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Diffstat (limited to 'boost/geometry/formulas/vincenty_direct.hpp')
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1 files changed, 185 insertions, 0 deletions
diff --git a/boost/geometry/formulas/vincenty_direct.hpp b/boost/geometry/formulas/vincenty_direct.hpp new file mode 100644 index 0000000000..f3647ff4e6 --- /dev/null +++ b/boost/geometry/formulas/vincenty_direct.hpp @@ -0,0 +1,185 @@ +// Boost.Geometry + +// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. + +// This file was modified by Oracle on 2014, 2016. +// Modifications copyright (c) 2014-2016 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_FORMULAS_VINCENTY_DIRECT_HPP +#define BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP + + +#include <boost/math/constants/constants.hpp> + +#include <boost/geometry/core/radius.hpp> +#include <boost/geometry/core/srs.hpp> + +#include <boost/geometry/util/condition.hpp> +#include <boost/geometry/util/math.hpp> + +#include <boost/geometry/algorithms/detail/flattening.hpp> + +#include <boost/geometry/formulas/differential_quantities.hpp> +#include <boost/geometry/formulas/result_direct.hpp> + + +#ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS +#define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000 +#endif + + +namespace boost { namespace geometry { namespace formula +{ + +/*! +\brief The solution of the direct 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, + bool EnableCoordinates = true, + bool EnableReverseAzimuth = false, + bool EnableReducedLength = false, + bool EnableGeodesicScale = false +> +class vincenty_direct +{ + static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale; + static const bool CalcCoordinates = EnableCoordinates || CalcQuantities; + static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities; + +public: + typedef result_direct<CT> result_type; + + template <typename T, typename Dist, typename Azi, typename Spheroid> + static inline result_type apply(T const& lo1, + T const& la1, + Dist const& distance, + Azi const& azimuth12, + Spheroid const& spheroid) + { + result_type result; + + CT const lon1 = lo1; + CT const lat1 = la1; + + if ( math::equals(distance, Dist(0)) || distance < Dist(0) ) + { + result.lon2 = lon1; + result.lat2 = lat1; + return result; + } + + CT const radius_a = CT(get_radius<0>(spheroid)); + CT const radius_b = CT(get_radius<2>(spheroid)); + CT const flattening = geometry::detail::flattening<CT>(spheroid); + + CT const sin_azimuth12 = sin(azimuth12); + CT const cos_azimuth12 = cos(azimuth12); + + // U: reduced latitude, defined by tan U = (1-f) tan phi + CT const one_min_f = CT(1) - flattening; + CT const tan_U1 = one_min_f * tan(lat1); + CT const sigma1 = atan2(tan_U1, cos_azimuth12); // (1) + + // may be calculated from tan using 1 sqrt() + CT const U1 = atan(tan_U1); + CT const sin_U1 = sin(U1); + CT const cos_U1 = cos(U1); + + CT const sin_alpha = cos_U1 * sin_azimuth12; // (2) + CT const sin_alpha_sqr = math::sqr(sin_alpha); + CT const cos_alpha_sqr = CT(1) - sin_alpha_sqr; + + CT const b_sqr = radius_b * radius_b; + CT const u_sqr = cos_alpha_sqr * (radius_a * radius_a - b_sqr) / b_sqr; + CT const A = CT(1) + (u_sqr/CT(16384)) * (CT(4096) + u_sqr*(CT(-768) + u_sqr*(CT(320) - u_sqr*CT(175)))); // (3) + CT const B = (u_sqr/CT(1024))*(CT(256) + u_sqr*(CT(-128) + u_sqr*(CT(74) - u_sqr*CT(47)))); // (4) + + CT s_div_bA = distance / (radius_b * A); + CT sigma = s_div_bA; // (7) + + CT previous_sigma; + CT sin_sigma; + CT cos_sigma; + CT cos_2sigma_m; + CT cos_2sigma_m_sqr; + + int counter = 0; // robustness + + do + { + previous_sigma = sigma; + + CT const two_sigma_m = CT(2) * sigma1 + sigma; // (5) + + sin_sigma = sin(sigma); + cos_sigma = cos(sigma); + CT const sin_sigma_sqr = math::sqr(sin_sigma); + cos_2sigma_m = cos(two_sigma_m); + cos_2sigma_m_sqr = math::sqr(cos_2sigma_m); + + CT const delta_sigma = B * sin_sigma * (cos_2sigma_m + + (B/CT(4)) * ( cos_sigma * (CT(-1) + CT(2)*cos_2sigma_m_sqr) + - (B/CT(6) * cos_2sigma_m * (CT(-3)+CT(4)*sin_sigma_sqr) * (CT(-3)+CT(4)*cos_2sigma_m_sqr)) )); // (6) + + sigma = s_div_bA + delta_sigma; // (7) + + ++counter; // robustness + + } while ( geometry::math::abs(previous_sigma - sigma) > CT(1e-12) + //&& geometry::math::abs(sigma) < pi + && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness + + if (BOOST_GEOMETRY_CONDITION(CalcCoordinates)) + { + result.lat2 + = atan2( sin_U1 * cos_sigma + cos_U1 * sin_sigma * cos_azimuth12, + one_min_f * math::sqrt(sin_alpha_sqr + math::sqr(sin_U1 * sin_sigma - cos_U1 * cos_sigma * cos_azimuth12))); // (8) + + CT const lambda = atan2( sin_sigma * sin_azimuth12, + cos_U1 * cos_sigma - sin_U1 * sin_sigma * cos_azimuth12); // (9) + CT const C = (flattening/CT(16)) * cos_alpha_sqr * ( CT(4) + flattening * ( CT(4) - CT(3) * cos_alpha_sqr ) ); // (10) + CT const L = lambda - (CT(1) - C) * flattening * sin_alpha + * ( sigma + C * sin_sigma * ( cos_2sigma_m + C * cos_sigma * ( CT(-1) + CT(2) * cos_2sigma_m_sqr ) ) ); // (11) + + result.lon2 = lon1 + L; + } + + if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth)) + { + result.reverse_azimuth + = atan2(sin_alpha, -sin_U1 * sin_sigma + cos_U1 * cos_sigma * cos_azimuth12); // (12) + } + + if (BOOST_GEOMETRY_CONDITION(CalcQuantities)) + { + typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities; + quantities::apply(lon1, lat1, result.lon2, result.lat2, + azimuth12, result.reverse_azimuth, + radius_b, flattening, + result.reduced_length, result.geodesic_scale); + } + + return result; + } + +}; + +}}} // namespace boost::geometry::formula + + +#endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP |