slippy.ml

(* https://wiki.openstreetmap.org/wiki/Slippy_map_tilenames#Zoom_levels *)


let pi = 3.1415926535897932384626433832795028841

let tile_number zoom lat lon =
  let n = 2. ** (float_of_int zoom) in 
  (* return (Math.floor((tt+180)/360*Math.pow(2,zoom1))); *)
  let xtile = int_of_float (floor ((lon +. 180.) /. 360. *. n)) in 
  (* (Math.floor((1-Math.log(Math.tan(lat*Math.PI/180) + 1/Math.cos(lat*Math.PI/180))/Math.PI)/2 *Math.pow(2,zoom2))) *)
  let t = tan (lat *. pi /. 180.) in 
  let c = 1. /. (cos (lat *. pi /. 180.)) in 
  let l = log (t +. c) in 
  let ytile =  int_of_float ((1. -. l /. pi) /. 2. *. n) in 
  (xtile, ytile)

let lat_lon_of_tile_number zoom x y = 
  let x = float_of_int x in 
  let y = float_of_int y in 
  let n = 2. ** (float_of_int zoom) in 
  let lon = x /. n *. 360. -. 180. in 
  let lat = (atan (sinh (pi -. (y /. n) *. (2. *. pi)))) *. (180. /. pi) in 
  (lat, lon)

let%test "osm_tile_encode" = 
  let zoom = 12 in 
  let test_points = [
  ((26.321429, -74.996991), (1194, 1737));
  ((30.094000, -115.405597), (734, 1688));
  ((40.437131, -112.463063), (768, 1544));
  ((30.017105, -70.710589), (1243, 1689));
  ((48.984368, -95.342902), (963, 1406));
  ((33.267652, -105.280272), (850, 1646));
  ((31.255513, -120.857241), (672, 1673));
  ((27.077942, -115.289042), (736, 1727));
  ((41.252644, -95.704571), (959, 1531));
  ((40.188486, -97.798719), (935, 1547));
  ((31.394933, -111.529368), (779, 1671));
  ((41.067748, -111.937154), (774, 1534));
  ((47.227250, -71.769764), (1231, 1436));
  ((42.504822, -107.183008), (828, 1512));
  ((33.961365, -67.391889), (1281, 1636));
  ((28.898628, -89.116261), (1034, 1704));
  ((27.511563, -95.900888), (956, 1722));
  ((45.656904, -93.555989), (983, 1462));
  ((43.346193, -114.418065), (746, 1499));
  ((29.080281, -73.965860), (1206, 1701));
  ((29.384627, -113.426766), (757, 1697));
  ((31.042557, -76.524991), (1177, 1676));
  ((26.315769, -113.755961), (753, 1737));
  ((34.872365, -67.656485), (1278, 1624));
  ((32.443602, -78.692860), (1152, 1657));
  ((48.324991, -106.224055), (839, 1418));
  ((32.422671, -114.979281), (739, 1657));
  ((40.534805, -106.626783), (834, 1542));
  ((38.641610, -77.235209), (1169, 1570));
  ((24.935830, -79.582983), (1142, 1754));
  ((37.127754, -90.230742), (1021, 1592));
  ((30.427954, -74.407584), (1201, 1684));
  ((32.703805, -115.933778), (728, 1653));
  ((37.786583, -71.804438), (1231, 1583));
  ((37.660920, -96.381761), (951, 1584));
  ((28.904582, -95.020379), (966, 1704));
  ((38.164259, -122.339735), (656, 1577));
  ((40.087168, -72.999264), (1217, 1549));
  ((45.888957, -106.202004), (839, 1459));
  ((40.392494, -95.607258), (960, 1544));
  ((39.919404, -103.961870), (865, 1551));
  ((31.923791, -98.581157), (926, 1664));
  ((26.271593, -81.010036), (1126, 1738));
  ((35.315861, -112.135589), (772, 1618));
  ((38.133778, -100.732939), (901, 1578));
  ((32.956867, -97.089128), (943, 1650));
  ((31.541555, -93.318561), (986, 1669));
  ((38.395766, -70.840015), (1241, 1574));
  ((32.482741, -120.399568), (678, 1656));
  ((25.795591, -119.044764), (693, 1744));
  ((32.227758, -116.803720), (719, 1660));
  ((30.079864, -95.450778), (961, 1688));
  ((35.315138, -106.065881), (841, 1618));
  ((31.263688, -90.977309), (1012, 1673));
  ((35.173366, -103.464978), (870, 1620));
  ((29.489563, -89.038553), (1034, 1696));
  ((30.988265, -76.113078), (1182, 1676));
  ((26.299601, -95.866895), (957, 1737));
  ((42.236239, -68.891739), (1264, 1516));
  ((39.864524, -121.139746), (669, 1552));
  ((33.757031, -70.080463), (1250, 1639));
  ((33.339098, -92.010888), (1001, 1645));
  ((28.045350, -112.482246), (768, 1715));
  ((26.806677, -93.654111), (982, 1731));
  ] in 
  List.fold_left (fun res ((lat, lon), (x, y)) -> 
    let res_x, res_y = tile_number zoom lat lon in 
    let _ = if (x != res_x || y != res_y) then Printf.printf "%d %d %d %d\n" x y res_x res_y in
    res && (x = res_x) && (y = res_y)
  ) true test_points

let%test "osm_tile_roundtrip" = 
  let top = 49.3457868 in
  let left = -124.7844079 in
  let right = -66.9513812 in
  let bottom =  24.7433195 in
  let zoom = 12 in 
  let rec test_coords_roundtrip it = 
    if it < 1 then true else (
      let lat = (Random.float (top -. bottom)) +. bottom in 
      let lon = (Random.float (right -. left)) +. left in 
      let x, y = tile_number zoom lat lon in 
      let lat_res, lon_res = lat_lon_of_tile_number zoom x y in 
      if abs (int_of_float (lat -. lat_res)) < 3 && abs (int_of_float (lon -. lon_res)) < 3 then 
        test_coords_roundtrip (it - 1) 
      else
        (Printf.printf "%d: %f %f -> %f %f\n" it lat lon lat_res lon_res; false)
    ) in 
  test_coords_roundtrip 100000
  
  (*
  
  Copyright 2019 Bob Poekert

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
  *)