-
Notifications
You must be signed in to change notification settings - Fork 214
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Merge pull request #489 from vissarion/feature_direct_formulas
Add direct formulas
- Loading branch information
Showing
15 changed files
with
1,274 additions
and
520 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,168 @@ | ||
| // Boost.Geometry | ||
|
|
||
| // Copyright (c) 2018 Oracle and/or its affiliates. | ||
|
|
||
| // Contributed and/or modified by Vissarion Fysikopoulos, 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_MERIDIAN_DIRECT_HPP | ||
| #define BOOST_GEOMETRY_FORMULAS_MERIDIAN_DIRECT_HPP | ||
|
|
||
| #include <boost/math/constants/constants.hpp> | ||
|
|
||
| #include <boost/geometry/core/radius.hpp> | ||
|
|
||
| #include <boost/geometry/util/condition.hpp> | ||
| #include <boost/geometry/util/math.hpp> | ||
|
|
||
| #include <boost/geometry/formulas/meridian_inverse.hpp> | ||
| #include <boost/geometry/formulas/flattening.hpp> | ||
| #include <boost/geometry/formulas/quarter_meridian.hpp> | ||
| #include <boost/geometry/formulas/result_direct.hpp> | ||
|
|
||
| namespace boost { namespace geometry { namespace formula | ||
| { | ||
|
|
||
| /*! | ||
| \brief Compute the direct geodesic problem on a meridian | ||
| */ | ||
|
|
||
| template < | ||
| typename CT, | ||
| bool EnableCoordinates = true, | ||
| bool EnableReverseAzimuth = false, | ||
| bool EnableReducedLength = false, | ||
| bool EnableGeodesicScale = false, | ||
| unsigned int Order = 4 | ||
| > | ||
| class meridian_direct | ||
| { | ||
| static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale; | ||
| static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities; | ||
| static const bool CalcCoordinates = EnableCoordinates || CalcRevAzimuth; | ||
|
|
||
| public: | ||
| typedef result_direct<CT> result_type; | ||
|
|
||
| template <typename T, typename Dist, typename Spheroid> | ||
| static inline result_type apply(T const& lo1, | ||
| T const& la1, | ||
| Dist const& distance, | ||
| bool north, | ||
| Spheroid const& spheroid) | ||
| { | ||
| result_type result; | ||
|
|
||
| CT const half_pi = math::half_pi<CT>(); | ||
| CT const pi = math::pi<CT>(); | ||
| CT const one_and_a_half_pi = pi + half_pi; | ||
| CT const c0 = 0; | ||
|
|
||
| CT azimuth = north ? c0 : pi; | ||
|
|
||
| if (BOOST_GEOMETRY_CONDITION(CalcCoordinates)) | ||
| { | ||
| CT s0 = meridian_inverse<CT, Order>::apply(la1, spheroid); | ||
| int signed_distance = north ? distance : -distance; | ||
| result.lon2 = lo1; | ||
| result.lat2 = apply(s0 + signed_distance, spheroid); | ||
| } | ||
|
|
||
| if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth)) | ||
| { | ||
| result.reverse_azimuth = azimuth; | ||
|
|
||
|
|
||
| if (result.lat2 > half_pi && | ||
| result.lat2 < one_and_a_half_pi) | ||
| { | ||
| result.reverse_azimuth = pi; | ||
| } | ||
| else if (result.lat2 < -half_pi && | ||
| result.lat2 > -one_and_a_half_pi) | ||
| { | ||
| result.reverse_azimuth = c0; | ||
| } | ||
|
|
||
| } | ||
|
|
||
| if (BOOST_GEOMETRY_CONDITION(CalcQuantities)) | ||
| { | ||
| CT const b = CT(get_radius<2>(spheroid)); | ||
| CT const f = formula::flattening<CT>(spheroid); | ||
|
|
||
| boost::geometry::math::normalize_spheroidal_coordinates | ||
| < | ||
| boost::geometry::radian, | ||
| double | ||
| >(result.lon2, result.lat2); | ||
|
|
||
| typedef differential_quantities | ||
| < | ||
| CT, | ||
| EnableReducedLength, | ||
| EnableGeodesicScale, | ||
| Order | ||
| > quantities; | ||
| quantities::apply(lo1, la1, result.lon2, result.lat2, | ||
| azimuth, result.reverse_azimuth, | ||
| b, f, | ||
| result.reduced_length, result.geodesic_scale); | ||
| } | ||
| return result; | ||
| } | ||
|
|
||
| // https://en.wikipedia.org/wiki/Meridian_arc#The_inverse_meridian_problem_for_the_ellipsoid | ||
| // latitudes are assumed to be in radians and in [-pi/2,pi/2] | ||
| template <typename T, typename Spheroid> | ||
| static CT apply(T m, Spheroid const& spheroid) | ||
| { | ||
| CT const f = formula::flattening<CT>(spheroid); | ||
| CT n = f / (CT(2) - f); | ||
| CT mp = formula::quarter_meridian<CT>(spheroid); | ||
| CT mu = geometry::math::pi<CT>()/CT(2) * m / mp; | ||
|
|
||
| if (Order == 0) | ||
| { | ||
| return mu; | ||
| } | ||
|
|
||
| CT H2 = 1.5 * n; | ||
|
|
||
| if (Order == 1) | ||
| { | ||
| return mu + H2 * sin(2*mu); | ||
| } | ||
|
|
||
| CT n2 = n * n; | ||
| CT H4 = 1.3125 * n2; | ||
|
|
||
| if (Order == 2) | ||
| { | ||
| return mu + H2 * sin(2*mu) + H4 * sin(4*mu); | ||
| } | ||
|
|
||
| CT n3 = n2 * n; | ||
| H2 -= 0.84375 * n3; | ||
| CT H6 = 1.572916667 * n3; | ||
|
|
||
| if (Order == 3) | ||
| { | ||
| return mu + H2 * sin(2*mu) + H4 * sin(4*mu) + H6 * sin(6*mu); | ||
| } | ||
|
|
||
| CT n4 = n2 * n2; | ||
| H4 -= 1.71875 * n4; | ||
| CT H8 = 2.142578125 * n4; | ||
|
|
||
| // Order 4 or higher | ||
| return mu + H2 * sin(2*mu) + H4 * sin(4*mu) + H6 * sin(6*mu) + H8 * sin(8*mu); | ||
| } | ||
| }; | ||
|
|
||
| }}} // namespace boost::geometry::formula | ||
|
|
||
| #endif // BOOST_GEOMETRY_FORMULAS_MERIDIAN_DIRECT_HPP |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Oops, something went wrong.