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// Boost.Geometry - gis-projections (based on PROJ4)
// Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
// This file was modified by Oracle on 2017, 2018, 2019.
// Modifications copyright (c) 2017-2019, 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)
// This file is converted from PROJ4, http://trac.osgeo.org/proj
// PROJ4 is originally written by Gerald Evenden (then of the USGS)
// PROJ4 is maintained by Frank Warmerdam
// PROJ4 is converted to Boost.Geometry by Barend Gehrels
// Last updated version of proj: 5.0.0
// Original copyright notice:
// This code was entirely written by Nathan Wagner
// and is in the public domain.
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
#ifndef BOOST_GEOMETRY_PROJECTIONS_ISEA_HPP
#define BOOST_GEOMETRY_PROJECTIONS_ISEA_HPP
#include <sstream>
#include <boost/core/ignore_unused.hpp>
#include <boost/geometry/core/assert.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/factory_entry.hpp>
#include <boost/geometry/srs/projections/impl/pj_param.hpp>
#include <boost/geometry/srs/projections/impl/projects.hpp>
#include <boost/geometry/util/math.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace isea
{
static const double epsilon = std::numeric_limits<double>::epsilon();
/* sqrt(5)/M_PI */
static const double isea_scale = 0.8301572857837594396028083;
/* 26.565051177 degrees */
static const double v_lat = 0.46364760899944494524;
/* 52.62263186 */
static const double e_rad = 0.91843818702186776133;
/* 10.81231696 */
static const double f_rad = 0.18871053072122403508;
/* R tan(g) sin(60) */
static const double table_g = 0.6615845383;
/* H = 0.25 R tan g = */
static const double table_h = 0.1909830056;
//static const double RPRIME = 0.91038328153090290025;
static const double isea_std_lat = 1.01722196792335072101;
static const double isea_std_lon = .19634954084936207740;
template <typename T>
inline T deg30_rad() { return T(30) * geometry::math::d2r<T>(); }
template <typename T>
inline T deg120_rad() { return T(120) * geometry::math::d2r<T>(); }
template <typename T>
inline T deg72_rad() { return T(72) * geometry::math::d2r<T>(); }
template <typename T>
inline T deg90_rad() { return geometry::math::half_pi<T>(); }
template <typename T>
inline T deg144_rad() { return T(144) * geometry::math::d2r<T>(); }
template <typename T>
inline T deg36_rad() { return T(36) * geometry::math::d2r<T>(); }
template <typename T>
inline T deg108_rad() { return T(108) * geometry::math::d2r<T>(); }
template <typename T>
inline T deg180_rad() { return geometry::math::pi<T>(); }
inline bool downtri(int tri) { return (((tri - 1) / 5) % 2 == 1); }
/*
* Proj 4 provides its own entry points into
* the code, so none of the library functions
* need to be global
*/
struct hex {
int iso;
int x, y, z;
};
/* y *must* be positive down as the xy /iso conversion assumes this */
inline
int hex_xy(struct hex *h) {
if (!h->iso) return 1;
if (h->x >= 0) {
h->y = -h->y - (h->x+1)/2;
} else {
/* need to round toward -inf, not toward zero, so x-1 */
h->y = -h->y - h->x/2;
}
h->iso = 0;
return 1;
}
inline
int hex_iso(struct hex *h) {
if (h->iso) return 1;
if (h->x >= 0) {
h->y = (-h->y - (h->x+1)/2);
} else {
/* need to round toward -inf, not toward zero, so x-1 */
h->y = (-h->y - (h->x)/2);
}
h->z = -h->x - h->y;
h->iso = 1;
return 1;
}
template <typename T>
inline
int hexbin2(T const& width, T x, T y, int *i, int *j)
