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-rw-r--r--boost/geometry/srs/projections/proj/tmerc.hpp751
1 files changed, 557 insertions, 194 deletions
diff --git a/boost/geometry/srs/projections/proj/tmerc.hpp b/boost/geometry/srs/projections/proj/tmerc.hpp
index 7c8ca6464c..6d645ec12c 100644
--- a/boost/geometry/srs/projections/proj/tmerc.hpp
+++ b/boost/geometry/srs/projections/proj/tmerc.hpp
@@ -1,9 +1,11 @@
// Boost.Geometry - gis-projections (based on PROJ4)
// Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
+// Copyright (c) 2023 Adam Wulkiewicz, Lodz, Poland.
-// This file was modified by Oracle on 2017, 2018, 2019.
-// Modifications copyright (c) 2017-2019, Oracle and/or its affiliates.
+// This file was modified by Oracle on 2017, 2018, 2019, 2022.
+// Modifications copyright (c) 2017-2022, Oracle and/or its affiliates.
+// Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle.
// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
// Use, modification and distribution is subject to the Boost Software License,
@@ -15,7 +17,7 @@
// PROJ4 is maintained by Frank Warmerdam
// PROJ4 is converted to Boost.Geometry by Barend Gehrels
-// Last updated version of proj: 5.0.0
+// Last updated version of proj: 8.2.1
// Original copyright notice:
@@ -40,8 +42,6 @@
#ifndef BOOST_GEOMETRY_PROJECTIONS_TMERC_HPP
#define BOOST_GEOMETRY_PROJECTIONS_TMERC_HPP
-#include <boost/geometry/util/math.hpp>
-
#include <boost/geometry/srs/projections/impl/base_static.hpp>
#include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
#include <boost/geometry/srs/projections/impl/projects.hpp>
@@ -49,6 +49,9 @@
#include <boost/geometry/srs/projections/impl/function_overloads.hpp>
#include <boost/geometry/srs/projections/impl/pj_mlfn.hpp>
+#include <boost/geometry/util/condition.hpp>
+#include <boost/geometry/util/math.hpp>
+
namespace boost { namespace geometry
{
@@ -59,226 +62,574 @@ namespace projections
namespace detail { namespace tmerc
{
- static const double epsilon10 = 1.e-10;
-
- template <typename T>
- inline T FC1() { return 1.; }
- template <typename T>
- inline T FC2() { return .5; }
- template <typename T>
- inline T FC3() { return .16666666666666666666666666666666666666; }
- template <typename T>
- inline T FC4() { return .08333333333333333333333333333333333333; }
- template <typename T>
- inline T FC5() { return .05; }
- template <typename T>
- inline T FC6() { return .03333333333333333333333333333333333333; }
- template <typename T>
- inline T FC7() { return .02380952380952380952380952380952380952; }
- template <typename T>
- inline T FC8() { return .01785714285714285714285714285714285714; }
-
- template <typename T>
- struct par_tmerc
- {
- T esp;
- T ml0;
- detail::en<T> en;
- };
+ static const double epsilon10 = 1.e-10;
+
+ /* Constant for "exact" transverse mercator */
+ static const int proj_etmerc_order = 6;
+
+ template <typename T>
+ inline T FC1() { return 1.; }
+ template <typename T>
+ inline T FC2() { return .5; }
+ template <typename T>
+ inline T FC3() { return .16666666666666666666666666666666666666; }
+ template <typename T>
+ inline T FC4() { return .08333333333333333333333333333333333333; }
+ template <typename T>
+ inline T FC5() { return .05; }
+ template <typename T>
+ inline T FC6() { return .03333333333333333333333333333333333333; }
+ template <typename T>
+ inline T FC7() { return .02380952380952380952380952380952380952; }
+ template <typename T>
+ inline T FC8() { return .01785714285714285714285714285714285714; }
+
+ template <typename T>
+ struct par_tmerc
+ {
+ T esp;
+ T ml0;
+ detail::en<T> en;
+ };
+
+ // More exact: Poder/Engsager
+ template <typename T>
+ struct par_tmerc_exact
+ {
+ T Qn; /* Merid. quad., scaled to the projection */
+ T Zb; /* Radius vector in polar coord. systems */
+ T cgb[6]; /* Constants for Gauss -> Geo lat */
+ T cbg[6]; /* Constants for Geo lat -> Gauss */
+ T utg[6]; /* Constants for transv. merc. -> geo */
+ T gtu[6]; /* Constants for geo -> transv. merc. */
+ };
+
+ template <typename T, typename Parameters>
+ struct base_tmerc_ellipsoid
+ {
+ par_tmerc<T> m_proj_parm;
- template <typename T, typename Parameters>
- struct base_tmerc_ellipsoid
+ // FORWARD(e_forward) ellipse
+ // Project coordinates from geographic (lon, lat) to cartesian (x, y)
+ inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
- par_tmerc<T> m_proj_parm;
-
- // FORWARD(e_forward) ellipse
- // Project coordinates from geographic (lon, lat) to cartesian (x, y)
- inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
+ static const T half_pi = detail::half_pi<T>();
+ static const T FC1 = tmerc::FC1<T>();
+ static const T FC2 = tmerc::FC2<T>();
+ static const T FC3 = tmerc::FC3<T>();
+ static const T FC4 = tmerc::FC4<T>();
+ static const T FC5 = tmerc::FC5<T>();
+ static const T FC6 = tmerc::FC6<T>();
+ static const T FC7 = tmerc::FC7<T>();
+ static const T FC8 = tmerc::FC8<T>();
+
+ T al, als, n, cosphi, sinphi, t;
+
+ /*
+ * Fail if our longitude is more than 90 degrees from the
+ * central meridian since the results are essentially garbage.
+ * Is error -20 really an appropriate return value?
+ *
+ * http://trac.osgeo.org/proj/ticket/5
+ */
+ if( lp_lon < -half_pi || lp_lon > half_pi )
{
- static const T half_pi = detail::half_pi<T>();
- static const T FC1 = tmerc::FC1<T>();
- static const T FC2 = tmerc::FC2<T>();
- static const T FC3 = tmerc::FC3<T>();
- static const T FC4 = tmerc::FC4<T>();
- static const T FC5 = tmerc::FC5<T>();
- static const T FC6 = tmerc::FC6<T>();
- static const T FC7 = tmerc::FC7<T>();
- static const T FC8 = tmerc::FC8<T>();
-
- T al, als, n, cosphi, sinphi, t;
-
- /*
- * Fail if our longitude is more than 90 degrees from the
- * central meridian since the results are essentially garbage.
- * Is error -20 really an appropriate return value?
- *
- * http://trac.osgeo.org/proj/ticket/5
- */
- if( lp_lon < -half_pi || lp_lon > half_pi )
- {
- xy_x = HUGE_VAL;
- xy_y = HUGE_VAL;
- BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
- return;
- }
+ xy_x = HUGE_VAL;
+ xy_y = HUGE_VAL;
+ BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
+ return;
+ }
+ sinphi = sin(lp_lat);
+ cosphi = cos(lp_lat);
+ t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
+ t *= t;
+ al = cosphi * lp_lon;
+ als = al * al;
+ al /= sqrt(1. - par.es * sinphi * sinphi);
+ n = this->m_proj_parm.esp * cosphi * cosphi;
+ xy_x = par.k0 * al * (FC1 +
+ FC3 * als * (1. - t + n +
+ FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t)
+ + FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
+ )));
+ xy_y = par.k0 * (pj_mlfn(lp_lat, sinphi, cosphi, this->m_proj_parm.en) - this->m_proj_parm.ml0 +
+ sinphi * al * lp_lon * FC2 * ( 1. +
+ FC4 * als * (5. - t + n * (9. + 4. * n) +
+ FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t)
+ + FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
+ ))));
+ }
+
+ // INVERSE(e_inverse) ellipsoid
+ // Project coordinates from cartesian (x, y) to geographic (lon, lat)
+ inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
+ {
+ static const T half_pi = detail::half_pi<T>();
+ static const T FC1 = tmerc::FC1<T>();
+ static const T FC2 = tmerc::FC2<T>();
+ static const T FC3 = tmerc::FC3<T>();
+ static const T FC4 = tmerc::FC4<T>();
+ static const T FC5 = tmerc::FC5<T>();
+ static const T FC6 = tmerc::FC6<T>();
+ static const T FC7 = tmerc::FC7<T>();
+ static const T FC8 = tmerc::FC8<T>();
+
+ T n, con, cosphi, d, ds, sinphi, t;
+
+ lp_lat = pj_inv_mlfn(this->m_proj_parm.ml0 + xy_y / par.k0, par.es, this->m_proj_parm.en);
+ if (fabs(lp_lat) >= half_pi) {
+ lp_lat = xy_y < 0. ? -half_pi : half_pi;
+ lp_lon = 0.;
+ } else {
sinphi = sin(lp_lat);
cosphi = cos(lp_lat);
t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
- t *= t;
- al = cosphi * lp_lon;
- als = al * al;
- al /= sqrt(1. - par.es * sinphi * sinphi);
n = this->m_proj_parm.esp * cosphi * cosphi;
- xy_x = par.k0 * al * (FC1 +
- FC3 * als * (1. - t + n +
- FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t)
- + FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
+ d = xy_x * sqrt(con = 1. - par.es * sinphi * sinphi) / par.k0;
+ con *= t;
+ t *= t;
+ ds = d * d;
+ lp_lat -= (con * ds / (1.-par.es)) * FC2 * (1. -
+ ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -
+ ds * FC6 * (61. + t * (90. - 252. * n +
+ 45. * t) + 46. * n
+ - ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
)));
- xy_y = par.k0 * (pj_mlfn(lp_lat, sinphi, cosphi, this->m_proj_parm.en) - this->m_proj_parm.ml0 +
- sinphi * al * lp_lon * FC2 * ( 1. +
- FC4 * als * (5. - t + n * (9. + 4. * n) +
- FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t)
- + FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
- ))));
+ lp_lon = d*(FC1 -
+ ds*FC3*( 1. + 2.*t + n -
+ ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n
+ - ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
+ ))) / cosphi;
}
+ }
- // INVERSE(e_inverse) ellipsoid
- // Project coordinates from cartesian (x, y) to geographic (lon, lat)
- inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
- {
- static const T half_pi = detail::half_pi<T>();
- static const T FC1 = tmerc::FC1<T>();
- static const T FC2 = tmerc::FC2<T>();
- static const T FC3 = tmerc::FC3<T>();
- static const T FC4 = tmerc::FC4<T>();
- static const T FC5 = tmerc::FC5<T>();
- static const T FC6 = tmerc::FC6<T>();
- static const T FC7 = tmerc::FC7<T>();
- static const T FC8 = tmerc::FC8<T>();
-
- T n, con, cosphi, d, ds, sinphi, t;
-
- lp_lat = pj_inv_mlfn(this->m_proj_parm.ml0 + xy_y / par.k0, par.es, this->m_proj_parm.en);
- if (fabs(lp_lat) >= half_pi) {
- lp_lat = xy_y < 0. ? -half_pi : half_pi;
- lp_lon = 0.;
- } else {
- sinphi = sin(lp_lat);
- cosphi = cos(lp_lat);
- t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
- n = this->m_proj_parm.esp * cosphi * cosphi;
- d = xy_x * sqrt(con = 1. - par.es * sinphi * sinphi) / par.k0;
- con *= t;
- t *= t;
- ds = d * d;
- lp_lat -= (con * ds / (1.-par.es)) * FC2 * (1. -
- ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -
- ds * FC6 * (61. + t * (90. - 252. * n +
- 45. * t) + 46. * n
- - ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
- )));
- lp_lon = d*(FC1 -
- ds*FC3*( 1. + 2.*t + n -
- ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n
- - ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
- ))) / cosphi;
- }
- }
+ static inline std::string get_name()
+ {
+ return "tmerc_ellipsoid";
+ }
- static inline std::string get_name()
- {
- return "tmerc_ellipsoid";
- }
+ };
- };
+ template <typename T, typename Parameters>
+ struct base_tmerc_ellipsoid_exact
+ {
+ par_tmerc_exact<T> m_proj_parm;
- template <typename T, typename Parameters>
- struct base_tmerc_spheroid
+ static inline std::string get_name()
{
- par_tmerc<T> m_proj_parm;
+ return "tmerc_ellipsoid";
+ }
- // FORWARD(s_forward) sphere
- // Project coordinates from geographic (lon, lat) to cartesian (x, y)
- inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
- {
- static const T half_pi = detail::half_pi<T>();
-
- T b, cosphi;
-
- /*
- * Fail if our longitude is more than 90 degrees from the
- * central meridian since the results are essentially garbage.
