1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129

use crate::{CoordFloat, Point};
use geographiclib_rs::{DirectGeodesic, Geodesic, InverseGeodesic};

/// Returns a new Point along a route between two existing points on an ellipsoidal model of the earth

pub trait GeodesicIntermediate<T: CoordFloat> {
    /// Returns a new Point along a route between two existing points on an ellipsoidal model of the earth
    ///
    /// # Examples
    ///
    /// ```
    /// # #[macro_use] extern crate approx;
    /// #
    /// use geo::GeodesicIntermediate;
    /// use geo::Point;
    ///
    /// let p1 = Point::new(10.0, 20.0);
    /// let p2 = Point::new(125.0, 25.0);
    /// let i20 = p1.geodesic_intermediate(&p2, 0.2);
    /// let i50 = p1.geodesic_intermediate(&p2, 0.5);
    /// let i80 = p1.geodesic_intermediate(&p2, 0.8);
    /// let i20_should = Point::new(29.842907, 29.951445);
    /// let i50_should = Point::new(65.879360, 37.722253);
    /// let i80_should = Point::new(103.556796, 33.506196);
    /// assert_relative_eq!(i20, i20_should, epsilon = 1.0e-6);
    /// assert_relative_eq!(i50, i50_should, epsilon = 1.0e-6);
    /// assert_relative_eq!(i80, i80_should, epsilon = 1.0e-6);
    /// ```

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

impl GeodesicIntermediate<f64> for Point {
    fn geodesic_intermediate(&self, other: &Point, f: f64) -> Point {
        let g = Geodesic::wgs84();
        let (total_distance, azi1, _azi2, _a12) =
            g.inverse(self.y(), self.x(), other.y(), other.x());
        let distance = total_distance * f;
        let (lat2, lon2) = g.direct(self.y(), self.x(), azi1, distance);

        Point::new(lon2, lat2)
    }

    fn geodesic_intermediate_fill(
        &self,
        other: &Point,
        max_dist: f64,
        include_ends: bool,
    ) -> Vec<Point> {
        let g = Geodesic::wgs84();
        let (total_distance, azi1, _azi2, _a12) =
            g.inverse(self.y(), self.x(), other.y(), other.x());

        if total_distance <= max_dist {
            return if include_ends {
                vec![*self, *other]
            } else {
                vec![]
            };
        }

        let number_of_points = (total_distance / max_dist).ceil();
        let interval = 1.0 / number_of_points;

        let mut current_step = interval;
        let mut points = if include_ends { vec![*self] } else { vec![] };

        while current_step < 1.0 {
            let (lat2, lon2) = g.direct(self.y(), self.x(), azi1, total_distance * current_step);
            let point = Point::new(lon2, lat2);
            points.push(point);
            current_step += interval;
        }

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

        points
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use approx::assert_relative_eq;

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

    #[test]
    fn various_f_values_test() {
        let p1 = Point::new(10.0, 20.0);
        let p2 = Point::new(125.0, 25.0);
        let i20 = p1.geodesic_intermediate(&p2, 0.2);
        let i50 = p1.geodesic_intermediate(&p2, 0.5);
        let i80 = p1.geodesic_intermediate(&p2, 0.8);
        let i20_should = Point::new(29.842907, 29.951445);
        let i50_should = Point::new(65.879360, 37.722253);
        let i80_should = Point::new(103.556796, 33.506196);
        assert_relative_eq!(i20, i20_should, epsilon = 1.0e-6);
        assert_relative_eq!(i50, i50_should, epsilon = 1.0e-6);
        assert_relative_eq!(i80, i80_should, epsilon = 1.0e-6);
    }

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