{
T z, rx, ry, rz;
T abs_dx, abs_dy, abs_dz;
int ix, iy, iz, s;
struct hex h;
static const T cos_deg30 = cos(deg30_rad<T>());
x = x / cos_deg30; /* rotated X coord */
y = y - x / 2.0; /* adjustment for rotated X */
/* adjust for actual hexwidth */
x /= width;
y /= width;
z = -x - y;
rx = floor(x + 0.5);
ix = (int)rx;
ry = floor(y + 0.5);
iy = (int)ry;
rz = floor(z + 0.5);
iz = (int)rz;
s = ix + iy + iz;
if (s) {
abs_dx = fabs(rx - x);
abs_dy = fabs(ry - y);
abs_dz = fabs(rz - z);
if (abs_dx >= abs_dy && abs_dx >= abs_dz) {
ix -= s;
} else if (abs_dy >= abs_dx && abs_dy >= abs_dz) {
iy -= s;
} else {
iz -= s;
}
}
h.x = ix;
h.y = iy;
h.z = iz;
h.iso = 1;
hex_xy(&h);
*i = h.x;
*j = h.y;
return ix * 100 + iy;
}
//enum isea_poly { isea_none = 0, isea_icosahedron = 20 };
//enum isea_topology { isea_hexagon=6, isea_triangle=3, isea_diamond=4 };
enum isea_address_form {
/*isea_addr_geo,*/ isea_addr_q2di, isea_addr_seqnum,
/*isea_addr_interleave,*/ isea_addr_plane, isea_addr_q2dd,
isea_addr_projtri, isea_addr_vertex2dd, isea_addr_hex
};
template <typename T>
struct isea_dgg {
T o_lat, o_lon, o_az; /* orientation, radians */
T radius; /* radius of the earth in meters, ignored 1.0 */
unsigned long serial;
//int pole; /* true if standard snyder */
int aperture; /* valid values depend on partitioning method */
int resolution;
int triangle; /* triangle of last transformed point */
int quad; /* quad of last transformed point */
//isea_poly polyhedron; /* ignored, icosahedron */
//isea_topology topology; /* ignored, hexagon */
isea_address_form output; /* an isea_address_form */
};
template <typename T>
struct isea_pt {
T x, y;
};
template <typename T>
struct isea_geo {
T lon, lat;
};
template <typename T>
struct isea_address {
T x,y; /* or i,j or lon,lat depending on type */
int type; /* enum isea_address_form */
int number;
};
/* ENDINC */
enum snyder_polyhedron {
snyder_poly_hexagon = 0, snyder_poly_pentagon = 1,
snyder_poly_tetrahedron = 2, snyder_poly_cube = 3,
snyder_poly_octahedron = 4, snyder_poly_dodecahedron = 5,
snyder_poly_icosahedron = 6
};
template <typename T>
struct snyder_constants {
T g, G, theta, ea_w, ea_a, ea_b, g_w, g_a, g_b;
};
template <typename T>
inline const snyder_constants<T> * constants()
{
/* TODO put these in radians to avoid a later conversion */
static snyder_constants<T> result[] = {
{23.80018260, 62.15458023, 60.0, 3.75, 1.033, 0.968, 5.09, 1.195, 1.0},
{20.07675127, 55.69063953, 54.0, 2.65, 1.030, 0.983, 3.59, 1.141, 1.027},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{37.37736814, 36.0, 30.0, 17.27, 1.163, 0.860, 13.14, 1.584, 1.0}
};
return result;
}
template <typename T>
inline const isea_geo<T> * vertex()
{
static isea_geo<T> result[] = {
{ 0.0, deg90_rad<T>()},
{ deg180_rad<T>(), v_lat},
{-deg108_rad<T>(), v_lat},
{-deg36_rad<T>(), v_lat},
{ deg36_rad<T>(), v_lat},
{ deg108_rad<T>(), v_lat},
{-deg144_rad<T>(), -v_lat},
{-deg72_rad<T>(), -v_lat},
{ 0.0, -v_lat},
{ deg72_rad<T>(), -v_lat},
{ deg144_rad<T>(), -v_lat},
{ 0.0, -deg90_rad<T>()}
};
return result;
}
/* TODO make an isea_pt array of the vertices as well */
static int tri_v1[] = {0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 2, 3, 4, 5, 1, 11, 11, 11, 11, 11};
/* triangle Centers */
template <typename T>
inline const isea_geo<T> * icostriangles()
{
static isea_geo<T> result[] = {
{ 0.0, 0.0},
{-deg144_rad<T>(), e_rad},
{-deg72_rad<T>(), e_rad},
{ 0.0, e_rad},
{ deg72_rad<T>(), e_rad},