- * Is error -20 really an appropriate return value?
- *
- * http://trac.osgeo.org/proj/ticket/5
- */
- if( lp_lon < -half_pi || lp_lon > half_pi )
- {
- xy_x = HUGE_VAL;
- xy_y = HUGE_VAL;
- BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
- return;
- }
+ /* Helper functions for "exact" transverse mercator */
+ inline
+ static T gatg(const T *p1, int len_p1, T B, T cos_2B, T sin_2B)
+ {
+ T h = 0, h1, h2 = 0;
+
+ const T two_cos_2B = 2*cos_2B;
+ const T* p = p1 + len_p1;
+ h1 = *--p;
+ while (p - p1) {
+ h = -h2 + two_cos_2B*h1 + *--p;
+ h2 = h1;
+ h1 = h;
+ }
+ return (B + h*sin_2B);
+ }
- cosphi = cos(lp_lat);
- b = cosphi * sin(lp_lon);
- if (fabs(fabs(b) - 1.) <= epsilon10)
- BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
+ /* Complex Clenshaw summation */
+ inline
+ static T clenS(const T *a, int size,
+ T sin_arg_r, T cos_arg_r,
+ T sinh_arg_i, T cosh_arg_i,
+ T *R, T *I)
+ {
+ T r, i, hr, hr1, hr2, hi, hi1, hi2;
+
+ /* arguments */
+ const T* p = a + size;
+ r = 2*cos_arg_r*cosh_arg_i;
+ i = -2*sin_arg_r*sinh_arg_i;
+
+ /* summation loop */
+ hi1 = hr1 = hi = 0;
+ hr = *--p;
+ for (; a - p;) {
+ hr2 = hr1;
+ hi2 = hi1;
+ hr1 = hr;
+ hi1 = hi;
+ hr = -hr2 + r*hr1 - i*hi1 + *--p;
+ hi = -hi2 + i*hr1 + r*hi1;
+ }
- xy_x = this->m_proj_parm.ml0 * log((1. + b) / (1. - b));
- xy_y = cosphi * cos(lp_lon) / sqrt(1. - b * b);
+ r = sin_arg_r*cosh_arg_i;
+ i = cos_arg_r*sinh_arg_i;
+ *R = r*hr - i*hi;
+ *I = r*hi + i*hr;
+ return *R;
+ }
- b = fabs( xy_y );
- if (b >= 1.) {
- if ((b - 1.) > epsilon10)
- BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
- else xy_y = 0.;
- } else
- xy_y = acos(xy_y);
+ /* Real Clenshaw summation */
+ static T clens(const T *a, int size, T arg_r)
+ {
+ T r, hr, hr1, hr2, cos_arg_r;
+
+ const T* p = a + size;
+ cos_arg_r = cos(arg_r);
+ r = 2*cos_arg_r;
+
+ /* summation loop */
+ hr1 = 0;
+ hr = *--p;
+ for (; a - p;) {
+ hr2 = hr1;
+ hr1 = hr;
+ hr = -hr2 + r*hr1 + *--p;
+ }
+ return sin(arg_r)*hr;
+ }
- if (lp_lat < 0.)
