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use crate::{CoordFloat, Point, MEAN_EARTH_RADIUS};
use num_traits::FromPrimitive;

/// Determine the distance between two geometries using the [haversine formula].
///
/// [haversine formula]: https://en.wikipedia.org/wiki/Haversine_formula
///
/// *Note*: this implementation uses a mean earth radius of 6371.088 km, based on the [recommendation of
/// the IUGG](ftp://athena.fsv.cvut.cz/ZFG/grs80-Moritz.pdf)
pub trait HaversineDistance<T, Rhs = Self> {
    /// Determine the distance between two geometries using the [haversine
    /// formula].
    ///
    /// # Units
    ///
    /// - return value: meters
    ///
    /// # Examples
    ///
    /// ```
    /// use geo::prelude::*;
    /// use geo::point;
    ///
    /// // New York City
    /// let p1 = point!(x: -74.006f64, y: 40.7128f64);
    ///
    /// // London
    /// let p2 = point!(x: -0.1278f64, y: 51.5074f64);
    ///
    /// let distance = p1.haversine_distance(&p2);
    ///
    /// assert_eq!(
    ///     5_570_230., // meters
    ///     distance.round()
    /// );
    /// ```
    ///
    /// [haversine formula]: https://en.wikipedia.org/wiki/Haversine_formula
    fn haversine_distance(&self, rhs: &Rhs) -> T;
}

impl<T> HaversineDistance<T, Point<T>> for Point<T>
where
    T: CoordFloat + FromPrimitive,
{
    fn haversine_distance(&self, rhs: &Point<T>) -> T {
        let two = T::one() + T::one();
        let theta1 = self.y().to_radians();
        let theta2 = rhs.y().to_radians();
        let delta_theta = (rhs.y() - self.y()).to_radians();
        let delta_lambda = (rhs.x() - self.x()).to_radians();
        let a = (delta_theta / two).sin().powi(2)
            + theta1.cos() * theta2.cos() * (delta_lambda / two).sin().powi(2);
        let c = two * a.sqrt().asin();
        T::from(MEAN_EARTH_RADIUS).unwrap() * c
    }
}

#[cfg(test)]
mod test {
    use crate::HaversineDistance;
    use crate::Point;

    #[test]
    fn distance1_test() {
        let a = Point::new(0., 0.);
        let b = Point::new(1., 0.);
        assert_relative_eq!(
            a.haversine_distance(&b),
            111195.0802335329_f64,
            epsilon = 1.0e-6
        );
    }

    #[test]
    fn distance2_test() {
        let a = Point::new(-72.1235, 42.3521);
        let b = Point::new(72.1260, 70.612);
        assert_relative_eq!(
            a.haversine_distance(&b),
            7130580.307935911_f64,
            epsilon = 1.0e-6
        );
    }

    #[test]
    fn distance3_test() {
        // this input comes from issue #100
        let a = Point::new(-77.036585, 38.897448);
        let b = Point::new(-77.009080, 38.889825);
        assert_relative_eq!(
            a.haversine_distance(&b),
            2526.823504306046_f64,
            epsilon = 1.0e-6
        );
    }

    #[test]
    fn distance3_test_f32() {
        // this input comes from issue #100
        let a = Point::<f32>::new(-77.03658, 38.89745);
        let b = Point::<f32>::new(-77.00908, 38.889825);
        assert_relative_eq!(a.haversine_distance(&b), 2526.8354_f32, epsilon = 1.0e-6);
    }
}