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git.proxmox.com Git - ceph.git/blob - ceph/src/boost/libs/geometry/test/algorithms/area/area_sph_geo.cpp
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1 // Boost.Geometry (aka GGL, Generic Geometry Library)
4 // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
5 // Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
6 // Copyright (c) 2009-2012 Mateusz Loskot, London, UK.
7 // Copyright (c) 2017 Adam Wulkiewicz, Lodz, Poland.
9 // This file was modified by Oracle on 2015, 2016, 2017.
10 // Modifications copyright (c) 2015-2017, Oracle and/or its affiliates.
12 // Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
13 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
15 // Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
16 // (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.
18 // Use, modification and distribution is subject to the Boost Software License,
19 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
20 // http://www.boost.org/LICENSE_1_0.txt)
22 #include <boost/geometry.hpp>
23 #include <geometry_test_common.hpp>
25 namespace bg
= boost::geometry
;
27 //Testing spherical and geographic strategies
28 template <typename CT
>
29 void test_spherical_geo()
35 typedef typename
bg::model::point
37 ct
, 2, bg::cs::geographic
<bg::degree
>
40 bg::strategy::area::geographic
42 bg::strategy::vincenty
,
46 bg::model::polygon
<pt_geo
> geometry_geo
;
50 typedef typename
bg::model::point
52 ct
, 2, bg::cs::spherical_equatorial
<bg::degree
>
54 bg::model::polygon
<pt
> geometry
;
56 // unit-sphere has area of 4-PI. Polygon covering 1/8 of it:
57 std::string poly
= "POLYGON((0 0,0 90,90 0,0 0))";
59 bg::strategy::area::spherical
62 > strategy_unary(1.0);
66 ct expected
= four
* boost::geometry::math::pi
<ct
>() / eight
;
67 bg::read_wkt(poly
, geometry
);
68 ct area
= bg::area(geometry
, strategy_unary
);
69 BOOST_CHECK_CLOSE(area
, expected
, 0.0001);
71 // With strategy, radius 2 -> 4 pi r^2
72 bg::strategy::area::spherical
77 area
= bg::area(geometry
, strategy
);
79 BOOST_CHECK_CLOSE(area
, two
* two
* expected
, 0.0001);
81 // Geographic total area of earth is about 510065626583900.6 (WGS84 ellipsoid)
82 // (510072000 in https://en.wikipedia.org/wiki/Earth)
83 // So the 1/8 is 6.375820332*10^13 and here we get something close to it
84 bg::read_wkt(poly
, geometry_geo
);
85 area
= bg::area(geometry_geo
, area_geographic
);
86 //GeoGraphicLib gives: 63758202715511.055
87 BOOST_CHECK_CLOSE(area
, 63758202715509.844, 0.0001);
90 // Wrangel Island (dateline crossing)
91 // With (spherical) Earth strategy
92 poly
= "POLYGON((-178.7858 70.7852, 177.4758 71.2333, 179.7436 71.5733, -178.7858 70.7852))";
94 bg::strategy::area::spherical
97 > spherical_earth(6373);
98 bg::read_wkt(poly
, geometry
);
99 area
= bg::area(geometry
, spherical_earth
);
100 // SQL Server gives: 4537.9654419375
101 // PostGIS gives: 4537.9311668307
102 // Note: those are Geographic, this test is Spherical
103 BOOST_CHECK_CLOSE(area
, 4506.6389, 0.001);
105 bg::read_wkt(poly
, geometry_geo
);
106 area
= bg::area(geometry_geo
, area_geographic
);
107 BOOST_CHECK_CLOSE(area
, 4537929936.5349159, 0.0001);
109 // Wrangel, more in detail
110 poly
= "POLYGON((-178.568604 71.564148,-178.017548 71.449692,-177.833313 71.3461,\
111 -177.502838 71.277466 ,-177.439453 71.226929,-177.620026 71.116638,\
112 -177.9389 71.037491,-178.8186 70.979965,-179.274445 70.907761,\
113 -180 70.9972,179.678314 70.895538,179.272766 70.888596,\
114 178.791016 70.7964,178.617737 71.035538,178.872192 71.217484,\
115 179.530273 71.4383 ,-180 71.535843 ,-179.628601 71.577194,\
116 -179.305298 71.551361,-179.03421 71.597748,-178.568604 71.564148))";
117 bg::read_wkt(poly
, geometry
);
118 area
= bg::area(geometry
, spherical_earth
);
119 // SQL Server gives: 7669.10402181435
120 // PostGIS gives: 7669.55565459832
121 BOOST_CHECK_CLOSE(area
, 7616.523769, 0.001);
123 bg::read_wkt(poly
, geometry_geo
);
124 area
= bg::area(geometry_geo
, area_geographic
);
125 BOOST_CHECK_CLOSE(area
, 7669498457.4130802, 0.0001);
127 // Check more at the equator
129 select 1,geography::STGeomFromText('POLYGON((-178.7858 10.7852 , 179.7436 11.5733 , \
130 177.4758 11.2333 , -178.7858 10.7852))',4326) .STArea()/1000000.0
131 union select 2,geography::STGeomFromText('POLYGON((-178.7858 20.7852 , 179.7436 21.5733 ,\
132 177.4758 21.2333 , -178.7858 20.7852))',4326) .STArea()/1000000.0
133 union select 3,geography::STGeomFromText('POLYGON((-178.7858 30.7852 , 179.7436 31.5733 , \
134 177.4758 31.2333 , -178.7858 30.7852))',4326) .STArea()/1000000.0
135 union select 0,geography::STGeomFromText('POLYGON((-178.7858 0.7852 , 179.7436 1.5733 , \
136 177.4758 1.2333 , -178.7858 0.7852))',4326) .STArea()/1000000.0
137 union select 4,geography::STGeomFromText('POLYGON((-178.7858 40.7852 , 179.7436 41.5733 , \
138 177.4758 41.2333 , -178.7858 40.7852))',4326) .STArea()/1000000.0
141 poly
= "POLYGON((-178.7858 0.7852, 177.4758 1.2333, 179.7436 1.5733, -178.7858 0.7852))";
142 bg::read_wkt(poly
, geometry
);
143 area
= bg::area(geometry
, spherical_earth
);
144 BOOST_CHECK_CLOSE(area
, 14136.09946, 0.001); // SQL Server gives: 14064.1902284513
145 bg::read_wkt(poly
, geometry_geo
);
146 area
= bg::area(geometry_geo
, area_geographic
);
147 BOOST_CHECK_CLOSE(area
, 14064129044.674297, 0.0001);
149 poly
= "POLYGON((-178.7858 10.7852, 177.4758 11.2333, 179.7436 11.5733, -178.7858 10.7852))";
150 bg::read_wkt(poly
, geometry
);
151 area
= bg::area(geometry
, spherical_earth
);
152 BOOST_CHECK_CLOSE(area
, 13760.2456, 0.001); // SQL Server gives: 13697.0941155193
153 bg::read_wkt(poly
, geometry_geo
);
154 area
= bg::area(geometry_geo
, area_geographic
);
155 BOOST_CHECK_CLOSE(area
, 13696308940.315653, 0.0001);
157 poly
= "POLYGON((-178.7858 20.7852, 177.4758 21.2333, 179.7436 21.5733, -178.7858 20.7852))";
158 bg::read_wkt(poly
, geometry
);
159 area
= bg::area(geometry
, spherical_earth
);
160 BOOST_CHECK_CLOSE(area
, 12987.8682, 0.001); // SQL Server gives: 12944.3970990317 -> -39m^2
161 bg::read_wkt(poly
, geometry_geo
);
162 area
= bg::area(geometry_geo
, area_geographic
);
163 BOOST_CHECK_CLOSE(area
, 12943176284.560806, 0.0001);
165 poly
= "POLYGON((-178.7858 30.7852, 177.4758 31.2333, 179.7436 31.5733, -178.7858 30.7852))";
166 bg::read_wkt(poly
, geometry
);
167 area
= bg::area(geometry
, spherical_earth
);
168 BOOST_CHECK_CLOSE(area
, 11856.3935, 0.001); // SQL Server gives: 11838.5338423574 -> -18m^2
169 bg::read_wkt(poly
, geometry_geo
);
170 area
= bg::area(geometry_geo