- xy_y = -xy_y;
- xy_y = this->m_proj_parm.esp * (xy_y - par.phi0);
+ /* Ellipsoidal, forward */
+ //static PJ_XY exact_e_fwd (PJ_LP lp, PJ *P)
+ inline void fwd(Parameters const& /*par*/,
+ T const& lp_lon,
+ T const& lp_lat,
+ T& xy_x, T& xy_y) const
+ {
+ //PJ_XY xy = {0.0,0.0};
+ //const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact);
+
+ /* ell. LAT, LNG -> Gaussian LAT, LNG */
+ T Cn = gatg (this->m_proj_parm.cbg, proj_etmerc_order, lp_lat,
+ cos(2*lp_lat), sin(2*lp_lat));
+ /* Gaussian LAT, LNG -> compl. sph. LAT */
+ const T sin_Cn = sin (Cn);
+ const T cos_Cn = cos (Cn);
+ const T sin_Ce = sin (lp_lon);
+ const T cos_Ce = cos (lp_lon);
+
+ const T cos_Cn_cos_Ce = cos_Cn*cos_Ce;
+ Cn = atan2 (sin_Cn, cos_Cn_cos_Ce);
+
+ const T inv_denom_tan_Ce = 1. / hypot (sin_Cn, cos_Cn_cos_Ce);
+ const T tan_Ce = sin_Ce*cos_Cn * inv_denom_tan_Ce;
+ #if 0
+ // Variant of the above: found not to be measurably faster
+ const T sin_Ce_cos_Cn = sin_Ce*cos_Cn;
+ const T denom = sqrt(1 - sin_Ce_cos_Cn * sin_Ce_cos_Cn);
+ const T tan_Ce = sin_Ce_cos_Cn / denom;
+ #endif
+
+ /* compl. sph. N, E -> ell. norm. N, E */
+ T Ce = asinh ( tan_Ce ); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
+
+ /*
+ * Non-optimized version:
+ * const T sin_arg_r = sin(2*Cn);
+ * const T cos_arg_r = cos(2*Cn);
+ *
+ * Given:
+ * sin(2 * Cn) = 2 sin(Cn) cos(Cn)
+ * sin(atan(y)) = y / sqrt(1 + y^2)
+ * cos(atan(y)) = 1 / sqrt(1 + y^2)
+ * ==> sin(2 * Cn) = 2 tan_Cn / (1 + tan_Cn^2)
+ *
+ * cos(2 * Cn) = 2cos^2(Cn) - 1
+ * = 2 / (1 + tan_Cn^2) - 1
+ */
+ const T two_inv_denom_tan_Ce = 2 * inv_denom_tan_Ce;
+ const T two_inv_denom_tan_Ce_square = two_inv_denom_tan_Ce * inv_denom_tan_Ce;
+ const T tmp_r = cos_Cn_cos_Ce * two_inv_denom_tan_Ce_square;
+ const T sin_arg_r = sin_Cn * tmp_r;
+ const T cos_arg_r = cos_Cn_cos_Ce * tmp_r - 1;
+
+ /*
+ * Non-optimized version:
+ * const T sinh_arg_i = sinh(2*Ce);
+ * const T cosh_arg_i = cosh(2*Ce);
+ *
+ * Given
+ * sinh(2 * Ce) = 2 sinh(Ce) cosh(Ce)
+ * sinh(asinh(y)) = y
+ * cosh(asinh(y)) = sqrt(1 + y^2)
+ * ==> sinh(2 * Ce) = 2 tan_Ce sqrt(1 + tan_Ce^2)
+ *
+ * cosh(2 * Ce) = 2cosh^2(Ce) - 1
+ * = 2 * (1 + tan_Ce^2) - 1
+ *
+ * and 1+tan_Ce^2 = 1 + sin_Ce^2 * cos_Cn^2 / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
+ * = (sin_Cn^2 + cos_Cn^2 * cos_Ce^2 + sin_Ce^2 * cos_Cn^2) / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
+ * = 1. / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
+ * = inv_denom_tan_Ce^2
+ *
+ */
+ const T sinh_arg_i = tan_Ce * two_inv_denom_tan_Ce;
+ const T cosh_arg_i = two_inv_denom_tan_Ce_square - 1;
+
+ T dCn, dCe;
+ Cn += clenS (this->m_proj_parm.gtu, proj_etmerc_order,
+ sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i,
+ &dCn, &dCe);
+ Ce += dCe;
+ if (fabs (Ce) <= 2.623395162778) {
+ xy_y = this->m_proj_parm.Qn * Cn + this->m_proj_parm.Zb; /* Northing */
+ xy_x = this->m_proj_parm.Qn * Ce; /* Easting */
+ } else {
+ BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
+ xy_x = xy_y = HUGE_VAL;
}
+ }
- // INVERSE(s_inverse) sphere
- // Project coordinates from cartesian (x, y) to geographic (lon, lat)
- inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
- {
- T h, g;
- h = exp(xy_x / this->m_proj_parm.esp);
- g = .5 * (h - 1. / h);
