webmerc 0.1.1

A Rust port of globalmaptiles.py
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
241
242
243
244
245
246
247
248
249
250
251
252
253

use std::f64::consts::{PI, TAU, FRAC_PI_4};


#[cfg(test)]
#[macro_use]
extern crate approx;

pub const MAX_ZOOM: u64 = 29;

type D = f64;
type M = f64;
type P = u64;
type Z = u64;
type T = u64;


#[derive(Debug)]
pub struct GlobalMercator {
    tile_size: u64,
    a: f64,
    initial_resolution: f64,
}

impl GlobalMercator {
    /// Create a new instance of the coordinate transformer
    ///
    /// Example:
    /// ```
    ///  let transformer = webmerc::GlobalMercator::new(256);
    ///  assert_eq!(transformer.tile_size(), 256);
    /// ```
    pub fn new(tile_size: u64) -> Self {
        let a = 6378137.0;
        let initial_resolution = TAU * a / (tile_size as f64);

        Self {
            tile_size,
            initial_resolution,
            a,
        }
    }

    /// Get the tile_size used to instantiate the transformer
    ///
    /// Example:
    /// ```
    /// let transformer = webmerc::GlobalMercator::new(256);
    /// assert_eq!(transformer.tile_size(), 256);
    /// ```
    pub fn tile_size(&self) -> u64 {
        self.tile_size
    }

    /// Converts given lat/lon in WGS84 Datum to XY in Spherical Mercator EPSG:3857
    ///
    /// Example:
    /// ```
    /// # #[macro_use] extern crate approx;
    /// let transformer = webmerc::GlobalMercator::new(256);
    /// let (x, y) = transformer.lat_lon_to_meters(10.0, 10.0);
    /// assert_relative_eq!(x, 1113194.91, epsilon = 1e-2);
    /// assert_relative_eq!(y, 1118889.97, epsilon = 1e-2);
    /// ```
    pub fn lat_lon_to_meters(&self, lon: D, lat: D) -> (M, M) {
        let mx = self.a * lon.to_radians();
        let my = self.a * f64::ln(f64::tan(FRAC_PI_4 + lat.to_radians() / 2.0));
        (mx, my)
    }

    /// Converts XY point from Spherical Mercator EPSG:3857 to lat/lon in WGS84 Datum
    ///
    /// ```
    /// # #[macro_use] extern crate approx;
    /// let transformer = webmerc::GlobalMercator::new(256);
    /// let (lon, lat) = transformer.meters_2_lat_lon(-20037508.0, -20037508.0);
    /// assert_relative_eq!(lon, -179.999997, epsilon = 1e-6);
    /// assert_relative_eq!(lat, -85.051129, epsilon = 1e-6);
    /// ```
    pub fn meters_2_lat_lon(&self, mx: M, my: M) -> (D, D) {
        let lon = (mx / self.a).to_degrees();
        let lat = (f64::atan(f64::sinh(my / self.a))).to_degrees();
        (lon, lat)
    }

    /// Converts pixel coordinates in given Zoom level of pyramid to EPSG:3857
    pub fn pixels_to_meters(&self, px: P, py: P, zoom: Z) -> (M, M) {
        let res = self.resolution(zoom);
        let mx = (px as f64) * res - PI * self.a;
        let my = (py as f64) * res - PI * self.a;
        (mx, my)
    }

    /// Converts EPSG:3857 to pyramid pixel coordinates in given Zoom level
    pub fn meters_to_pixels(&self, mx: M, my: M, zoom: Z) -> (P, P) {
        let res = self.resolution(zoom);
        let px = M::floor((mx + PI * self.a) / res) as P;
        let py = M::floor((my + PI * self.a) / res) as P;
        (px, py)
    }

    /// Returns a Tile covering region in given pixel coordinates
    pub fn pixels_to_tile(&self, px: P, py: P) -> (T, T) {
        let tx = f64::ceil(px as f64 / self.tile_size as f64) as u64 - 1;
        let ty = f64::ceil(py as f64 / self.tile_size as f64) as u64 - 1;
        (tx, ty)
    }

    /// Move the origin of pixel coordinates to top-left corner
    pub fn pixels_to_raster(&self, px: P, py: P, zoom: Z) -> (P, P) {
        let map_size = (self.tile_size) << zoom;
        (px, map_size - py)
    }

    /// Returns tile for given mercator coordinates
    pub fn meters_to_tile(&self, mx: M, my: M, zoom: Z) -> (T, T) {
        let (px, py) = self.meters_to_pixels(mx, my, zoom);
        self.pixels_to_tile(px, py)
    }

    /// Returns bounds of the given tile in EPSG:3857 coordinates
    pub fn tile_bounds(&self, tx: T, ty: T, zoom: Z) -> (M, M, M, M) {
        let (minx, miny) = self.pixels_to_meters(tx * self.tile_size, ty * self.tile_size, zoom);
        let (maxx, maxy) = self.pixels_to_meters(
            (tx + 1) * self.tile_size,
            (ty + 1) * self.tile_size,
            zoom,
        );
        (minx, miny, maxx, maxy)
    }

