geo 0.9.1

Geospatial primitives and algorithms
Documentation 
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use num_traits::{Float, FromPrimitive};
use ::Point;

/// Returns a new Point along a great circle route between two existing points

pub trait HaversineIntermediate<T: Float> {
    /// Returns a new Point along a great circle route between two existing points.
    ///
    /// ```
    /// # extern crate geo;
    /// # #[macro_use] extern crate approx;
    /// #
    /// use geo::Point;
    /// use geo::algorithm::haversine_intermediate::HaversineIntermediate;
    ///
    /// # fn main() {
    /// let p1 = Point::<f64>::new(10.0,  20.0);
    /// let p2 = Point::<f64>::new(125.0, 25.0);
    /// let i20        = p1.haversine_intermediate(&p2, 0.2);
    /// let i50        = p1.haversine_intermediate(&p2, 0.5);
    /// let i80        = p1.haversine_intermediate(&p2, 0.8);
    /// let i20_should = Point::new(29.8,  29.9);
    /// let i50_should = Point::new(65.8,  37.7);
    /// let i80_should = Point::new(103.5, 33.5);
    /// assert_relative_eq!(i20.x(), i20_should.x(), epsilon=0.2);
    /// assert_relative_eq!(i20.y(), i20_should.y(), epsilon=0.2);
    /// assert_relative_eq!(i50.x(), i50_should.x(), epsilon=0.2);
    /// assert_relative_eq!(i50.y(), i50_should.y(), epsilon=0.2);
    /// assert_relative_eq!(i80.x(), i80_should.x(), epsilon=0.2);
    /// assert_relative_eq!(i80.y(), i80_should.y(), epsilon=0.2);
    /// # }
    /// ```

    fn haversine_intermediate(&self, other: &Point<T>, f: T) -> Point<T>;
    fn haversine_intermediate_fill(&self, other: &Point<T>, max_dist: T, include_ends: bool) -> Vec<Point<T>>;
}

impl<T> HaversineIntermediate<T> for Point<T>
where
    T: Float + FromPrimitive,
{
    fn haversine_intermediate(&self, other: &Point<T>, f: T) -> Point<T> {
        let params = get_params(&self, &other);
        let point  = get_point(&params, f);
        point
    }

    fn haversine_intermediate_fill(&self, other: &Point<T>, max_dist: T, include_ends: bool) -> Vec<Point<T>> {
        let params = get_params(&self, &other);
        let HaversineParams { d, .. } = params;

        let total_distance   = d * T::from(6371000.0).unwrap();

        if total_distance <= max_dist {
            if include_ends {
                return vec![self.clone(), other.clone()];
            } else {
                return vec![];
            }
        }

        let number_of_points = (total_distance / max_dist).ceil();
        let interval         = T::one() / number_of_points;

        let mut current_step = interval;
        let mut points = if include_ends { vec![self.clone()] } else { vec![] };

        while current_step < T::one() {
            let point  = get_point(&params, current_step);
            points.push(point);
            current_step = current_step + interval;
        }

        if include_ends {
            points.push(other.clone());
        }

        points
    }
}


struct HaversineParams<T: Float + FromPrimitive> {
    d: T, n: T, o: T, p: T, q: T, r: T, s: T,
}


fn get_point<T: Float + FromPrimitive>(params: &HaversineParams<T>, f: T) -> Point<T> {
    let one = T::one();

    let HaversineParams { d, n, o, p, q, r, s } = *params;

    let a = ((one - f) * d).sin() / d.sin();
    let b = (f * d).sin() / d.sin();

    let x = a * n + b * o;
    let y = a * p + b * q;
    let z = a * r + b * s;

    let lat = z.atan2(x.hypot(y));
    let lon = y.atan2(x);

    Point::new(lon.to_degrees(), lat.to_degrees())
}


fn get_params<T: Float + FromPrimitive>(p1: &Point<T>, p2: &Point<T>) -> HaversineParams<T> {
    let one = T::one();
    let two = one + one;

    let lat1 = p1.y().to_radians();
    let lon1 = p1.x().to_radians();
    let lat2 = p2.y().to_radians();
    let lon2 = p2.x().to_radians();

    let (lat1_sin, lat1_cos) = lat1.sin_cos();
    let (lat2_sin, lat2_cos) = lat2.sin_cos();
    let (lon1_sin, lon1_cos) = lon1.sin_cos();
    let (lon2_sin, lon2_cos) = lon2.sin_cos();

    let m = lat1_cos * lat2_cos;

    let n = lat1_cos * lon1_cos;
    let o = lat2_cos * lon2_cos;
    let p = lat1_cos * lon1_sin;
    let q = lat2_cos * lon2_sin;

    let k = (
        ((lat1 - lat2) / two).sin().powi(2) +
        m * ((lon1 - lon2) / two).sin().powi(2)
    ).sqrt();

    let d = two * k.asin();

