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/*
* (C) Copyright 1996- ECMWF.
*
* This software is licensed under the terms of the Apache Licence Version 2.0
* which can be obtained at http://www.apache.org/licenses/LICENSE-2.0.
* In applying this licence, ECMWF does not waive the privileges and immunities
* granted to it by virtue of its status as an intergovernmental organisation nor
* does it submit to any jurisdiction.
*/
#include <cmath>
#include <limits>
#include <vector>
#include "eckit/geometry/GreatCircle.h"
#include "eckit/geometry/Point2.h"
#include "eckit/testing/Test.h"
namespace eckit::test {
using namespace geometry;
struct PointLonLat : Point2 {
PointLonLat(double x, double y) : Point2(x, y) {}
const double& lon() const { return x_[0]; }
const double& lat() const { return x_[1]; }
};
// -----------------------------------------------------------------------------
// test great circles
CASE("test great circles intersections") {
using types::is_approximately_equal;
using types::is_approximately_greater_or_equal;
auto is_approximately_equal_longitude = [](double lon1, double lon2,
double epsilon = std::numeric_limits<double>::epsilon()) -> bool {
while (lon2 < lon1) {
lon2 += 360;
}
while (lon1 >= lon1 + 360) {
lon2 -= 360;
}
return is_approximately_equal(lon1, lon2, epsilon) || is_approximately_equal(lon1, lon2 - 360, epsilon);
};
auto is_approximately_pole = [](double lat, double epsilon = std::numeric_limits<double>::epsilon()) -> bool {
return is_approximately_equal(std::abs(lat), 90., epsilon);
};
auto is_approximately_equator = [](double lat, double epsilon = std::numeric_limits<double>::epsilon()) -> bool {
return is_approximately_equal(lat, 0., epsilon);
};
const std::vector<double> latitudes{
90, 60, 45, 30, 0, -30, -45, -60, -90,
};
const std::vector<double> longitudes{
-181, -180, -135, -90, -45, 0, 45, 90, 135, 180, 225, 270, 315, 360, 361,
};
const std::vector<PointLonLat> antipodes{
{0, 0}, {180, 0}, {-180, 0}, {0, 0}, {-90, 0}, {90, 0}, {90, 0},
{-90, 0}, {0, 90}, {0, -90}, {0, -90}, {0, 90}, {45, 45}, {225, -45},
};
SECTION("example intersection with meridian and parallel") {
// latitude at Valparaíso-Shanghai mid-point
const PointLonLat P1(-71.6, -33.);
const PointLonLat P2(121.8, 31.4);
GreatCircle gc(P1, P2);
const PointLonLat mid(-159.18, -6.81);
auto lats = gc.latitude(mid.lon());
EXPECT(lats.size() == 1 && is_approximately_equal(lats[0], mid.lat(), 0.01));
auto lons = gc.longitude(mid.lat());
EXPECT(lons.size() == 2);
EXPECT(is_approximately_equal_longitude(lons[0], mid.lon(), 0.01) ||
is_approximately_equal_longitude(lons[1], mid.lon(), 0.01));
}
SECTION("mal-formed great circle") {
for (size_t i = 0; i < antipodes.size(); i += 2) {
const PointLonLat& A(antipodes[i]);
const PointLonLat& B(antipodes[i + 1]);
EXPECT_THROWS_AS(GreatCircle(A, A), BadValue);
EXPECT_THROWS_AS(GreatCircle(B, B), BadValue);
EXPECT_THROWS_AS(GreatCircle(A, B), BadValue);
if (is_approximately_pole(A.lat())) {
for (double lon1_gc : longitudes) {
for (double lon2_gc : longitudes) {
EXPECT_THROWS_AS(GreatCircle({lon1_gc, A.lat()}, {lon2_gc, A.lat()}), BadValue);
