blh 0.3.0

conversion between geodetic and geocentric coordinates
Documentation 
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
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240

extern crate euclid;
#[macro_use] extern crate approx;

use euclid::{Degrees, Radians};
use approx::ApproxEq;

pub mod ellipsoid;
use ellipsoid::*;

use std::f64;
use std::marker::PhantomData;
use std::fmt::{self, Debug, Formatter};

trait DegreesExt<T> {
    fn to_radians(&self) -> Radians<T>;
}

impl DegreesExt<f64> for Degrees<f64> {
    #[inline]
    fn to_radians(&self) -> Radians<f64> {
        Radians::new(self.get() * f64::consts::PI / 180.0)
    }
}

trait RadiansExt<T> {
    fn to_degrees(&self) -> Degrees<T>;
}

impl RadiansExt<f64> for Radians<f64> {
    #[inline]
    fn to_degrees(&self) -> Degrees<f64> {
        Degrees::new(self.get() / f64::consts::PI * 180.0)
    }
}

/// A position on the earth represented by latitude [rad], longitude [rad], and geoid height [m].
pub struct GeodeticCoord<E> {
    pub lat: Radians<f64>,
    pub lon: Radians<f64>,
    pub hgt: f64,
    _ellipsoid: PhantomData<E>,
}

impl<E> GeodeticCoord<E> {
    /// Construct a geodetic coord with latitude/longitude in radians.
    #[inline]
    pub fn new(lat: Radians<f64>, lon: Radians<f64>, hgt: f64) -> Self {
        GeodeticCoord {
            lat: lat,
            lon: lon,
            hgt: hgt,
            _ellipsoid: PhantomData,
        }
    }

    /// Construct a geodetic coord with latitude/longitude in degrees.
    #[inline]
    pub fn from_degrees(lat: Degrees<f64>, lon: Degrees<f64>, hgt: f64) -> Self {
        GeodeticCoord {
            lat: lat.to_radians(),
            lon: lon.to_radians(),
            hgt: hgt,
            _ellipsoid: PhantomData,
        }
    }
}

impl<E> PartialEq for GeodeticCoord<E> {
    #[inline]
    fn eq(&self, other: &GeodeticCoord<E>) -> bool {
        let &GeodeticCoord { lat: slat, lon: slon, hgt: shgt, .. } = self;
        let &GeodeticCoord { lat: olat, lon: olon, hgt: ohgt, .. } = other;
        (slat, slon, shgt) == (olat, olon, ohgt)
    }
}

impl<E> ApproxEq for GeodeticCoord<E> {
    type Epsilon = f64;

    fn default_epsilon() -> f64 {
        f64::default_epsilon()
    }

    fn default_max_relative() -> f64 {
        f64::default_epsilon()
    }

    fn default_max_ulps() -> u32 {
        f64::default_max_ulps()
    }

    fn relative_eq(&self, other: &GeodeticCoord<E>, epsilon: f64, max_relative: f64) -> bool {
        self.lat.get().relative_eq(&other.lat.get(), epsilon, max_relative) &&
            self.lon.get().relative_eq(&other.lon.get(), epsilon, max_relative) &&
            self.hgt.relative_eq(&other.hgt, epsilon, max_relative)
    }

    fn ulps_eq(&self, other: &GeodeticCoord<E>, epsilon: f64, max_ulps: u32) -> bool {
        self.lat.get().ulps_eq(&other.lat.get(), epsilon, max_ulps) &&
            self.lon.get().ulps_eq(&other.lon.get(), epsilon, max_ulps) &&
            self.hgt.ulps_eq(&other.hgt, epsilon, max_ulps)
    }
}

impl<E: Ellipsoid> Debug for GeodeticCoord<E> {
    fn fmt(&self, f: &mut Formatter) -> Result<(), fmt::Error> {
        f.debug_struct(&format!("GeodeticCoord<{}>", E::name()))
            .field("lat", &self.lat)
            .field("lon", &self.lon)
            .field("hgt", &self.hgt)
            .finish()
    }
}

impl<E> Clone for GeodeticCoord<E> {
    #[inline]
    fn clone(&self) -> Self {
        GeodeticCoord {
            lat: self.lat,
            lon: self.lon,
            hgt: self.hgt,
            _ellipsoid: PhantomData,
        }
    }
}