- h = cos(par.phi0 + xy_y / this->m_proj_parm.esp);
- lp_lat = asin(sqrt((1. - h * h) / (1. + g * g)));
+ /* Ellipsoidal, inverse */
+ inline void inv(Parameters const& /*par*/,
+ T const& xy_x,
+ T const& xy_y,
+ T& lp_lon,
+ T& lp_lat) const
+ {
+ //PJ_LP lp = {0.0,0.0};
+ //const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact);
+
+ /* normalize N, E */
+ T Cn = (xy_y - this->m_proj_parm.Zb)/this->m_proj_parm.Qn;
+ T Ce = xy_x/this->m_proj_parm.Qn;
+
+ if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */
+ /* norm. N, E -> compl. sph. LAT, LNG */
+ const T sin_arg_r = sin(2*Cn);
+ const T cos_arg_r = cos(2*Cn);
+
+ //const T sinh_arg_i = sinh(2*Ce);
+ //const T cosh_arg_i = cosh(2*Ce);
+ const T exp_2_Ce = exp(2*Ce);
+ const T half_inv_exp_2_Ce = 0.5 / exp_2_Ce;
+ const T sinh_arg_i = 0.5 * exp_2_Ce - half_inv_exp_2_Ce;
+ const T cosh_arg_i = 0.5 * exp_2_Ce + half_inv_exp_2_Ce;
+
+ T dCn_ignored, dCe;
+ Cn += clenS(this->m_proj_parm.utg, proj_etmerc_order,
+ sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i,
+ &dCn_ignored, &dCe);
+ Ce += dCe;
+
+ /* compl. sph. LAT -> Gaussian LAT, LNG */
+ const T sin_Cn = sin (Cn);
+ const T cos_Cn = cos (Cn);
+
+ #if 0
+ // Non-optimized version:
+ T sin_Ce, cos_Ce;
+ Ce = atan (sinh (Ce)); // Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI);
+ sin_Ce = sin (Ce);
+ cos_Ce = cos (Ce);
+ Ce = atan2 (sin_Ce, cos_Ce*cos_Cn);
+ Cn = atan2 (sin_Cn*cos_Ce, hypot (sin_Ce, cos_Ce*cos_Cn));
+ #else
+ /*
+ * One can divide both member of Ce = atan2(...) by cos_Ce, which gives:
+ * Ce = atan2 (tan_Ce, cos_Cn) = atan2(sinh(Ce), cos_Cn)
+ *
+ * and the same for Cn = atan2(...)
+ * Cn = atan2 (sin_Cn, hypot (sin_Ce, cos_Ce*cos_Cn)/cos_Ce)
+ * = atan2 (sin_Cn, hypot (sin_Ce/cos_Ce, cos_Cn))
+ * = atan2 (sin_Cn, hypot (tan_Ce, cos_Cn))
+ * = atan2 (sin_Cn, hypot (sinhCe, cos_Cn))
+ */
+ const T sinhCe = sinh (Ce);
+ Ce = atan2 (sinhCe, cos_Cn);
+ const T modulus_Ce = hypot (sinhCe, cos_Cn);
+ Cn = atan2 (sin_Cn, modulus_Ce);
+ #endif
+
+ /* Gaussian LAT, LNG -> ell. LAT, LNG */
+
+ // Optimization of the computation of cos(2*Cn) and sin(2*Cn)
+ const T tmp = 2 * modulus_Ce / (sinhCe * sinhCe + 1);
+ const T sin_2_Cn = sin_Cn * tmp;
+ const T cos_2_Cn = tmp * modulus_Ce - 1.;
+ //const T cos_2_Cn = cos(2 * Cn);
+ //const T sin_2_Cn = sin(2 * Cn);
+
+ lp_lat = gatg (this->m_proj_parm.cgb, proj_etmerc_order, Cn, cos_2_Cn, sin_2_Cn);
+ lp_lon = Ce;
+ }
+ else {
+ BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
+ lp_lat = lp_lon = HUGE_VAL;
+ }
+ }
- /* Make sure that phi is on the correct hemisphere when false northing is used */
- if (xy_y < 0. && -lp_lat+par.phi0 < 0.0) lp_lat = -lp_lat;
+ };
- lp_lon = (g != 0.0 || h != 0.0) ? atan2(g, h) : 0.;
- }
+ template <typename T, typename Parameters>
+ struct base_tmerc_spheroid
+ {
+ par_tmerc<T> m_proj_parm;
- static inline std::string get_name()
+ // FORWARD(s_forward) sphere
+ // Project coordinates from geographic (lon, lat) to cartesian (x, y)
+ inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
+ {
+ static const T half_pi = detail::half_pi<T>();
+
+ T b, cosphi;
+
+ /*
+ * Fail if our longitude is more than 90 degrees from the
+ * central meridian since the results are essentially garbage.