EXPECT_THROWS_AS(GreatCircle({lon1_gc, B.lat()}, {lon2_gc, B.lat()}), BadValue);
}
}
}
}
}
SECTION("intersection at quadrants") {
for (double lat_gc : latitudes) {
if (!is_approximately_pole(lat_gc) && !is_approximately_equator(lat_gc)) {
for (double lon_gc : longitudes) {
GreatCircle gc({lon_gc, lat_gc}, {lon_gc + 90, 0});
EXPECT(!gc.crossesPoles());
auto lon_at_equator = gc.longitude(0);
EXPECT(lon_at_equator.size() == 2);
EXPECT((is_approximately_equal_longitude(lon_gc + 90, lon_at_equator[0]) &&
is_approximately_equal_longitude(lon_gc - 90, lon_at_equator[1])) ||
(is_approximately_equal_longitude(lon_gc - 90, lon_at_equator[0]) &&
is_approximately_equal_longitude(lon_gc + 90, lon_at_equator[1])));
auto lon_extrema1 = gc.longitude(lat_gc);
EXPECT(lon_extrema1.size() == 1 && is_approximately_equal_longitude(lon_extrema1[0], lon_gc, 0.01));
auto lon_extrema2 = gc.longitude(-lat_gc);
EXPECT(lon_extrema2.size() == 1 &&
is_approximately_equal_longitude(lon_extrema2[0], lon_gc + 180, 0.01));
}
}
}
}
SECTION("intersection with parallels when crossing the poles") {
for (double lon : longitudes) {
for (double lat : latitudes) {
{
GreatCircle gc({lon, -10}, {lon, 10});
EXPECT(gc.crossesPoles());
auto lons = gc.longitude(lat);
size_t N = is_approximately_pole(lat) ? 1 : 2;
EXPECT(lons.size() == N);
if (N == 1) {
EXPECT(is_approximately_equal_longitude(lons[0], lon));
}
else {
EXPECT(is_approximately_equal_longitude(lons[0] + 180, lons[1]));
EXPECT(is_approximately_equal_longitude(lons[0], lon) ||
is_approximately_equal_longitude(lons[1], lon));
}
}
if (!is_approximately_pole(lat) && !is_approximately_equator(lat)) {
GreatCircle gc({lon, lat}, {lon + 180, lat});
EXPECT(gc.crossesPoles());
auto lons = gc.longitude(lat);
EXPECT(lons.size() == 2);
EXPECT(is_approximately_equal_longitude(lons[0] + 180, lons[1]));
EXPECT(is_approximately_equal_longitude(lons[0], lon) ||
is_approximately_equal_longitude(lons[1], lon));
}
}
}
}
SECTION("intersection with parallels") {
for (double lat_gc : latitudes) {
if (/* avoid mal-forming */ !is_approximately_pole(lat_gc)) {
for (double lat : latitudes) {
GreatCircle gc({-1, lat_gc}, {1, lat_gc});
EXPECT(!gc.crossesPoles());
auto lons = gc.longitude(lat);
size_t N = is_approximately_equator(lat_gc) ? 0.
: is_approximately_greater_or_equal(std::abs(lat_gc), std::abs(lat)) ? 2
: 0;
EXPECT(lons.size() == N);
for (auto lon : lons) {
auto lats = gc.latitude(lon);
EXPECT(lats.size() == 1 && is_approximately_equal(lats[0], lat, 0.01));
}
}
}
}
}
SECTION("equator great circle intersection with meridian and parallel") {
for (double lon : longitudes) {
GreatCircle eq({lon - 1, 0}, {lon + 1, 0});
EXPECT(!eq.crossesPoles());
// non-intersection with parallels
for (double lat : latitudes) {
EXPECT(eq.longitude(lat).empty());
}
// intersect one latitude only, for specific longitudes
auto lats = eq.latitude(lon);
EXPECT(lats.size() == 1 && is_approximately_equator(lats[0]));
}
}
}
// -----------------------------------------------------------------------------
} // namespace eckit::test
int main(int argc, char** argv) {
return eckit::testing::run_tests(argc, argv);
}
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