{ deg144_rad<T>(), e_rad},
{-deg144_rad<T>(), f_rad},
{-deg72_rad<T>(), f_rad},
{ 0.0, f_rad},
{ deg72_rad<T>(), f_rad},
{ deg144_rad<T>(), f_rad},
{-deg108_rad<T>(), -f_rad},
{-deg36_rad<T>(), -f_rad},
{ deg36_rad<T>(), -f_rad},
{ deg108_rad<T>(), -f_rad},
{ deg180_rad<T>(), -f_rad},
{-deg108_rad<T>(), -e_rad},
{-deg36_rad<T>(), -e_rad},
{ deg36_rad<T>(), -e_rad},
{ deg108_rad<T>(), -e_rad},
{ deg180_rad<T>(), -e_rad},
};
return result;
}
template <typename T>
inline T az_adjustment(int triangle)
{
T adj;
isea_geo<T> v;
isea_geo<T> c;
v = vertex<T>()[tri_v1[triangle]];
c = icostriangles<T>()[triangle];
/* TODO looks like the adjustment is always either 0 or 180 */
/* at least if you pick your vertex carefully */
adj = atan2(cos(v.lat) * sin(v.lon - c.lon),
cos(c.lat) * sin(v.lat)
- sin(c.lat) * cos(v.lat) * cos(v.lon - c.lon));
return adj;
}
template <typename T>
inline isea_pt<T> isea_triangle_xy(int triangle)
{
isea_pt<T> c;
T Rprime = 0.91038328153090290025;
triangle = (triangle - 1) % 20;
c.x = table_g * ((triangle % 5) - 2) * 2.0;
if (triangle > 9) {
c.x += table_g;
}
switch (triangle / 5) {
case 0:
c.y = 5.0 * table_h;
break;
case 1:
c.y = table_h;
break;
case 2:
c.y = -table_h;
break;
case 3:
c.y = -5.0 * table_h;
break;
default:
/* should be impossible */
BOOST_THROW_EXCEPTION( projection_exception() );
};
c.x *= Rprime;
c.y *= Rprime;
return c;
}
/* snyder eq 14 */
template <typename T>
inline T sph_azimuth(T const& f_lon, T const& f_lat, T const& t_lon, T const& t_lat)
{
T az;
az = atan2(cos(t_lat) * sin(t_lon - f_lon),
cos(f_lat) * sin(t_lat)
- sin(f_lat) * cos(t_lat) * cos(t_lon - f_lon)
);
return az;
}
/* coord needs to be in radians */
template <typename T>
inline int isea_snyder_forward(isea_geo<T> * ll, isea_pt<T> * out)
{
static T const two_pi = detail::two_pi<T>();
static T const d2r = geometry::math::d2r<T>();
int i;
/*
* spherical distance from center of polygon face to any of its
* vertexes on the globe
*/
T g;
/*
* spherical angle between radius vector to center and adjacent edge
* of spherical polygon on the globe
*/
T G;
/*
* plane angle between radius vector to center and adjacent edge of
* plane polygon
*/
T theta;
/* additional variables from snyder */
T q, Rprime, H, Ag, Azprime, Az, dprime, f, rho,
x, y;
/* variables used to store intermediate results */
T cot_theta, tan_g, az_offset;
/* how many multiples of 60 degrees we adjust the azimuth */
int Az_adjust_multiples;
snyder_constants<T> c;
/*
* TODO by locality of reference, start by trying the same triangle
* as last time
*/
/* TODO put these constants in as radians to begin with */
c = constants<T>()[snyder_poly_icosahedron];
theta = c.theta * d2r;
g = c.g * d2r;
G = c.G * d2r;
for (i = 1; i <= 20; i++) {
T z;
isea_geo<T> center;
center = icostriangles<T>()[i];
/* step 1 */
z = acos(sin(center.lat) * sin(ll->lat)
+ cos(center.lat) * cos(ll->lat) * cos(ll->lon - center.lon));
/* not on this triangle */
if (z > g + 0.000005) { /* TODO DBL_EPSILON */
continue;
}
Az = sph_azimuth(center.lon, center.lat, ll->lon, ll->lat);
/* step 2 */
/* This calculates "some" vertex coordinate */
az_offset = az_adjustment<T>(i);
Az -= az_offset;
/* TODO I don't know why we do this. It's not in snyder */
/* maybe because we should have picked a better vertex */
if (Az < 0.0) {
Az += two_pi;
}
/*
* adjust Az for the point to fall within the range of 0 to
* 2(90 - theta) or 60 degrees for the hexagon, by
