MarbleMath.h

// SPDX-License-Identifier: LGPL-2.1-or-later
//
// SPDX-FileCopyrightText: 2007 Torsten Rahn <tackat@kde.org>
// SPDX-FileCopyrightText: 2007 Inge Wallin <ingwa@kde.org>
//
 
#ifndef MARBLE_MARBLEMATH_H
#define MARBLE_MARBLEMATH_H
 
#include <QtGlobal>
 
#include <cmath>
 
namespace
{
const qreal a1 = 1.0 / 6.0;
const qreal a2 = 1.0 / 24.0;
const qreal a3 = 61.0 / 5040;
const qreal a4 = 277.0 / 72576.0;
const qreal a5 = 50521.0 / 39916800.0;
const qreal a6 = 41581.0 / 95800320.0;
const qreal a7 = 199360981.0 / 1307674368000.0;
const qreal a8 = 228135437.0 / 4184557977600.0;
const qreal a9 = 2404879675441.0 / 121645100408832000.0;
const qreal a10 = 14814847529501.0 / 2043637686868377600.0;
const qreal a11 = 69348874393137901.0 / 25852016738884976640000.0;
const qreal a12 = 238685140977801337.0 / 238634000666630553600000.0;
const qreal a13 = 4087072509293123892361.0 / 10888869450418352160768000000.0;
const qreal a14 = 454540704683713199807.0 / 3209350995912777478963200000.0;
const qreal a15 = 441543893249023104553682821.0 / 8222838654177922817725562880000000.0;
const qreal a16 = 2088463430347521052196056349.0 / 102156677868375135241390522368000000.0;
}
 
namespace Marble
{
 
/**
 * @brief This method calculates the shortest distance between two points on a sphere.
 * @brief See: https://en.wikipedia.org/wiki/Great-circle_distance
 * @param lon1 longitude of first point in radians
 * @param lat1 latitude of first point in radians
 * @param lon2 longitude of second point in radians
 * @param lat2 latitude of second point in radians
 */
inline qreal distanceSphere(qreal lon1, qreal lat1, qreal lon2, qreal lat2)
{
    qreal h1 = sin(0.5 * (lat2 - lat1));
    qreal h2 = sin(0.5 * (lon2 - lon1));
    qreal d = h1 * h1 + cos(lat1) * cos(lat2) * h2 * h2;
 
    return 2.0 * atan2(sqrt(d), sqrt(1.0 - d));
}
 
/**
 * @brief This method roughly calculates the shortest distance between two points on a sphere.
 * @brief It's probably faster than distanceSphere(...) but for 7 significant digits only has
 * @brief an accuracy of about 1 arcmin.
 * @brief See: https://en.wikipedia.org/wiki/Great-circle_distance
 */
inline qreal distanceSphereApprox(qreal lon1, qreal lat1, qreal lon2, qreal lat2)
{
    return acos(sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon1 - lon2));
}
 
/**
 * @brief This method is a fast Mac Laurin power series approximation of the
 * @brief inverse Gudermannian. The inverse Gudermannian gives the vertical
 * @brief position y in the Mercator projection in terms of the latitude.
 * @brief See: https://en.wikipedia.org/wiki/Mercator_projection
 */
inline qreal gdInv(qreal x)
{
    const qreal x2 = x * x;
    return x
        + x * x2
        * (a1
           + x2
               * (a2
                  + x2
                      * (a3
                         + x2
                             * (a4
                                + x2
                                    * (a5
                                       + x2
                                           * (a6
                                              + x2
                                                  * (a7
                                                     + x2
                                                         * (a8
                                                            + x2
                                                                * (a9
                                                                   + x2
                                                                       * (a10
                                                                          + x2
                                                                              * (a11
                                                                                 + x2 * (a12 + x2 * (a13 + x2 * (a14 + x2 * (a15 + x2 * (a16))))))))))))))));
}
 
}
 
/**
 * @brief This method is a fast Mac Laurin power series approximation of the
 *        Gudermannian. The Gudermannian gives the latitude
 *        in the Mercator projection in terms of the vertical position y.
 *        See: https://en.wikipedia.org/wiki/Mercator_projection
 */
inline qreal gd(qreal x)
{
    /*
    const qreal x2 = x * x;
    return x
         - x * x2 * (  a1
         - x2 * ( a2  - x2 * ( a3  - x2 * ( a4  - x2 * ( a5
         - x2 * ( a6  - x2 * ( a7  - x2 * ( a8  - x2 * ( a9
         - x2 * ( a10 - x2 * ( a11 - x2 * ( a12 - x2 * ( a13
         - x2 * ( a14 - x2 * ( a15 - x2 * ( a16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) );
    */
 
    return atan(sinh(x));
}
 
#endif