    HaversineParams { d, n, o, p, q, r: lat1_sin, s: lat2_sin }
}


#[cfg(test)]
mod test {
    use super::*;
    use algorithm::haversine_intermediate::HaversineIntermediate;

    #[test]
    fn f_is_zero_or_one_test() {
        let p1 = Point::<f64>::new(10.0, 20.0);
        let p2 = Point::<f64>::new(15.0, 25.0);
        let i0   = p1.haversine_intermediate(&p2, 0.0);
        let i100 = p1.haversine_intermediate(&p2, 1.0);
        assert_relative_eq!(i0.x(), p1.x(), epsilon=1.0e-6);
        assert_relative_eq!(i0.y(), p1.y(), epsilon=1.0e-6);
        assert_relative_eq!(i100.x(), p2.x(), epsilon=1.0e-6);
        assert_relative_eq!(i100.y(), p2.y(), epsilon=1.0e-6);
    }

    #[test]
    fn various_f_values_test() {
        let p1 = Point::<f64>::new(10.0,  20.0);
        let p2 = Point::<f64>::new(125.0, 25.0);
        let i20  = p1.haversine_intermediate(&p2, 0.2);
        let i50  = p1.haversine_intermediate(&p2, 0.5);
        let i80  = p1.haversine_intermediate(&p2, 0.8);
        let i20_should = Point::new(29.83519,  29.94841);
        let i50_should = Point::new(65.87471,  37.72201);
        let i80_should = Point::new(103.56036, 33.50518);
        assert_relative_eq!(i20.x(), i20_should.x(), epsilon=0.2);
        assert_relative_eq!(i20.y(), i20_should.y(), epsilon=0.2);
        assert_relative_eq!(i50.x(), i50_should.x(), epsilon=0.2);
        assert_relative_eq!(i50.y(), i50_should.y(), epsilon=0.2);
        assert_relative_eq!(i80.x(), i80_should.x(), epsilon=0.2);
        assert_relative_eq!(i80.y(), i80_should.y(), epsilon=0.2);
    }

    #[test]
    fn should_be_north_pole_test() {
        let p1 = Point::<f64>::new(0.0,   10.0);
        let p2 = Point::<f64>::new(180.0, 10.0);
        let i50  = p1.haversine_intermediate(&p2, 0.5);
        let i50_should = Point::new(90.0, 90.0);
        assert_relative_eq!(i50.x(), i50_should.x(), epsilon=1.0e-6);
        assert_relative_eq!(i50.y(), i50_should.y(), epsilon=1.0e-6);
    }

    #[test]
    fn should_be_start_end_test() {
        let p1 = Point::<f64>::new(30.0, 40.0);
        let p2 = Point::<f64>::new(40.0, 50.0);
        let max_dist = 1500000.0; // meters
        let include_ends = true;
        let route = p1.haversine_intermediate_fill(&p2, max_dist, include_ends);
        assert_eq!(route, vec![p1, p2]);
    }

    #[test]
    fn should_add_i50_test() {
        let p1 = Point::<f64>::new(30.0, 40.0);
        let p2 = Point::<f64>::new(40.0, 50.0);
        let max_dist = 1000000.0; // meters
        let include_ends = true;
        let i50 = p1.clone().haversine_intermediate(&p2, 0.5);
        let route = p1.haversine_intermediate_fill(&p2, max_dist, include_ends);
        assert_eq!(route, vec![p1, i50, p2]);
    }

    #[test]
    fn should_add_i25_i50_i75_test() {
        let p1 = Point::<f64>::new(30.0, 40.0);
        let p2 = Point::<f64>::new(40.0, 50.0);
        let max_dist = 400000.0; // meters
        let include_ends = true;
        let i25 = p1.clone().haversine_intermediate(&p2, 0.25);
        let i50 = p1.clone().haversine_intermediate(&p2, 0.5);
        let i75 = p1.clone().haversine_intermediate(&p2, 0.75);
        let route = p1.haversine_intermediate_fill(&p2, max_dist, include_ends);
        assert_eq!(route, vec![p1, i25, i50, i75, p2]);
    }
}