* and therefore 120 degrees for the triangle
* of the icosahedron
* subtracting or adding multiples of 60 degrees to Az and
* recording the amount of adjustment
*/
Az_adjust_multiples = 0;
while (Az < 0.0) {
Az += deg120_rad<T>();
Az_adjust_multiples--;
}
while (Az > deg120_rad<T>() + epsilon) {
Az -= deg120_rad<T>();
Az_adjust_multiples++;
}
/* step 3 */
cot_theta = 1.0 / tan(theta);
tan_g = tan(g); /* TODO this is a constant */
/* Calculate q from eq 9. */
/* TODO cot_theta is cot(30) */
q = atan2(tan_g, cos(Az) + sin(Az) * cot_theta);
/* not in this triangle */
if (z > q + 0.000005) {
continue;
}
/* step 4 */
/* Apply equations 5-8 and 10-12 in order */
/* eq 5 */
/* Rprime = 0.9449322893 * R; */
/* R' in the paper is for the truncated */
Rprime = 0.91038328153090290025;
/* eq 6 */
H = acos(sin(Az) * sin(G) * cos(g) - cos(Az) * cos(G));
/* eq 7 */
/* Ag = (Az + G + H - deg180_rad) * M_PI * R * R / deg180_rad; */
Ag = Az + G + H - deg180_rad<T>();
/* eq 8 */
Azprime = atan2(2.0 * Ag, Rprime * Rprime * tan_g * tan_g - 2.0 * Ag * cot_theta);
/* eq 10 */
/* cot(theta) = 1.73205080756887729355 */
dprime = Rprime * tan_g / (cos(Azprime) + sin(Azprime) * cot_theta);
/* eq 11 */
f = dprime / (2.0 * Rprime * sin(q / 2.0));
/* eq 12 */
rho = 2.0 * Rprime * f * sin(z / 2.0);
/*
* add back the same 60 degree multiple adjustment from step
* 2 to Azprime
*/
Azprime += deg120_rad<T>() * Az_adjust_multiples;
/* calculate rectangular coordinates */
x = rho * sin(Azprime);
y = rho * cos(Azprime);
/*
* TODO
* translate coordinates to the origin for the particular
* hexagon on the flattened polyhedral map plot
*/
out->x = x;
out->y = y;
return i;
}
/*
* should be impossible, this implies that the coordinate is not on
* any triangle
*/
//fprintf(stderr, "impossible transform: %f %f is not on any triangle\n",
// ll->lon * geometry::math::r2d<double>(), ll->lat * geometry::math::r2d<double>());
std::stringstream ss;
ss << "impossible transform: " << ll->lon * geometry::math::r2d<T>()
<< " " << ll->lat * geometry::math::r2d<T>() << " is not on any triangle.";
BOOST_THROW_EXCEPTION( projection_exception(ss.str()) );
/* not reached */
return 0; /* supresses a warning */
}
/*
* return the new coordinates of any point in orginal coordinate system.
* Define a point (newNPold) in orginal coordinate system as the North Pole in
* new coordinate system, and the great circle connect the original and new
* North Pole as the lon0 longitude in new coordinate system, given any point
* in orginal coordinate system, this function return the new coordinates.
*/
/* formula from Snyder, Map Projections: A working manual, p31 */
/*
* old north pole at np in new coordinates
* could be simplified a bit with fewer intermediates
*
* TODO take a result pointer
*/
template <typename T>
inline isea_geo<T> snyder_ctran(isea_geo<T> * np, isea_geo<T> * pt)
{
static T const pi = detail::pi<T>();
static T const two_pi = detail::two_pi<T>();
isea_geo<T> npt;
T alpha, phi, lambda, lambda0, beta, lambdap, phip;
T sin_phip;
T lp_b; /* lambda prime minus beta */
T cos_p, sin_a;
phi = pt->lat;
lambda = pt->lon;
alpha = np->lat;
beta = np->lon;
lambda0 = beta;
cos_p = cos(phi);
sin_a = sin(alpha);
/* mpawm 5-7 */
sin_phip = sin_a * sin(phi) - cos(alpha) * cos_p * cos(lambda - lambda0);
/* mpawm 5-8b */
/* use the two argument form so we end up in the right quadrant */
lp_b = atan2(cos_p * sin(lambda - lambda0),