    /// Returns bounds of the given tile in latitude/longitude using WGS84 datum
    pub fn tile_lat_lon_bounds(&self, tx: T, ty: T, zoom: Z) -> (D, D, D, D) {
        let (min_x, min_y, max_x, max_y) = self.tile_bounds(tx, ty, zoom);
        let (min_lon, min_lat) = self.meters_2_lat_lon(min_x, min_y);
        let (max_lon, max_lat) = self.meters_2_lat_lon(max_x, max_y);
        (min_lon, min_lat, max_lon, max_lat)
    }

    /// Resolution (meters/pixel) for given zoom level (measured at Equator)
    pub fn resolution(&self, zoom: Z) -> f64 {
        self.initial_resolution / (2.0f64.powi(zoom as i32))
    }

    /// Maximal scaledown zoom of the pyramid closest to the pixelSize.
    pub fn zoom_for_pixel_size(&self, pixel_size: f64) -> Z {
        for i in 0..=MAX_ZOOM {
            if pixel_size > self.resolution(i) {
                return std::cmp::max(0, i - 1);
            }
        }
        panic!("Invalid pixel_size: {}", pixel_size);
    }

    /// Converts TMS tile coordinates to Google Tile coordinates and vice versa
    pub fn google_tile(&self, tx: T, ty: T, zoom: Z) -> (T, T) {
        (tx, (2u64.pow(zoom as u32) - 1) - ty)
    }

    /// Converts TMS tile coordinates to Microsoft quad_tree
    pub fn quad_tree(&self, tx: T, ty: T, zoom: Z) -> String {
        let mut quad_key = String::new();
        let ty = (f64::powi(2.0, zoom as i32) - 1.0) as T - ty;
        for i in (1..(zoom + 1) as i32).rev() {
            let mut digit = 0;
            let mask = 1 << (i - 1);
            if (tx & mask) != 0 {
                digit += 1;
            }
            if (ty & mask) != 0 {
                digit += 2;
            }
            quad_key.push_str(format!("{}", digit).as_str());
        }
        quad_key
    }
}

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

    #[test]
    fn test_new() {
        let transformer = GlobalMercator::new(256);
        assert_eq!(transformer.tile_size, 256);
    }

    #[test]
    fn lat_lon_to_meters() {
        let transformer = GlobalMercator::new(256);
        let (x, y) = transformer.lat_lon_to_meters(0.0, 0.0);
        assert_relative_eq!(x, 0.0, epsilon = 1e-9);
        assert_relative_eq!(y, 0.0, epsilon = 1e-9);

        let (x, y) = transformer.lat_lon_to_meters(10.0, 10.0);
        assert_relative_eq!(x, 1113194.91, epsilon = 1e-2);
        assert_relative_eq!(y, 1118889.97, epsilon = 1e-2);

        // These are the max lat lon for Google maps. More North or South and numerical errors occur
        let (x, y) = transformer.lat_lon_to_meters(179.999_996_920_671_83, 85.051_128_514_163);
        assert_relative_eq!(x, 20037508.0, epsilon = 1e-2);
        assert_relative_eq!(y, 20037508.0, epsilon = 1e-2);

        let (x, y) = transformer.lat_lon_to_meters(180.0, 85.0);
        assert_relative_eq!(x, 20037508.34, epsilon = 5e-3);
        assert_relative_eq!(y, 19971868.88, epsilon = 5e-3);
        //
        let (x, y) = transformer.lat_lon_to_meters(-180.0, -85.0);
        assert_relative_eq!(x, -20037508.34, epsilon = 5e-3);
        assert_relative_eq!(y, -19971868.88, epsilon = 5e-3);
    }

    #[test]
    fn meters_to_lat_lon() {
        let transformer = GlobalMercator::new(256);
        let (lon, lat) = transformer.meters_2_lat_lon(0.0, 0.0);
        assert_relative_eq!(lon, 0.0, epsilon = f64::EPSILON);
        assert_relative_eq!(lat, 0.0, epsilon = f64::EPSILON);

        let (lon, lat) = transformer.meters_2_lat_lon(-20037508.0, -20037508.0);
        assert_relative_eq!(lon, -179.999997, epsilon = 1e-6);
        assert_relative_eq!(lat, -85.051129, epsilon = 1e-6);

        let (lon, lat) = transformer.meters_2_lat_lon(20037508.0, 20037508.0);
        assert_relative_eq!(lon, 179.999997, epsilon = 1e-6);
        assert_relative_eq!(lat, 85.051129, epsilon = 1e-6);
    }

    #[test]
    fn tile_bounds() {
        let transformer = GlobalMercator::new(256);

        let c = 20_037_508.34;

        for z in 0..MAX_ZOOM {
            let num_tiles = 2u64.pow(z as u32);
            let m = c * 2.0 / (num_tiles as f64) - c;

            let bounds = transformer.tile_bounds(0, 0, z);
            assert_relative_eq!(bounds.0, -c, epsilon = 5e-3);
            assert_relative_eq!(bounds.1, -c, epsilon = 5e-3);
            assert_relative_eq!(bounds.2, m, epsilon = 5e-3);
            assert_relative_eq!(bounds.3, m, epsilon = 5e-3);

            let bounds = transformer.tile_bounds(num_tiles - 1, 0, z);
            assert_relative_eq!(bounds.0, -m, epsilon = 5e-3);
            assert_relative_eq!(bounds.1, -c, epsilon = 5e-3);
            assert_relative_eq!(bounds.2, c, epsilon = 5e-3);
            assert_relative_eq!(bounds.3, m, epsilon = 5e-3);
        }
    }
}