+ * Is error -20 really an appropriate return value?
+ *
+ * http://trac.osgeo.org/proj/ticket/5
+ */
+ if( lp_lon < -half_pi || lp_lon > half_pi )
{
- return "tmerc_spheroid";
+ xy_x = HUGE_VAL;
+ xy_y = HUGE_VAL;
+ BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
+ return;
}
- };
+ cosphi = cos(lp_lat);
+ b = cosphi * sin(lp_lon);
+ if (fabs(fabs(b) - 1.) <= epsilon10)
+ BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
+
+ xy_x = this->m_proj_parm.ml0 * log((1. + b) / (1. - b));
+ xy_y = cosphi * cos(lp_lon) / sqrt(1. - b * b);
+
+ b = fabs( xy_y );
+ if (b >= 1.) {
+ if ((b - 1.) > epsilon10)
+ BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
+ else xy_y = 0.;
+ } else
+ xy_y = acos(xy_y);
+
+ if (lp_lat < 0.)
+ xy_y = -xy_y;
+ xy_y = this->m_proj_parm.esp * (xy_y - par.phi0);
+ }
- template <typename Parameters, typename T>
- inline void setup(Parameters const& par, par_tmerc<T>& proj_parm)
+ // INVERSE(s_inverse) sphere
+ // Project coordinates from cartesian (x, y) to geographic (lon, lat)
+ inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
- if (par.es != 0.0) {
- proj_parm.en = pj_enfn<T>(par.es);
- proj_parm.ml0 = pj_mlfn(par.phi0, sin(par.phi0), cos(par.phi0), proj_parm.en);
- proj_parm.esp = par.es / (1. - par.es);
- } else {
- proj_parm.esp = par.k0;
- proj_parm.ml0 = .5 * proj_parm.esp;
- }
+ T h, g;
+
+ h = exp(xy_x / this->m_proj_parm.esp);
+ g = .5 * (h - 1. / h);
+ h = cos(par.phi0 + xy_y / this->m_proj_parm.esp);
+ lp_lat = asin(sqrt((1. - h * h) / (1. + g * g)));
+
+ /* Make sure that phi is on the correct hemisphere when false northing is used */
+ if (xy_y < 0. && -lp_lat+par.phi0 < 0.0) lp_lat = -lp_lat;
+
+ lp_lon = (g != 0.0 || h != 0.0) ? atan2(g, h) : 0.;
}
+ static inline std::string get_name()
+ {
+ return "tmerc_spheroid";
+ }
+
+ };
+
+ template <typename Parameters, typename T>
+ inline void setup(Parameters const& par, par_tmerc<T>& proj_parm)
+ {
+ if (par.es != 0.0) {
+ proj_parm.en = pj_enfn<T>(par.es);
+ proj_parm.ml0 = pj_mlfn(par.phi0, sin(par.phi0), cos(par.phi0), proj_parm.en);
+ proj_parm.esp = par.es / (1. - par.es);
+ } else {
+ proj_parm.esp = par.k0;
+ proj_parm.ml0 = .5 * proj_parm.esp;
+ }
+ }
+
+ template <typename Parameters, typename T>
+ inline void setup_exact(Parameters const& par, par_tmerc_exact<T>& proj_parm)
+ {
+ assert( par.es > 0 );
+
+ /* third flattening n */
+ //since we do not keep n in parameters we compute it here;
+ const T n = pow(tan(asin(par.e)/2),2);
+ T np = n;
+
+ /* COEF. OF TRIG SERIES GEO <-> GAUSS */
+ /* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
+ /* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
+ /* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */
+
+ proj_parm.cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 +
+ n*(-2854/675.0 ))))));
+ proj_parm.cbg[0] = n*(-2 + n*( 2/3.0 + n*( 4/3.0 + n*(-82/45.0 + n*(32/45.0 +
+ n*( 4642/4725.0))))));
+ np *= n;
+ proj_parm.cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 +
+ n*( 2323/945.0)))));
+ proj_parm.cbg[1] = np*(5/3.0 + n*(-16/15.0 + n*( -13/9.0 + n*( 904/315.0 +
+ n*(-1522/945.0)))));
+ np *= n;
+ /* n^5 coeff corrected from 1262/105 -> -1262/105 */
+ proj_parm.cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 +
+ n*( 73814/2835.0))));
+ proj_parm.cbg[2] = np*(-26/15.0 + n*( 34/21.0 + n*( 8/5.0 +
+ n*(-12686/2835.0))));
+ np *= n;
+ /* n^5 coeff corrected from 322/35 -> 332/35 */