(sin_a * cos_p * cos(lambda - lambda0) + cos(alpha) * sin(phi)));
lambdap = lp_b + beta;
/* normalize longitude */
/* TODO can we just do a modulus ? */
lambdap = fmod(lambdap, two_pi);
while (lambdap > pi)
lambdap -= two_pi;
while (lambdap < -pi)
lambdap += two_pi;
phip = asin(sin_phip);
npt.lat = phip;
npt.lon = lambdap;
return npt;
}
template <typename T>
inline isea_geo<T> isea_ctran(isea_geo<T> * np, isea_geo<T> * pt, T const& lon0)
{
static T const pi = detail::pi<T>();
static T const two_pi = detail::two_pi<T>();
isea_geo<T> npt;
np->lon += pi;
npt = snyder_ctran(np, pt);
np->lon -= pi;
npt.lon -= (pi - lon0 + np->lon);
/*
* snyder is down tri 3, isea is along side of tri1 from vertex 0 to
* vertex 1 these are 180 degrees apart
*/
npt.lon += pi;
/* normalize longitude */
npt.lon = fmod(npt.lon, two_pi);
while (npt.lon > pi)
npt.lon -= two_pi;
while (npt.lon < -pi)
npt.lon += two_pi;
return npt;
}
/* in radians */
/* fuller's at 5.2454 west, 2.3009 N, adjacent at 7.46658 deg */
template <typename T>
inline int isea_grid_init(isea_dgg<T> * g)
{
if (!g)
return 0;
//g->polyhedron = isea_icosahedron;
g->o_lat = isea_std_lat;
g->o_lon = isea_std_lon;
g->o_az = 0.0;
g->aperture = 4;
g->resolution = 6;
g->radius = 1.0;
//g->topology = isea_hexagon;
return 1;
}
template <typename T>
inline int isea_orient_isea(isea_dgg<T> * g)
{
if (!g)
return 0;
g->o_lat = isea_std_lat;
g->o_lon = isea_std_lon;
g->o_az = 0.0;
return 1;
}
template <typename T>
inline int isea_orient_pole(isea_dgg<T> * g)
{
static T const half_pi = detail::half_pi<T>();
if (!g)
return 0;
g->o_lat = half_pi;
g->o_lon = 0.0;
g->o_az = 0;
return 1;
}
template <typename T>
inline int isea_transform(isea_dgg<T> * g, isea_geo<T> * in,
isea_pt<T> * out)
{
isea_geo<T> i, pole;
int tri;
pole.lat = g->o_lat;
pole.lon = g->o_lon;
i = isea_ctran(&pole, in, g->o_az);
tri = isea_snyder_forward(&i, out);
out->x *= g->radius;
out->y *= g->radius;
g->triangle = tri;
return tri;
}
template <typename T>
inline void isea_rotate(isea_pt<T> * pt, T const& degrees)
{
static T const d2r = geometry::math::d2r<T>();
static T const two_pi = detail::two_pi<T>();
T rad;
T x, y;
rad = -degrees * d2r;
while (rad >= two_pi) rad -= two_pi;
while (rad <= -two_pi) rad += two_pi;
x = pt->x * cos(rad) + pt->y * sin(rad);
y = -pt->x * sin(rad) + pt->y * cos(rad);
pt->x = x;
pt->y = y;
}
template <typename T>
inline int isea_tri_plane(int tri, isea_pt<T> *pt, T const& radius)
{
isea_pt<T> tc; /* center of triangle */
if (downtri(tri)) {
isea_rotate(pt, 180.0);
}
tc = isea_triangle_xy<T>(tri);
tc.x *= radius;
tc.y *= radius;
pt->x += tc.x;
pt->y += tc.y;
return tri;
}
/* convert projected triangle coords to quad xy coords, return quad number */
template <typename T>
inline int isea_ptdd(int tri, isea_pt<T> *pt)
{
int downtri, quad;
downtri = (((tri - 1) / 5) % 2 == 1);
quad = ((tri - 1) % 5) + ((tri - 1) / 10) * 5 + 1;
isea_rotate(pt, downtri ? 240.0 : 60.0);
if (downtri) {
pt->x += 0.5;
/* pt->y += cos(30.0 * M_PI / 180.0); */
pt->y += .86602540378443864672;
}
return quad;
}
template <typename T>
inline int isea_dddi_ap3odd(isea_dgg<T> *g, int quad, isea_pt<T> *pt, isea_pt<T> *di)
{
static T const pi = detail::pi<T>();
isea_pt<T> v;
T hexwidth;
T sidelength; /* in hexes */
int d, i;
int maxcoord;
hex h;
/* This is the number of hexes from apex to base of a triangle */
sidelength = (math::pow(T(2), g->resolution) + T(1)) / T(2);
/* apex to base is cos(30deg) */