impl<E> Copy for GeodeticCoord<E> {
}

/// A position on the earth represented by x [m], y [m], and z [m] in geocentric (ECEF) coordinate.
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct GeocentricCoord {
    pub x: f64,
    pub y: f64,
    pub z: f64,
}

impl GeocentricCoord {
    #[inline]
    pub fn new(x: f64, y: f64, z: f64) -> Self {
        GeocentricCoord {
            x: x,
            y: y,
            z: z,
        }
    }
}

impl ApproxEq for GeocentricCoord {
    type Epsilon = f64;

    fn default_epsilon() -> f64 {
        f64::default_epsilon()
    }

    fn default_max_relative() -> f64 {
        f64::default_epsilon()
    }

    fn default_max_ulps() -> u32 {
        f64::default_max_ulps()
    }

    fn relative_eq(&self, other: &GeocentricCoord, epsilon: f64, max_relative: f64) -> bool {
        self.x.relative_eq(&other.x, epsilon, max_relative) &&
            self.y.relative_eq(&other.y, epsilon, max_relative) &&
            self.z.relative_eq(&other.z, epsilon, max_relative)
    }

    fn ulps_eq(&self, other: &GeocentricCoord, epsilon: f64, max_ulps: u32) -> bool {
        self.x.ulps_eq(&other.x, epsilon, max_ulps) &&
            self.y.ulps_eq(&other.y, epsilon, max_ulps) &&
            self.z.ulps_eq(&other.z, epsilon, max_ulps)
    }
}

impl<E: Ellipsoid> From<GeocentricCoord> for GeodeticCoord<E> {
    fn from(xyz: GeocentricCoord) -> GeodeticCoord<E> {
        if xyz ==
            (GeocentricCoord {
                x: 0.0,
                y: 0.0,
                z: 0.0,
            })
        {
            GeodeticCoord::new(Radians::new(0.0), Radians::new(0.0), 0.0)
        } else {
            let GeocentricCoord { x, y, z } = xyz;

            let radius = E::radius();
            let polar_radius = E::polar_radius();

            // eccentricity
            let e = E::ecc();
            // second eccentricity ^2
            let e2 = E::second_ecc().powi(2);

            let t = f64::atan2(radius * z, polar_radius * f64::sqrt(x.powi(2) + y.powi(2)));

            let lat = f64::atan2(z + e2 * polar_radius * f64::sin(t).powi(3),
                                 f64::sqrt(x.powi(2) + y.powi(2)) -
                                 e.powi(2) * radius * f64::cos(t).powi(3));

            // Prime vertical's radius of carvative
            let pv_rc = radius / f64::sqrt(1.0 - e.powi(2) * f64::sin(lat).powi(2));

            let lon = f64::atan2(y, x);
            let hgt = f64::sqrt((x.powi(2) + y.powi(2))) / f64::cos(lat) - pv_rc;

            GeodeticCoord::new(Radians::new(lat), Radians::new(lon), hgt)
        }
    }
}

impl<E: Ellipsoid> From<GeodeticCoord<E>> for GeocentricCoord {
    fn from(blh: GeodeticCoord<E>) -> GeocentricCoord {
        let (lat, lon) = (blh.lat.get(), blh.lon.get());

        // Prime vertical's radius of carvative
        let pv_rc = E::radius() / f64::sqrt(1.0 - E::ecc().powi(2) * f64::sin(lat).powi(2));

        GeocentricCoord {
            x: (pv_rc + blh.hgt) * f64::cos(lat) * f64::cos(lon),
            y: (pv_rc + blh.hgt) * f64::cos(lat) * f64::sin(lon),
            z: (pv_rc * (1.0 - E::ecc().powi(2)) + blh.hgt) * f64::sin(lat),
        }
    }
}

#[test]
fn test_pos_conversion() {
    use ellipsoid::WGS84;

    let blh = GeodeticCoord::<WGS84>::from_degrees(Degrees::new(31.0), Degrees::new(131.0), 100.0);
    assert_relative_eq!(GeodeticCoord::from(GeocentricCoord::from(blh)), blh);

    let xyz = GeocentricCoord::new(-3957314.620, 3310254.137, 3737540.043);
    assert_relative_eq!(GeocentricCoord::from(GeodeticCoord::<WGS84>::from(xyz)), xyz,
        epsilon = 0.1);
}