convert lat/lon to tile x/y and back

pkgs/maps/assert.fnl

@@ -17,8 +17,16 @@
                (.. "\nexpected " ve# "\ngot " va#)
                ))))
 
+(fn expect-near [actual expected]
+  `(let [delta# (math.abs (- ,actual ,expected))
+         e# ,expected
+         a# ,actual]
+     (assert (< delta# 0.00000001)
+             (..  "expected " e# " to be approximately " a#))))
+
+
 (fn define-tests [& body]
   (when _G.RUNNING_TESTS
     `(do ,(unpack body))))
 
-{ : define-tests : expect : expect=  }
+{ : define-tests : expect : expect= : expect-near }

pkgs/maps/tiles.fnl

@@ -2,6 +2,7 @@
 (local { : dict_to_query } (require :http.util))
 (local json (require :json))
 
+(import-macros { : define-tests : expect : expect= : expect-near } :assert)
 (local { : view } (require :fennel))
 
 
@@ -33,3 +34,38 @@
     (print (view headers))
     (print (view (json.decode (stream:get_body_as_string))))))
       
+(fn sinh [x] (/ (- 1 (math.exp (* -2 x))) (* 2 (math.exp (- x)))))
+
+(expect (< (math.abs  (- (sinh 2) 3.626860407847)) 0.001))
+
+(fn tile->latlon [xtile ytile zoom]
+  (let [n (^ 2 zoom)
+        lon-deg (- (/ (* xtile 360) n) 180.0)
+        lat-rad (math.atan
+                 (sinh (* math.pi (- 1 (/ (* 2 ytile) n))))
+                 )]
+
+    (values (/ (* lat-rad 180) math.pi) lon-deg)))
+
+(let [(lat lon) (tile->latlon 0 0 0)]
+  (expect= lon -180)
+  (expect-near lat 85.05112877)
+  )
+
+(let [(lat lon) (tile->latlon 232798 103246 18)]
+  (expect-near lon 139.699401855)
+  (expect-near lat 35.6595278648)
+  )
+
+(fn latlon->tile [lat lon zoom]
+  (let [n (^ 2 zoom)
+        x (* n (/ (+ lon 180) 360))
+        t1 (/ (* lat math.pi) 180)
+        t (math.log (+ (math.tan t1) (/ 1 (math.cos t1))))
+        y (* (- 1 (/ t math.pi)) (/ n 2))]
+    (values x y)))
+
+(let [(x y) (latlon->tile 52.1234 -0.53 17)]
+  (expect= (math.floor x) 65343)
+  (expect= (math.floor y) 43221))
+