hexwidth = cos(pi / 6.0) / sidelength;
/* TODO I think sidelength is always x.5, so
* (int)sidelength * 2 + 1 might be just as good
*/
maxcoord = (int) (sidelength * 2.0 + 0.5);
v = *pt;
hexbin2(hexwidth, v.x, v.y, &h.x, &h.y);
h.iso = 0;
hex_iso(&h);
d = h.x - h.z;
i = h.x + h.y + h.y;
/*
* you want to test for max coords for the next quad in the same
* "row" first to get the case where both are max
*/
if (quad <= 5) {
if (d == 0 && i == maxcoord) {
/* north pole */
quad = 0;
d = 0;
i = 0;
} else if (i == maxcoord) {
/* upper right in next quad */
quad += 1;
if (quad == 6)
quad = 1;
i = maxcoord - d;
d = 0;
} else if (d == maxcoord) {
/* lower right in quad to lower right */
quad += 5;
d = 0;
}
} else if (quad >= 6) {
if (i == 0 && d == maxcoord) {
/* south pole */
quad = 11;
d = 0;
i = 0;
} else if (d == maxcoord) {
/* lower right in next quad */
quad += 1;
if (quad == 11)
quad = 6;
d = maxcoord - i;
i = 0;
} else if (i == maxcoord) {
/* upper right in quad to upper right */
quad = (quad - 4) % 5;
i = 0;
}
}
di->x = d;
di->y = i;
g->quad = quad;
return quad;
}
template <typename T>
inline int isea_dddi(isea_dgg<T> *g, int quad, isea_pt<T> *pt, isea_pt<T> *di)
{
isea_pt<T> v;
T hexwidth;
int sidelength; /* in hexes */
hex h;
if (g->aperture == 3 && g->resolution % 2 != 0) {
return isea_dddi_ap3odd(g, quad, pt, di);
}
/* todo might want to do this as an iterated loop */
if (g->aperture >0) {
sidelength = (int) (math::pow(T(g->aperture), T(g->resolution / T(2))) + T(0.5));
} else {
sidelength = g->resolution;
}
hexwidth = 1.0 / sidelength;
v = *pt;
isea_rotate(&v, -30.0);
hexbin2(hexwidth, v.x, v.y, &h.x, &h.y);
h.iso = 0;
hex_iso(&h);
/* we may actually be on another quad */
if (quad <= 5) {
if (h.x == 0 && h.z == -sidelength) {
/* north pole */
quad = 0;
h.z = 0;
h.y = 0;
h.x = 0;
} else if (h.z == -sidelength) {
quad = quad + 1;
if (quad == 6)
quad = 1;
h.y = sidelength - h.x;
h.z = h.x - sidelength;
h.x = 0;
} else if (h.x == sidelength) {
quad += 5;
h.y = -h.z;
h.x = 0;
}
} else if (quad >= 6) {
if (h.z == 0 && h.x == sidelength) {
/* south pole */
quad = 11;
h.x = 0;
h.y = 0;
h.z = 0;
} else if (h.x == sidelength) {
quad = quad + 1;
if (quad == 11)
quad = 6;
h.x = h.y + sidelength;
h.y = 0;
h.z = -h.x;
} else if (h.y == -sidelength) {
quad -= 4;
h.y = 0;
h.z = -h.x;
}
}
di->x = h.x;
di->y = -h.z;
g->quad = quad;
return quad;
}
template <typename T>
inline int isea_ptdi(isea_dgg<T> *g, int tri, isea_pt<T> *pt,
isea_pt<T> *di)
{
isea_pt<T> v;
int quad;
v = *pt;
quad = isea_ptdd(tri, &v);
quad = isea_dddi(g, quad, &v, di);
return quad;
}
/* q2di to seqnum */
template <typename T>
inline int isea_disn(isea_dgg<T> *g, int quad, isea_pt<T> *di)
{
int sidelength;
int sn, height;
int hexes;
if (quad == 0) {
g->serial = 1;
return g->serial;
}
/* hexes in a quad */
hexes = (int) (math::pow(T(g->aperture), T(g->resolution)) + T(0.5));
if (quad == 11) {
g->serial = 1 + 10 * hexes + 1;
return g->serial;
}
if (g->aperture == 3 && g->resolution % 2 == 1) {
height = (int) (math::pow(T(g->aperture), T((g->resolution - 1) / T(2))));
sn = ((int) di->x) * height;
sn += ((int) di->y) / height;
sn += (quad - 1) * hexes;
sn += 2;
} else {
sidelength = (int) (math::pow(T(g->aperture), T(g->resolution / T(2))) + T(0.5));
sn = (int) ((quad - 1) * hexes + sidelength * di->x + di->y + 2);
}
g->serial = sn;
return sn;
}
/* TODO just encode the quad in the d or i coordinate
* quad is 0-11, which can be four bits.
