inline FloatLatitude yToLat(const double y)
{
const auto clamped_y = std::max(-180., std::min(180., y));
const double normalized_lat =
detail::RAD_TO_DEGREE * 2. * std::atan(std::exp(clamped_y * detail::DEGREE_TO_RAD));
return FloatLatitude(std::round(normalized_lat * COORDINATE_PRECISION) / COORDINATE_PRECISION - 90.);
}
inline double latToYapprox(const FloatLatitude latitude)
{
if (latitude < FloatLatitude(-70.) || latitude > FloatLatitude(70.))
return latToY(latitude);
// Approximate the inverse Gudermannian function with the Padé approximant [11/11]: deg → deg
// Coefficients are computed for the argument range [-70°,70°] by Remez algorithm |err|_∞=3.387e-12
const auto x = static_cast<double>(latitude);
return
horner(x, 0.00000000000000000000000000e+00, 1.00000000000089108431373566e+00, 2.34439410386997223035693483e-06,
-3.21291701673364717170998957e-04, -6.62778508496089940141103135e-10, 3.68188055470304769936079078e-08,
6.31192702320492485752941578e-14, -1.77274453235716299127325443e-12, -2.24563810831776747318521450e-18,
3.13524754818073129982475171e-17, 2.09014225025314211415458228e-23, -9.82938075991732185095509716e-23) /
horner(x, 1.00000000000000000000000000e+00, 2.34439410398970701719081061e-06, -3.72061271627251952928813333e-04,
-7.81802389685429267252612620e-10, 5.18418724186576447072888605e-08, 9.37468561198098681003717477e-14,
-3.30833288607921773936702558e-12, -4.78446279888774903983338274e-18, 9.32999229169156878168234191e-17,
9.17695141954265959600965170e-23, -8.72130728982012387640166055e-22, -3.23083224835967391884404730e-28);
}
inline std::pair<double, FloatCoordinate> projectPointOnSegment(const FloatCoordinate &source,
const FloatCoordinate &target,
const FloatCoordinate &coordinate)
{
const FloatCoordinate slope_vector{target.lon - source.lon, target.lat - source.lat};
const FloatCoordinate rel_coordinate{coordinate.lon - source.lon, coordinate.lat - source.lat};
// dot product of two un-normed vectors
const auto unnormed_ratio = static_cast<double>(slope_vector.lon * rel_coordinate.lon) +
static_cast<double>(slope_vector.lat * rel_coordinate.lat);
// squared length of the slope vector
const auto squared_length = static_cast<double>(slope_vector.lon * slope_vector.lon) +
static_cast<double>(slope_vector.lat * slope_vector.lat);
if (squared_length < std::numeric_limits<double>::epsilon())
{
return {0, source};
}
const double normed_ratio = unnormed_ratio / squared_length;
double clamped_ratio = normed_ratio;
if (clamped_ratio > 1.)
{
clamped_ratio = 1.;
}
else if (clamped_ratio < 0.)
{
clamped_ratio = 0.;
}
return {clamped_ratio,
{
FloatLongitude(1.0 - clamped_ratio) * source.lon +
target.lon * FloatLongitude(clamped_ratio),
FloatLatitude(1.0 - clamped_ratio) * source.lat +
target.lat * FloatLatitude(clamped_ratio),
}};
}
bool FloatCoordinate::IsValid() const
{
return !(lat > FloatLatitude(90) || lat < FloatLatitude(-90) || lon > FloatLongitude(180) ||
lon < FloatLongitude(-180));
}
inline FloatLatitude clamp(const FloatLatitude lat)
{
return std::max(std::min(lat, FloatLatitude(detail::MAX_LATITUDE)),
FloatLatitude(-detail::MAX_LATITUDE));
}