, area_geographic
);
171 BOOST_CHECK_CLOSE(area
, 11837280445.349375, 0.0001);
173 poly
= "POLYGON((-178.7858 40.7852, 177.4758 41.2333, 179.7436 41.5733, -178.7858 40.7852))";
174 bg::read_wkt(poly
, geometry
);
175 area
= bg::area(geometry
, spherical_earth
);
176 BOOST_CHECK_CLOSE(area
, 10404.627685523914, 0.001);
177 // SQL Server gives: 10412.0607137119, -> +8m^2
178 bg::read_wkt(poly
, geometry_geo
);
179 area
= bg::area(geometry_geo
, area_geographic
);
180 BOOST_CHECK_CLOSE(area
, 10411098789.39222, 0.0001);
183 poly
= "POLYGON((0 40,1 42,0 44,2 43,4 44,3 42,4 40,2 41,0 40))";
184 bg::read_wkt(poly
, geometry
);
185 area
= bg::area(geometry
, spherical_earth
);
186 BOOST_CHECK_CLOSE(area
, 73538.2958, 0.001); // SQL Server gives: 73604.2047689719
187 bg::read_wkt(poly
, geometry_geo
);
188 area
= bg::area(geometry_geo
, area_geographic
);
189 BOOST_CHECK_CLOSE(area
, 73604208172.719223, 0.0001);
191 // With hole POLYGON((0 40,4 40,4 44,0 44,0 40),(1 41,2 43,3 42,1 41))
192 poly
= "POLYGON((0 40,0 44,4 44,4 40,0 40),(1 41,3 42,2 43,1 41))";
193 bg::read_wkt(poly
, geometry
);
194 area
= bg::area(geometry
, spherical_earth
);
195 BOOST_CHECK_CLOSE(area
, 133233.844876, 0.001); // SQL Server gives: 133353.335
196 bg::read_wkt(poly
, geometry_geo
);
197 area
= bg::area(geometry_geo
, area_geographic
);
198 BOOST_CHECK_CLOSE(area
, 133353077343.10347, 0.0001);
200 // mean Earth's radius^2
201 double r2
= bg::math::sqr(bg::get_radius
<0>(bg::srs::sphere
<double>()));
205 std::string poly1
= "POLYGON((-10 0,-10 10,0 10,0 0,-10 0))";
206 std::string poly2
= "POLYGON((0 0,0 10,10 10,10 0,0 0))";
207 std::string poly3
= "POLYGON((-5 0,-5 10,5 10,5 0,-5 0))";
208 bg::read_wkt(poly1
, geometry
);
209 ct area1
= bg::area(geometry
);
210 bg::read_wkt(poly2
, geometry
);
211 ct area2
= bg::area(geometry
);
212 bg::read_wkt(poly3
, geometry
);
213 ct area3
= bg::area(geometry
);
214 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
215 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
216 BOOST_CHECK_CLOSE(area1
* r2
, 1233204227903.1848, 0.001);
218 bg::read_wkt(poly1
, geometry_geo
);
219 area1
= bg::area(geometry_geo
, area_geographic
);
220 bg::read_wkt(poly2
, geometry_geo
);
221 area2
= bg::area(geometry_geo
, area_geographic
);
222 bg::read_wkt(poly3
, geometry_geo
);
223 area3
= bg::area(geometry_geo
, area_geographic
);
224 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
225 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
226 BOOST_CHECK_CLOSE(area1
, 1227877191611.2805, 0.001);
229 std::string poly1
= "POLYGON((-10 -5,-10 5,0 5,0 -5,-10 -5))";
230 std::string poly2
= "POLYGON((0 -5,0 5,10 5,10 -5,0 -5))";
231 std::string poly3
= "POLYGON((-5 -5,-5 5,5 5,5 -5,-5 -5))";
232 bg::read_wkt(poly1
, geometry
);
233 ct area1
= bg::area(geometry
);
234 bg::read_wkt(poly2
, geometry
);
235 ct area2
= bg::area(geometry
);
236 bg::read_wkt(poly3
, geometry
);
237 ct area3
= bg::area(geometry
);
238 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
239 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
240 BOOST_CHECK_CLOSE(area1
* r2
, 1237986107636.0261, 0.001);
242 bg::read_wkt(poly1
, geometry_geo
);
243 area1
= bg::area(geometry_geo
, area_geographic
);
244 bg::read_wkt(poly2
, geometry_geo