* d' = d << 4 + q, d = d' >> 4, q = d' & 0xf
*/
/* convert a q2di to global hex coord */
template <typename T>
inline int isea_hex(isea_dgg<T> *g, int tri, isea_pt<T> *pt,
isea_pt<T> *hex)
{
isea_pt<T> v;
#ifdef BOOST_GEOMETRY_PROJECTIONS_FIXME
int sidelength;
int d, i, x, y;
#endif // BOOST_GEOMETRY_PROJECTIONS_FIXME
int quad;
quad = isea_ptdi(g, tri, pt, &v);
hex->x = ((int)v.x << 4) + quad;
hex->y = v.y;
return 1;
#ifdef BOOST_GEOMETRY_PROJECTIONS_FIXME
d = (int)v.x;
i = (int)v.y;
/* Aperture 3 odd resolutions */
if (g->aperture == 3 && g->resolution % 2 != 0) {
int offset = (int)(pow(T(3.0), T(g->resolution - 1)) + 0.5);
d += offset * ((g->quad-1) % 5);
i += offset * ((g->quad-1) % 5);
if (quad == 0) {
d = 0;
i = offset;
} else if (quad == 11) {
d = 2 * offset;
i = 0;
} else if (quad > 5) {
d += offset;
}
x = (2*d - i) /3;
y = (2*i - d) /3;
hex->x = x + offset / 3;
hex->y = y + 2 * offset / 3;
return 1;
}
/* aperture 3 even resolutions and aperture 4 */
sidelength = (int) (pow(T(g->aperture), T(g->resolution / 2.0)) + 0.5);
if (g->quad == 0) {
hex->x = 0;
hex->y = sidelength;
} else if (g->quad == 11) {
hex->x = sidelength * 2;
hex->y = 0;
} else {
hex->x = d + sidelength * ((g->quad-1) % 5);
if (g->quad > 5) hex->x += sidelength;
hex->y = i + sidelength * ((g->quad-1) % 5);
}
return 1;
#endif // BOOST_GEOMETRY_PROJECTIONS_FIXME
}
template <typename T>
inline isea_pt<T> isea_forward(isea_dgg<T> *g, isea_geo<T> *in)
{
int tri;
isea_pt<T> out, coord;
tri = isea_transform(g, in, &out);
if (g->output == isea_addr_plane) {
isea_tri_plane(tri, &out, g->radius);
return out;
}
/* convert to isea standard triangle size */
out.x = out.x / g->radius * isea_scale;
out.y = out.y / g->radius * isea_scale;
out.x += 0.5;
out.y += 2.0 * .14433756729740644112;
switch (g->output) {
case isea_addr_projtri:
/* nothing to do, already in projected triangle */
break;
case isea_addr_vertex2dd:
g->quad = isea_ptdd(tri, &out);
break;
case isea_addr_q2dd:
/* Same as above, we just don't print as much */
g->quad = isea_ptdd(tri, &out);
break;
case isea_addr_q2di:
g->quad = isea_ptdi(g, tri, &out, &coord);
return coord;
break;
case isea_addr_seqnum:
isea_ptdi(g, tri, &out, &coord);
/* disn will set g->serial */
isea_disn(g, g->quad, &coord);
return coord;
break;
case isea_addr_hex:
isea_hex(g, tri, &out, &coord);
return coord;
break;
default:
// isea_addr_plane handled above
BOOST_GEOMETRY_ASSERT(false);
break;
}
return out;
}
/*
* Proj 4 integration code follows
*/
template <typename T>
struct par_isea
{
isea_dgg<T> dgg;
};
template <typename T, typename Parameters>
struct base_isea_spheroid
{
par_isea<T> m_proj_parm;
// FORWARD(s_forward)
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
isea_pt<T> out;
isea_geo<T> in;
in.lon = lp_lon;
in.lat = lp_lat;
isea_dgg<T> copy = this->m_proj_parm.dgg;
out = isea_forward(©, &in);
xy_x = out.x;
xy_y = out.y;
}
static inline std::string get_name()
{
return "isea_spheroid";
}
};
template <typename T>
inline void isea_orient_init(srs::detail::proj4_parameters const& params,
par_isea<T>& proj_parm)
{
std::string opt = pj_get_param_s(params, "orient");
if (! opt.empty()) {
if (opt == std::string("isea")) {
isea_orient_isea(&proj_parm.dgg);
} else if (opt == std::string("pole")) {
isea_orient_pole(&proj_parm.dgg);
} else {
BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
}
}
}
template <typename T>
inline void isea_orient_init(srs::dpar::parameters<T> const& params,
par_isea<T>& proj_parm)
{
typename srs::dpar::parameters<T>::const_iterator
it = pj_param_find(params, srs::dpar::orient);
if (it != params.end()) {
srs::dpar::value_orient o = static_cast<srs::dpar::value_orient>(it->template get_value<int>());
if (o == srs::dpar::orient_isea) {
isea_orient_isea(&proj_parm.dgg);
} else if (o == srs::dpar::orient_pole) {
isea_orient_pole(&proj_parm.dgg);
} else {
BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
}
}
}
template <typename T>
inline void isea_mode_init(srs::detail::proj4_parameters const& params,
par_isea<T>& proj_parm)
{
std::string opt = pj_get_param_s(params, "mode");
if (! opt.empty()) {
if (opt == std::string("plane")) {
proj_parm.dgg.output = isea_addr_plane;
} else if (opt == std::string("di")) {
proj_parm.dgg.output = isea_addr_q2di;
} else if (opt == std::string("dd")) {
proj_parm.dgg.output = isea_addr_q2dd;
} else if (opt == std::string("hex")) {
proj_parm.dgg.output = isea_addr_hex;
} else {
BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
}
}
}
template <typename T>
inline void isea_mode_init(srs::dpar::parameters<T> const& params,
par_isea<T>& proj_parm)
{
typename srs::dpar::parameters<T>::const_iterator
it = pj_param_find(params, srs::dpar::mode);
if (it != params.end()) {
srs::dpar::value_mode m = static_cast<srs::dpar::value_mode>(it->template get_value<int>());
if (m == srs::dpar::mode_plane) {
proj_parm.dgg.output = isea_addr_plane;
} else if (m == srs::dpar::mode_di) {
proj_parm.dgg.output = isea_addr_q2di;
} else if (m == srs::dpar::mode_dd) {
proj_parm.dgg.output = isea_addr_q2dd;
} else if (m == srs::dpar::mode_hex) {
proj_parm.dgg.output = isea_addr_hex;
} else {
BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
}
}
}
// Icosahedral Snyder Equal Area
template <typename Params, typename T>
inline void setup_isea(Params const& params, par_isea<T>& proj_parm)
{
std::string opt;
isea_grid_init(&proj_parm.dgg);
proj_parm.dgg.output = isea_addr_plane;
/* proj_parm.dgg.radius = par.a; / * otherwise defaults to 1 */
/* calling library will scale, I think */
isea_orient_init(params, proj_parm);
pj_param_r<srs::spar::azi>(params, "azi", srs::dpar::azi, proj_parm.dgg.o_az);
pj_param_r<srs::spar::lon_0>(params, "lon_0", srs::dpar::lon_0, proj_parm.dgg.o_lon);
pj_param_r<srs::spar::lat_0>(params, "lat_0", srs::dpar::lat_0, proj_parm.dgg.o_lat);
// TODO: this parameter is set below second time
pj_param_i<srs::spar::aperture>(params, "aperture", srs::dpar::aperture, proj_parm.dgg.aperture);
// TODO: this parameter is set below second time
pj_param_i<srs::spar::resolution>(params, "resolution", srs::dpar::resolution, proj_parm.dgg.resolution);
isea_mode_init(params, proj_parm);
// TODO: pj_param_exists -> pj_get_param_b ?
if (pj_param_exists<srs::spar::rescale>(params, "rescale", srs::dpar::rescale)) {
proj_parm.dgg.radius = isea_scale;
}
if (pj_param_i<srs::spar::resolution>(params, "resolution", srs::dpar::resolution, proj_parm.dgg.resolution)) {
/* empty */
} else {
proj_parm.dgg.resolution = 4;
}
if (pj_param_i<srs::spar::aperture>(params, "aperture", srs::dpar::aperture, proj_parm.dgg.aperture)) {
/* empty */
} else {
proj_parm.dgg.aperture = 3;
}
}
}} // namespace detail::isea
#endif // doxygen
/*!
\brief Icosahedral Snyder Equal Area projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Spheroid
\par Projection parameters
- orient (string)
- azi: Azimuth (or Gamma) (degrees)
- lon_0: Central meridian (degrees)
- lat_0: Latitude of origin (degrees)
- aperture (integer)
- resolution (integer)
- mode (string)
- rescale
\par Example
\image html ex_isea.gif
*/
template <typename T, typename Parameters>
struct isea_spheroid : public detail::isea::base_isea_spheroid<T, Parameters>
{
template <typename Params>
inline isea_spheroid(Params const& params, Parameters const& )
{
detail::isea::setup_isea(params, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_F(srs::spar::proj_isea, isea_spheroid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_F(isea_entry, isea_spheroid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(isea_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(isea, isea_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_ISEA_HPP
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