view DEPENDENCIES/generic/include/boost/geometry/algorithms/detail/vincenty_inverse.hpp @ 109:c4758b1b1089

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// Boost.Geometry

// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.

// This file was modified by Oracle on 2014.
// Modifications copyright (c) 2014 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)

#ifndef BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
#define BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP


#include <boost/math/constants/constants.hpp>

#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/core/srs.hpp>

#include <boost/geometry/util/math.hpp>

#include <boost/geometry/algorithms/detail/flattening.hpp>


#ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
#define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
#endif


namespace boost { namespace geometry { namespace detail
{

/*!
\brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975
\author See
    - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
    - http://www.icsm.gov.au/gda/gdav2.3.pdf
\author Adapted from various implementations to get it close to the original document
    - http://www.movable-type.co.uk/scripts/LatLongVincenty.html
    - http://exogen.case.edu/projects/geopy/source/geopy.distance.html
    - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink

*/
template <typename CT>
class vincenty_inverse
{
public:
    template <typename T1, typename T2, typename Spheroid>
    vincenty_inverse(T1 const& lon1,
                     T1 const& lat1,
                     T2 const& lon2,
                     T2 const& lat2,
                     Spheroid const& spheroid)
        : is_result_zero(false)
    {
        if (math::equals(lat1, lat2) && math::equals(lon1, lon2))
        {
            is_result_zero = true;
            return;
        }

        CT const c1 = 1;
        CT const c2 = 2;
        CT const c3 = 3;
        CT const c4 = 4;
        CT const c16 = 16;
        CT const c_e_12 = CT(1e-12);

        CT const pi = geometry::math::pi<CT>();
        CT const two_pi = c2 * pi;

        // lambda: difference in longitude on an auxiliary sphere
        CT L = lon2 - lon1;
        CT lambda = L;

        if (L < -pi) L += two_pi;
        if (L > pi) L -= two_pi;

        radius_a = CT(get_radius<0>(spheroid));
        radius_b = CT(get_radius<2>(spheroid));
        CT const flattening = geometry::detail::flattening<CT>(spheroid);

        // U: reduced latitude, defined by tan U = (1-f) tan phi
        CT const one_min_f = c1 - flattening;
        CT const tan_U1 = one_min_f * tan(lat1); // above (1)
        CT const tan_U2 = one_min_f * tan(lat2); // above (1)

        // calculate sin U and cos U using trigonometric identities
        CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1));
        CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2));
        // cos = 1 / sqrt(1 + tan^2)
        cos_U1 = c1 / temp_den_U1;
        cos_U2 = c1 / temp_den_U2;
        // sin = tan / sqrt(1 + tan^2)
        sin_U1 = tan_U1 / temp_den_U1;
        sin_U2 = tan_U2 / temp_den_U2;

        // calculate sin U and cos U directly
        //CT const U1 = atan(tan_U1);
        //CT const U2 = atan(tan_U2);
        //cos_U1 = cos(U1);
        //cos_U2 = cos(U2);
        //sin_U1 = tan_U1 * cos_U1; // sin(U1);
        //sin_U2 = tan_U2 * cos_U2; // sin(U2);

        CT previous_lambda;

        int counter = 0; // robustness

        do
        {
            previous_lambda = lambda; // (13)
            sin_lambda = sin(lambda);
            cos_lambda = cos(lambda);
            sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14)
            CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15)
            sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17)
            cos2_alpha = c1 - math::sqr(sin_alpha);
            cos2_sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18)

            CT C = flattening/c16 * cos2_alpha * (c4 + flattening * (c4 - c3 * cos2_alpha)); // (10)
            sigma = atan2(sin_sigma, cos_sigma); // (16)
            lambda = L + (c1 - C) * flattening * sin_alpha *
                (sigma + C * sin_sigma * ( cos2_sigma_m + C * cos_sigma * (-c1 + c2 * math::sqr(cos2_sigma_m)))); // (11)

            ++counter; // robustness

        } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12
               && geometry::math::abs(lambda) < pi
               && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
    }

    inline CT distance() const
    {
        if ( is_result_zero )
        {
            return CT(0);
        }

        // Oops getting hard here
        // (again, problem is that ttmath cannot divide by doubles, which is OK)
        CT const c1 = 1;
        CT const c2 = 2;
        CT const c3 = 3;
        CT const c4 = 4;
        CT const c6 = 6;
        CT const c47 = 47;
        CT const c74 = 74;
        CT const c128 = 128;
        CT const c256 = 256;
        CT const c175 = 175;
        CT const c320 = 320;
        CT const c768 = 768;
        CT const c1024 = 1024;
        CT const c4096 = 4096;
        CT const c16384 = 16384;

        //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1)
        CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1)

        CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3)
        CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4)
        CT delta_sigma = B * sin_sigma * ( cos2_sigma_m + (B/c4) * (cos(sigma)* (-c1 + c2 * cos2_sigma_m)
            - (B/c6) * cos2_sigma_m * (-c3 + c4 * math::sqr(sin_sigma)) * (-c3 + c4 * cos2_sigma_m))); // (6)

        return radius_b * A * (sigma - delta_sigma); // (19)
    }

    inline CT azimuth12() const
    {
        return is_result_zero ?
               CT(0) :
               atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
    }

    inline CT azimuth21() const
    {
        // NOTE: signs of X and Y are different than in the original paper
        return is_result_zero ?
               CT(0) :
               atan2(-cos_U1 * sin_lambda, sin_U1 * cos_U2 - cos_U1 * sin_U2 * cos_lambda); // (21)
    }

private:
    // alpha: azimuth of the geodesic at the equator
    CT cos2_alpha;
    CT sin_alpha;

    // sigma: angular distance p1,p2 on the sphere
    // sigma1: angular distance on the sphere from the equator to p1
    // sigma_m: angular distance on the sphere from the equator to the midpoint of the line
    CT sigma;
    CT sin_sigma;
    CT cos2_sigma_m;

    CT sin_lambda;
    CT cos_lambda;

    // set only once
    CT cos_U1;
    CT cos_U2;
    CT sin_U1;
    CT sin_U2;

    // set only once
    CT radius_a;
    CT radius_b;

    bool is_result_zero;
};

}}} // namespace boost::geometry::detail


#endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP