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
194
195
196

use super::Location;
use std::f64::consts::PI;
use std::fmt;

/// Distance represents a physical distance in a certain unit.
pub struct Distance(f64);

impl fmt::Display for Distance {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "{} meters", self.meters())
    }
}

impl Distance {
    /// Create a distance in meters.
    pub fn from_meters<P: Into<f64>>(m: P) -> Self {
        return Distance(m.into());
    }

    /// Return the distance in meters.
    pub fn meters(&self) -> f64 {
        return self.0;
    }
}

/// DistanceResult is a struct to hold results from Vincenty's inverse formula.
pub struct DistanceResult {
    pub distance: Distance,
    _initial_bearing: Option<f64>,
    _final_bearing: Option<f64>,
    _iterations: i32,
}

/// Compute the Vincenty Inverse formula on two points 'start' and 'end'.
pub fn vincenty_inverse(
    start: &Location,
    end: &Location,
    _accuracy: f64,
    _precision: f64,
) -> Result<DistanceResult, String> {
    // WGS-84 geocentric datum parameters
    let a: f64 = 6378137.0; // Semi-major axis
    let b: f64 = 6356752.314245; // Semi-minor axis
    let f: f64 = 1.0 / 298.257223563; // Inverse-flattening

    // Start and end points in Radians
    let p1 = (start.0.to_radians(), start.1.to_radians());
    let p2 = (end.0.to_radians(), end.1.to_radians());

    // Difference in longitudes
    let l = p2.1 - p1.1;

    // u = 'reduced latitude'
    let (tan_u1, tan_u2) = ((1.0 - f) * p1.0.tan(), (1.0 - f) * p2.0.tan());
    let (cos_u1, cos_u2) = (
        1.0 / (1.0 + tan_u1 * tan_u1).sqrt(),
        1.0 / (1.0 + tan_u2 * tan_u2).sqrt(),
    );
    let (sin_u1, sin_u2) = (tan_u1 * cos_u1, tan_u2 * cos_u2);

    // First approximation
    let mut lambda = l;
    let mut iter_limit = 100;
    let mut cos_sq_alpha = 0.0;
    let (mut sin_sigma, mut cos_sigma, mut cos2_sigma_m, mut sigma) = (0.0, 0.0, 0.0, 0.0);
    let (mut _sin_lambda, mut _cos_lambda) = (0.0, 0.0);
    loop {
        _sin_lambda = lambda.sin();
        _cos_lambda = lambda.cos();
        let sin_sq_sigma = (cos_u2 * _sin_lambda) * (cos_u2 * _sin_lambda)
            + (cos_u1 * sin_u2 - sin_u1 * cos_u2 * _cos_lambda)
                * (cos_u1 * sin_u2 - sin_u1 * cos_u2 * _cos_lambda);

        // Points coincide
        if sin_sq_sigma == 0.0 {
            break;
        }

        sin_sigma = sin_sq_sigma.sqrt();
        cos_sigma = sin_u1 * sin_u2 + cos_u1 * cos_u2 * _cos_lambda;
        sigma = sin_sigma.atan2(cos_sigma);
        let sin_alpha = cos_u1 * cos_u2 * _sin_lambda / sin_sigma;
        cos_sq_alpha = 1.0 - sin_alpha * sin_alpha;
        cos2_sigma_m = if cos_sq_alpha != 0.0 {
            cos_sigma - 2.0 * sin_u1 * sin_u2 / cos_sq_alpha
        } else {
            0.0
        };
        let c = f / 16.0 * cos_sq_alpha * (4.0 + f * (4.0 - 3.0 * cos_sq_alpha));
        let lambda_prime = lambda;
        lambda = l
            + (1.0 - c)
                * f
                * sin_alpha
                * (sigma
                    + c * sin_sigma
                        * (cos2_sigma_m
                            + c * cos_sigma * (-1.0 + 2.0 * cos2_sigma_m * cos2_sigma_m)));

        iter_limit -= 1;
        if (lambda - lambda_prime).abs() > 1e-12 && iter_limit > 0 {
            continue;
        }

        break;
    }

    if iter_limit <= 0 {
        return Err("formula failed to converge".to_string());
    }

    let u_sq = cos_sq_alpha * (a * a - b * b) / (b * b);
    let cap_a = 1.0 + u_sq / 16384.0 * (4096.0 + u_sq * (-768.0 + u_sq * (320.0 - 175.0 * u_sq)));
    let cap_b = u_sq / 1024.0 * (256.0 + u_sq * (-128.0 + u_sq * (74.0 - 47.0 * u_sq)));

    let delta_sigma = cap_b
        * sin_sigma
        * (cos2_sigma_m
            + cap_b / 4.0
                * (cos_sigma * (-1.0 + 2.0 * cos2_sigma_m * cos2_sigma_m)
                    - cap_b / 6.0
                        * cos2_sigma_m
                        * (-3.0 + 4.0 * sin_sigma * sin_sigma)
                        * (-3.0 + 4.0 * cos2_sigma_m * cos2_sigma_m)));
    let s = b * cap_a * (sigma - delta_sigma);

    let mut alpha_1 = cos_u2 * _sin_lambda.atan2(cos_u1 * sin_u2 - sin_u1 * cos_u2 * _cos_lambda);
    let mut alpha_2 = cos_u1 * _sin_lambda.atan2(-sin_u1 * cos_u2 + cos_u1 * sin_u2 * _cos_lambda);

    alpha_1 = (alpha_1 + 2.0 * PI) % (2.0 * PI);
    alpha_2 = (alpha_2 + 2.0 * PI) % (2.0 * PI);

    Ok(DistanceResult {
        distance: Distance::from_meters((s * 1000.0).round() / 1000.0),
        _initial_bearing: if s == 0.0 {
            None
        } else {
            Some(alpha_1.to_degrees())
        },
        _final_bearing: if s == 0.0 {
            None
        } else {
            Some(alpha_2.to_degrees())
        },
        _iterations: iter_limit,
    })
}

/// Get the center of a list of coordinates.
pub fn center_of_coords(coords: &[&Location]) -> Location {
    let (mut x, mut y, mut z) = (0.0, 0.0, 0.0);

    for loc in coords.iter() {
        let lat = loc.0.to_radians();
        let lon = loc.1.to_radians();

        x += lat.cos() * lon.cos();
        y += lat.cos() * lon.sin();
        z += lat.sin();
    }

    let number_of_locations = coords.len() as f64;
    x /= number_of_locations;
    y /= number_of_locations;
    z /= number_of_locations;

    let hyp = (x * x + y * y).sqrt();
    let lon = y.atan2(x);
    let lat = z.atan2(hyp);

    // Convert to degrees and round to 6 digits
    let lon = lon.to_degrees();
    let lon = (lon * 10.0_f64.powi(6)).round() / 10.0_f64.powi(6);

    let lat = lat.to_degrees();
    let lat = (lat * 10.0_f64.powi(6)).round() / 10.0_f64.powi(6);

    Location(lat, lon)
}

/// Implementation of Haversine distance between two points.
pub fn haversine_distance_to(start: &Location, end: &Location) -> Distance {
    let haversine_fn = |theta: f64| (1.0 - theta.cos()) / 2.0;

    let phi1 = start.latitude().to_radians();
    let phi2 = end.latitude().to_radians();
    let lambda1 = start.longitude().to_radians();
    let lambda2 = end.longitude().to_radians();

    let hav_delta_phi = haversine_fn(phi2 - phi1);
    let hav_delta_lambda = phi1.cos() * phi2.cos() * haversine_fn(lambda2 - lambda1);
    let total_delta = hav_delta_phi + hav_delta_lambda;

    let dist = (2.0 * 6371e3 * total_delta.sqrt().asin() * 1000.0).round() / 1000.0;
    Distance::from_meters(dist)
}