mars is a sphere: account for wrapping x values and scaling when y>0

rover.fnl

@@ -5,20 +5,29 @@
 (macro expect [text actual expected]
   `(let [actual# ,actual]
      (or (match actual#
-           ,expected true
-           _# false)
+           ,expected true)
          (assert false (view {
                               :text ,text
-                              :expected ,expected
+                              :expected ,(view expected)
                               :actual actual#
                               })))))
 
+
+(fn wrap-longitude [x]
+  (if (<= x -180) (wrap-longitude (+ x 360))
+      (< 180 x)   (wrap-longitude (- x 360))
+      x))
+
 (fn drive [{: x : y : direction} distance]
-  (match direction
-    :n {:y (+ y distance)}
-    :s {:y (- y distance)}
-    :w {:x (- x distance)}
-    :e {:x (+ x distance)}))
+  (let [distance
+        (if (. {:w true :e true} direction)
+            (/  distance (math.cos (/ (* math.pi y) 180)))
+            distance)]
+    (match direction
+      :n {:y (+ y distance)}
+      :s {:y (- y distance)}
+      :w {:x (wrap-longitude (- x distance))}
+      :e {:x (wrap-longitude (+ x distance))})))
 
 (fn turn-left [direction]
   {:direction
@@ -117,6 +126,30 @@
           (execute r [:l :l :f :f :f :r :f :b])
           {:x 1 :y 4 :direction :e}))
 
+;; Circumference of mars is  3,376.2km (about half that of earth).
+;; We choose the unit of distance to be equal to one  degree at the equator
+;; (about 60km), so if we travel the same linear distance at a higher
+;; latitude, we will move be a larger number of degrees
+
+(expect "At 60 degrees latitude, one unit of drive is two degrees"
+        (execute (rover 0 60 :e) [:f])
+        (where {:x x :y 60 :direction :e}
+               (< (math.abs (- x 2)) 0.000001)
+               ))
+
+(expect "At 45 degrees latitude, one unit of drive is (sqrt 2) degrees"
+        (execute (rover 0 45 :e) [:f])
+        (where {:x x } (< (math.abs (- x 1.4141)) 0.001)))
+
+;; valid longitudes are -180 .. 180
+
+(expect "Longitude wraps from positive to  negative when travelling west"
+        (execute (rover -179 0 :w) [:f :f :f])
+        {:x 178 :y 0 :direction :w})
+
+(expect "Longitude wraps from negative to positive when travelling east"
+        (execute (rover 179 0 :e) [:f :f :f])
+        {:x -178 :y 0 :direction :e})
 
 "if we travel west past x=-180, x becomes positive 180"
 "if we travel east past x=180, x becomes -180"