+ proj_parm.cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0)));
+ proj_parm.cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0)));
+ np *= n;
+ proj_parm.cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 ));
+ proj_parm.cbg[4] = np*(-734/315.0 + n*( 109598/31185.0));
+ np *= n;
+ proj_parm.cgb[5] = np*(601676/22275.0 );
+ proj_parm.cbg[5] = np*(444337/155925.0);
+
+ /* Constants of the projections */
+ /* Transverse Mercator (UTM, ITM, etc) */
+ np = n*n;
+ /* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
+ proj_parm.Qn = par.k0/(1 + n) * (1 + np*(1/4.0 + np*(1/64.0 + np/256.0)));
+ /* coef of trig series */
+ /* utg := ell. N, E -> sph. N, E, KW p194 (65) */
+ /* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
+ proj_parm.utg[0] = n*(-0.5 + n*( 2/3.0 + n*(-37/96.0 + n*( 1/360.0 +
+ n*( 81/512.0 + n*(-96199/604800.0))))));
+ proj_parm.gtu[0] = n*( 0.5 + n*(-2/3.0 + n*( 5/16.0 + n*(41/180.0 +
+ n*(-127/288.0 + n*( 7891/37800.0 ))))));
+ proj_parm.utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 +
+ n*( 1118711/3870720.0)))));
+ proj_parm.gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 +
+ n*(-1983433/1935360.0)))));
+ np *= n;
+ proj_parm.utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 +
+ n*( -5569/90720.0 ))));
+ proj_parm.gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 +
+ n*(167603/181440.0))));
+ np *= n;
+ proj_parm.utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0)));
+ proj_parm.gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0)));
+ np *= n;
+ proj_parm.utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0));
+ proj_parm.gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0));
+ np *= n;
+ proj_parm.utg[5] = np*(-20648693/638668800.0);
+ proj_parm.gtu[5] = np*(212378941/319334400.0);
+
+ /* Gaussian latitude value of the origin latitude */
+ const T Z = base_tmerc_ellipsoid_exact<T, Parameters>::gatg (proj_parm.cbg, proj_etmerc_order, par.phi0, cos(2*par.phi0), sin(2*par.phi0));
+
+ /* Origin northing minus true northing at the origin latitude */
+ /* i.e. true northing = N - par.Zb */
+ proj_parm.Zb = - proj_parm.Qn*(Z + base_tmerc_ellipsoid_exact<T, Parameters>::clens(proj_parm.gtu, proj_etmerc_order, 2*Z));
+ }
+
}} // namespace detail::tmerc
#endif // doxygen
@@ -295,6 +646,8 @@ namespace projections
\par Example
\image html ex_tmerc.gif
*/
+ //approximate tmerc algorithm
+ /*
template <typename T, typename Parameters>
struct tmerc_ellipsoid : public detail::tmerc::base_tmerc_ellipsoid<T, Parameters>
{
@@ -304,6 +657,16 @@ namespace projections
detail::tmerc::setup(par, this->m_proj_parm);
}
};
+ */
+ template <typename T, typename Parameters>
+ struct tmerc_ellipsoid : public detail::tmerc::base_tmerc_ellipsoid_exact<T, Parameters>
+ {
+ template <typename Params>
+ inline tmerc_ellipsoid(Params const&, Parameters const& par)
+ {
+ detail::tmerc::setup_exact(par, this->m_proj_parm);
+ }
+ };
/*!
\brief Transverse Mercator projection
@@ -334,10 +697,10 @@ namespace projections
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_tmerc, tmerc_spheroid, tmerc_ellipsoid)
-
+
// Factory entry(s) - dynamic projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(tmerc_entry, tmerc_spheroid, tmerc_ellipsoid)
-
+
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(tmerc_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(tmerc, tmerc_entry)
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-06 14:02:49 +0000