math.cljs

(def tau (* 2 Math/PI))

(defn clamp [n minimum maximum]
  (min (max n minimum) maximum))

(defn sph-v [long lat alt]; A polar vector
  {:longitude (mod long 360)
   :latitude (clamp lat -90 90)
   :altitude (max alt 0)})

(defn uniform [n]; A list of equidistant fractions from 0 to 1
  (map #(/ % n) (range n)))

(defn long-transform [n]
  (* tau n))

(defn lat-transform [n]
  (Math/acos (- (* 2 n) 1)))

(defn sphere-hmap [resolution]; A list of uniformly distributed vectors on the surface of a sphere
  (for [u (map uniform (range n))
        v (map uniform (range n))]
    (sph-v (long-transform u) (lat-transform v) 1)))

(defn pythagorean [x y]
  (Math/sqrt (+ (Math/sqr x) (Math/sqr y))))

(defn great-circles [theta phi]; Distance across the sphere surface
  (*  2
      (Math/arcsin2 (Math/sqrt
        (Math/sqr (Math/sin (/ phi 2)))
        (*  (Math/cos phi)
            (Math/sqr (Math/sin (/ theta 2))))))))

(defn surface-distance [along alat ar blong blat br]; Distance across the sphere surface with height difference
  (pythagorean
    (great-circles
      (Math/abs (mod (- along blong) 180))
      (Math/abs (- alat blat)))
    (Math/abs (- ar br))))

(defn square-smooth [sphere long lat r]; Smoothing function over a sphere
  (map
    (fn [p]
      (update p :altitude ;for each point, change the height
        (fn [n]
          (*  (/ (+ n r) 2) ;mean of the point we're smoothing and the reference point
              (let [x (surface-distance ; the further the point we're smoothing is from the reference point, the less we alter it
                      long lat r
                      (:longitude p) (:latitude p) (:altitude p))]
                (Math/pow 2 (Math/pow (* -1 x) 2)))))))
    sphere))

(defn smooth-sphere [sphere];processes a whole sphere and
  (reduce
    (fn [sph p];for each point in the sphere
      (map #(update % :altitude
              (/ (+ (:altitude p) (:altitude %)) 2));get the mean of the resultant sphere
            (square-smooth sphere (:longitude p) (:latitude p) (:altitude p))));and a sphere smoothed for that point
    sphere))