// Orders Bounds by their midpoint. This is really only useful if the bounds
// are arranged in a grid and are of equal size (like during a MetaQuery).
inline bool operator<(const Bounds& lhs, const Bounds& rhs)
{
const auto& lhsMid(lhs.mid());
const auto& rhsMid(rhs.mid());
return
(lhsMid.x < rhsMid.x) ||
(lhsMid.x == rhsMid.x && lhsMid.y < rhsMid.y) ||
(lhsMid.x == rhsMid.x && lhsMid.y == rhsMid.y && lhsMid.z < rhsMid.z);
}
TEST(Infer, Reprojection)
{
const std::string path(test::dataPath() + "ellipsoid-single-nyc");
const std::string badPath(path + "-wrong-srs");
const Bounds utmBounds(
Point(580621.19214, 4504618.31537, -50),
Point(580850.55166, 4504772.01557, 50));
{
Inference inference(path);
inference.go();
ASSERT_TRUE(inference.done());
checkBoundsNear(inference.bounds(), nycBounds);
const Delta* d(inference.delta());
ASSERT_TRUE(d);
EXPECT_EQ(d->scale(), Scale(.01));
checkPointNear(d->offset(), nycCenter, 20.0);
}
{
const Reprojection r("", "EPSG:26918");
Inference inference(path, &r);
inference.go();
ASSERT_TRUE(inference.done());
checkBoundsNear(inference.bounds(), utmBounds);
const Delta* d(inference.delta());
ASSERT_TRUE(d);
EXPECT_EQ(d->scale(), Scale(.01));
checkPointNear(d->offset(), utmBounds.mid(), 20.0);
}
{
const Reprojection r("EPSG:3857", "EPSG:26918", true);
Inference inference(badPath, &r);
inference.go();
ASSERT_TRUE(inference.done());
const Delta* d(inference.delta());
ASSERT_TRUE(d);
EXPECT_EQ(d->scale(), Scale(.01));
checkPointNear(d->offset(), utmBounds.mid(), 20.0);
}
}
// Returns true if these Bounds share any area in common with another.
bool overlaps(const Bounds& other, bool force2d = false) const
{
Point otherMid(other.mid());
return
std::abs(m_mid.x - otherMid.x) <=
width() / 2.0 + other.width() / 2.0 &&
std::abs(m_mid.y - otherMid.y) <=
depth() / 2.0 + other.depth() / 2.0 &&
(force2d || std::abs(m_mid.z - otherMid.z) <=
height() / 2.0 + other.height() / 2.0);
}
Transformation Inference::calcTransformation()
{
// We have our full bounds and info for all files in EPSG:4978. Now:
// 1) determine a transformation matrix so outward is up
// 2) transform our file info and bounds accordingly
// We're going to use our Point class to represent Vectors in this function.
using Vector = Point;
// Let O = (0,0,0) be the origin (center of the earth). This is our native
// projection system with unit vectors i=(1,0,0), j=(0,1,0), and k=(0,0,1).
// Let P = bounds.mid(), our transformed origin point.
// Let S be the sphere centered at O with radius ||P||.
// Let T = the plane tangent to S at P.
// Now, we can define our desired coordinate system:
//
// k' = "up" = normalized vector O->P
//
// j' = "north" = the normalized projected vector onto tangent plane T, of
// the north pole vector (0,0,1) from the non-transformed coordinate system.
//
// i' = "east" = j' cross k'
// Determine normalized vector k'.
const Point p(bounds().mid());
const Vector up(Vector::normalize(p));
// Project the north pole vector onto k'.
const Vector northPole(0, 0, 1);
const double dot(Point::dot(up, northPole));
const Vector proj(up * dot);
// Subtract that projection from the north pole vector to project it onto
// tangent plane T - then normalize to determine vector j'.
const Vector north(Vector::normalize(northPole - proj));
// Finally, calculate j' cross k' to determine i', which should turn out to
// be normalized since the inputs are orthogonal and normalized.
const Vector east(Vector::cross(north, up));
// First, rotate so up is outward from the center of the earth.
const std::vector<double> rotation
{
east.x, east.y, east.z, 0,
north.x, north.y, north.z, 0,
up.x, up.y, up.z, 0,
0, 0, 0, 1
};
// Then, translate around our current best guess at a center point. This
// should be close enough to the origin for reasonable precision.
const Bounds tentativeCenter(
m_executor.transform(bounds(), rotation));
const std::vector<double> translation
{
1, 0, 0, -tentativeCenter.mid().x,
0, 1, 0, -tentativeCenter.mid().y,
0, 0, 1, -tentativeCenter.mid().z,
0, 0, 0, 1
};
return matrix::multiply(translation, rotation);
}