);
245 area2
= bg::area(geometry_geo
, area_geographic
);
246 bg::read_wkt(poly3
, geometry_geo
);
247 area3
= bg::area(geometry_geo
, area_geographic
);
248 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
249 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
250 BOOST_CHECK_CLOSE(area1
, 1232514639151.6477, 0.001);
252 // around 180 meridian
254 std::string poly1
= "POLYGON((-180 0,-180 10,-170 10,-170 0,-180 0))";
255 std::string poly2
= "POLYGON((175 0,175 10,-175 10,-175 0,175 0))";
256 std::string poly3
= "POLYGON((170 0,170 10,180 10,180 0,170 0))";
257 std::string poly4
= "POLYGON((170 0,170 10,-180 10,-180 0,170 0))";
258 std::string poly5
= "POLYGON((180 0,180 10,-170 10,-170 0,180 0))";
259 bg::read_wkt(poly1
, geometry
);
260 ct area1
= bg::area(geometry
);
261 bg::read_wkt(poly2
, geometry
);
262 ct area2
= bg::area(geometry
);
263 bg::read_wkt(poly3
, geometry
);
264 ct area3
= bg::area(geometry
);
265 bg::read_wkt(poly4
, geometry
);
266 ct area4
= bg::area(geometry
);
267 bg::read_wkt(poly5
, geometry
);
268 ct area5
= bg::area(geometry
);
269 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
270 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
271 BOOST_CHECK_CLOSE(area3
, area4
, 0.001);
272 BOOST_CHECK_CLOSE(area4
, area5
, 0.001);
273 BOOST_CHECK_CLOSE(area1
* r2
, 1233204227903.1833, 0.001);
275 bg::read_wkt(poly1
, geometry_geo
);
276 area1
= bg::area(geometry_geo
, area_geographic
);
277 bg::read_wkt(poly2
, geometry_geo
);
278 area2
= bg::area(geometry_geo
, area_geographic
);
279 bg::read_wkt(poly3
, geometry_geo
);
280 area3
= bg::area(geometry_geo
, area_geographic
);
281 bg::read_wkt(poly4
, geometry_geo
);
282 area4
= bg::area(geometry_geo
, area_geographic
);
283 bg::read_wkt(poly5
, geometry_geo
);
284 area5
= bg::area(geometry_geo
, area_geographic
);
285 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
286 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
287 BOOST_CHECK_CLOSE(area3
, area4
, 0.001);
288 BOOST_CHECK_CLOSE(area4
, area5
, 0.001);
289 BOOST_CHECK_CLOSE(area1
, 1227877191611.2805, 0.001);
292 std::string poly1
= "POLYGON((-180 -5,-180 5,-170 5,-170 -5,-180 -5))";
293 std::string poly2
= "POLYGON((175 -5,175 5,-175 5,-175 -5,175 -5))";
294 std::string poly3
= "POLYGON((170 -5,170 5,180 5,180 -5,170 -5))";
295 std::string poly4
= "POLYGON((170 -5,170 5,180 5,180 -5,170 -5))";
296 std::string poly5
= "POLYGON((180 -5,180 5,-170 5,-170 -5,180 -5))";
297 bg::read_wkt(poly1
, geometry
);
298 ct area1
= bg::area(geometry
);
299 bg::read_wkt(poly2
, geometry
);
300 ct area2
= bg::area(geometry
);
301 bg::read_wkt(poly3
, geometry
);
302 ct area3
= bg::area(geometry
);
303 bg::read_wkt(poly4
, geometry
);
304 ct area4
= bg::area(geometry
);
305 bg::read_wkt(poly5
, geometry
);
306 ct area5
= bg::area(geometry
);
307 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
308 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
309 BOOST_CHECK_CLOSE(area3
, area4
, 0.001);
310 BOOST_CHECK_CLOSE(area4
, area5
, 0.001);
311 BOOST_CHECK_CLOSE(area1
* r2
, 1237986107636.0247, 0.001);
313 bg::read_wkt(poly1
, geometry_geo
);
314 area1
= bg::area(geometry_geo
, area_geographic
);
315 bg::read_wkt(poly2
, geometry_geo
);
316 area2
= bg::area(geometry_geo
, area_geographic
