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
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193

// SPDX-License-Identifier: MIT
/*
 * Copyright (c) [2023 - Present] Emily Matheys <emilymatt96@gmail.com>
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

use nalgebra::{Point2, RealField, Scalar};
use num_traits::Float;

#[inline]
fn half_angle_sine_squared<T>(input: T) -> T
where
    T: Float,
{
    (input.to_radians() / (T::one() + T::one())).sin().powi(2)
}

/// Calculates the Haversine distance between two points on a sphere using floating-point arithmetic.
///
/// # Arguments
/// * `point_a`: A [`Point2'] representing the first geographical point.
/// * `point_b`: A [`Point2`] representing the second geographical point.
/// * `sphere_radius`: A `T` representing the radius of the sphere, typically the Earth's radius in kilometers or miles.
///
/// # Generics
/// `T`: Either an [`prim@f32`] or [`prim@f64`]
///
/// # Returns
/// A 'T', the distance between `point_a` and `point_b` along the surface of the sphere, using the Haversine formula.
#[cfg_attr(
    feature = "tracing",
    tracing::instrument("Calculate Haversine Distance", skip_all)
)]
pub fn calculate_haversine_distance<T>(
    point_a: Point2<T>,
    point_b: Point2<T>,
    sphere_radius: T,
) -> T
where
    T: Scalar + Float,
{
    let delta_lat = point_b.x - point_a.x;
    let delta_lon = point_b.y - point_a.y;

    let lat1_radians = point_a.x.to_radians();
    let lat2_radians = point_b.x.to_radians();

    let basic_haversine = half_angle_sine_squared(delta_lat)
        + half_angle_sine_squared(delta_lon) * lat1_radians.cos() * lat2_radians.cos();

    let inverse_haversine = (T::one() + T::one())
        * basic_haversine
            .sqrt()
            .atan2((T::one() - basic_haversine).sqrt());

    sphere_radius * inverse_haversine
}

/// Calculates the initial bearing (forward azimuth) from the first point to the second point.
///
/// This function computes the initial bearing, or forward azimuth, between two points on the surface
/// of a sphere, assuming a spherical model. The bearing is the direction one must travel
/// from the first point to reach the second point, expressed as an angle from North (0 radians)
/// in a clockwise direction.
///
/// # Arguments
/// * `point_a`: A [`Point2`] representing the starting geographical point (latitude and longitude).
/// * `point_b`: A [`Point2`] representing the destination geographical point (latitude and longitude).
///
/// # Generics
/// `T`: Either an [`prim@f32`] or [`prim@f64`]
///
/// # Returns
/// * A value that representing the initial bearing from `point_a` to `point_b`, in radians.
/// The result is normalized to a range of 0 to 2 PI radians.
#[cfg_attr(
    feature = "tracing",
    tracing::instrument("Calculate Bearing Between Points", skip_all)
)]
pub fn calculate_sphere_bearing<T>(point_a: Point2<T>, point_b: Point2<T>) -> T
where
    T: Scalar + Float + RealField,
{
    let lat1_rad = point_a.x.to_radians();
    let lat2_rad = point_b.x.to_radians();

    let lon_delta_radians = (point_b.y - point_a.y).to_radians();

    let x = <T as Float>::sin(lon_delta_radians) * <T as Float>::cos(lat2_rad);
    let y = (<T as Float>::cos(lat1_rad) * <T as Float>::sin(lat2_rad))
        - (<T as Float>::sin(lat1_rad)
            * <T as Float>::cos(lat2_rad)
            * <T as Float>::cos(lon_delta_radians));

    (<T as Float>::atan2(x, y) + T::two_pi()) % T::two_pi()
}

#[cfg(feature = "pregenerated")]
macro_rules! impl_haversine_formula {
    ($prec:expr, doc $doc:tt) => {
        ::paste::paste! {
            #[doc = "A " $doc "-precision implementation of the Haversine formula and adjacent utilities"]
            pub mod [<$doc _precision>] {
                #[doc = "Calculates the Haversine distance between two points on a sphere using " $doc "-precision floating-point arithmetic."]
                #[doc = ""]
                #[doc = "# Arguments"]
                #[doc = "* `point_a`: A [`Point2'](nalgebra::Point2) representing the first geographical point."]
                #[doc = "* `point_b`: A [`Point2`](nalgebra::Point2) representing the second geographical point."]
                #[doc = "* `sphere_radius`: The radius of the sphere, typically the Earth's radius in kilometers or miles."]
                #[doc = ""]
                #[doc = "# Returns"]
                #[doc = "A '" $prec "', the distance between `point_a` and `point_b` along the surface of the sphere, using the Haversine formula."]
                pub fn calculate_haversine_distance(point_a: nalgebra::Point2<$prec>, point_b: nalgebra::Point2<$prec>, sphere_radius: $prec) -> $prec {
                    super::calculate_haversine_distance(point_a,point_b,sphere_radius)
                }

                #[doc = "Calculates the initial bearing (forward azimuth) from the first point to the second point."]
                #[doc = ""]
                #[doc = "This function computes the initial bearing, or forward azimuth, between two points on the surface"]
                #[doc = "of a sphere, assuming a spherical model. The bearing is the direction one must travel"]
                #[doc = "from the first point to reach the second point, expressed as an angle from North (0 radians)"]
                #[doc = "in a clockwise direction."]
                #[doc = ""]
                #[doc = "# Arguments"]
                #[doc = "* `point_a`: A [`Point2`](nalgebra::Point2) representing the starting geographical point (latitude and longitude)."]
                #[doc = "* `point_b`: A [`Point2`](nalgebra::Point2) representing the destination geographical point (latitude and longitude)."]
                #[doc = ""]
                #[doc = "# Returns"]
                #[doc = "* A value that representing the initial bearing from `point_a` to `point_b`, in radians. The result is normalized"]
                #[doc = "  to a range of 0 to 2 PI radians."]
                pub fn calculate_sphere_bearing(point_a: nalgebra::Point2<$prec>, point_b: nalgebra::Point2<$prec>) -> $prec {
                    super::calculate_sphere_bearing(point_a,point_b)}
                }
            }
        }
}

#[cfg(feature = "pregenerated")]
impl_haversine_formula!(f32, doc single);
#[cfg(feature = "pregenerated")]
impl_haversine_formula!(f64, doc double);

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

    #[test]
    fn test_distance() {
        let point_a = Point2::new(52.5200, 13.4050); // Berlin, Germany
        let point_b = Point2::new(48.8566, 2.3522); // Paris, France

        let earth_radius_km = 6371.0;
        let distance =
            double_precision::calculate_haversine_distance(point_a, point_b, earth_radius_km);
        let expected_distance = 877.46; // Approximate distance in km
        assert!(
            (distance - expected_distance).abs() < 0.01,
            "Distance between Berlin and Paris should be roughly 877.46 km, found {}",
            distance
        );
    }

    #[test]
    fn test_bearing() {
        let point_a = Point2::new(39.099_91, -94.581213); // Kansas City
        let point_b = Point2::new(38.627_09, -90.200_2); // St Louis

        let bearing = single_precision::calculate_sphere_bearing(point_a, point_b);
        let expected_bearing = 96.51; // Approximate bearing in degrees
        assert!(
            (bearing - expected_bearing.to_radians()).abs() < 0.01,
            "Bearing from Kansas City to St Louis should be roughly 96.51 degrees, found {}",
            bearing.to_degrees()
        );
    }
}