Pi(); }
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/**
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* The \e y projection.
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*
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* @param[in] sbet sin(β).
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* @param[in] cbet cos(β).
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* @return \e y.
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**********************************************************************/
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Math::real y(real sbet, real cbet) const {
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real sbet1 = _b * sbet, cbet1 = _c * cbet; norm(sbet1, cbet1);
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return Math::sq(_c / _b)
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* _ey.Pi(sbet1, cbet1, _ey.Delta(sbet1, cbet1));
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}
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/**
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* The \e y projection.
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*
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* @param[in] bet β (in degrees).
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* @return \e y (in degrees).
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*
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* β must be in (−180°, 180°].
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**********************************************************************/
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Math::real y(real bet) const {
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real sbet, cbet;
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Math::sincosd(bet, sbet, cbet);
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return y(sbet, cbet) / Math::degree();
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}
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};
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} // namespace GeographicLib
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#endif // GEOGRAPHICLIB_JACOBICONFORMAL_HPP
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