);
317 bg::read_wkt(poly3
, geometry_geo
);
318 area3
= bg::area(geometry_geo
, area_geographic
);
319 bg::read_wkt(poly4
, geometry_geo
);
320 area4
= bg::area(geometry_geo
, area_geographic
);
321 bg::read_wkt(poly5
, geometry_geo
);
322 area5
= bg::area(geometry_geo
, area_geographic
);
323 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
324 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
325 BOOST_CHECK_CLOSE(area3
, area4
, 0.001);
326 BOOST_CHECK_CLOSE(area4
, area5
, 0.001);
327 BOOST_CHECK_CLOSE(area1
, 1232514639151.6477, 0.001);
331 std::string poly1
= "POLYGON((0 80,-90 80,-180 80,90 80,0 80))";
332 std::string poly2
= "POLYGON((0 80,-90 80,180 80,90 80,0 80))";
333 std::string poly3
= "POLYGON((0 -80,90 -80,-180 -80,-90 -80,0 -80))";
334 std::string poly4
= "POLYGON((0 -80,90 -80,180 -80,-90 -80,0 -80))";
335 bg::read_wkt(poly1
, geometry
);
336 ct area1
= bg::area(geometry
);
337 bg::read_wkt(poly2
, geometry
);
338 ct area2
= bg::area(geometry
);
339 bg::read_wkt(poly3
, geometry
);
340 ct area3
= bg::area(geometry
);
341 bg::read_wkt(poly4
, geometry
);
342 ct area4
= bg::area(geometry
);
343 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
344 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
345 BOOST_CHECK_CLOSE(area3
, area4
, 0.001);
347 bg::read_wkt(poly1
, geometry_geo
);
348 area1
= bg::area(geometry_geo
, area_geographic
);
349 bg::read_wkt(poly2
, geometry_geo
);
350 area2
= bg::area(geometry_geo
, area_geographic
);
351 bg::read_wkt(poly3
, geometry_geo
);
352 area3
= bg::area(geometry_geo
, area_geographic
);
353 bg::read_wkt(poly4
, geometry_geo
);
354 area4
= bg::area(geometry_geo
, area_geographic
);
355 BOOST_CHECK_CLOSE(area1
, area2
, 0.001);
356 BOOST_CHECK_CLOSE(area2
, area3
, 0.001);
357 BOOST_CHECK_CLOSE(area3
, area4
, 0.001);
361 bg::model::ring
<pt
> aurha
; // a'dam-utr-rott.-den haag-a'dam
362 std::string poly
= "POLYGON((4.892 52.373,5.119 52.093,4.479 51.930,\
363 4.23 52.08,4.892 52.373))";
364 bg::read_wkt(poly
, aurha
);
367 // Create colatitudes (measured from pole)
368 BOOST_FOREACH(pt& p, aurha)
370 bg::set<1>(p, ct(90) - bg::get<1>(p));
374 bg::strategy::area::spherical
377 > area_spherical(6372.795);
378 area
= bg::area(aurha
, area_spherical
);
379 BOOST_CHECK_CLOSE(area
, 1476.645675, 0.0001);
381 bg::read_wkt(poly
, geometry_geo
);
382 area
= bg::area(geometry_geo
, area_geographic
);
383 BOOST_CHECK_CLOSE(area
, 1481555970.0765088, 0.001);
385 // SQL Server gives: 1481.55595960659
386 // for select geography::STGeomFromText('POLYGON((4.892 52.373,4.23 52.08,
387 // 4.479 51.930,5.119 52.093,4.892 52.373))',4326).STArea()/1000000.0
391 bg::model::polygon
<pt
, false> geometry_sph
;
392 std::string wkt
= "POLYGON((0 0, 5 0, 5 5, 0 5, 0 0))";
393 bg::read_wkt(wkt
, geometry_sph
);
395 area
= bg::area(geometry_sph
, bg::strategy::area::spherical
<>(6371228.0));
396 BOOST_CHECK_CLOSE(area
, 308932296103.83051, 0.0001);
398 bg::model::polygon
<pt_geo
, false> geometry_geo
;
399 bg::read_wkt(wkt
, geometry_geo
);
401 area
= bg::area(geometry_geo
, bg::strategy::area::geographic
<>(bg::srs::spheroid
<double>(6371228.0, 6371228.0)));
402 BOOST_CHECK_CLOSE(area
, 308932296103.82574, 0.001);
406 int test_main(int, char* [])
409 test_spherical_geo
<double>();