Midpoint Circle Algorithm (Bresenham)

midpoint-circle-algorithm.clj

; https://en.wikipedia.org/wiki/Midpoint_circle_algorithm

(defn mirror-point [x0 y0 x y]
  [[(+ x0 x) (+ y0 y)]
   [(+ x0 y) (+ y0 x)]
   [(- x0 y) (+ y0 x)]
   [(- x0 x) (+ y0 y)]
   [(- x0 x) (- y0 y)]
   [(- x0 y) (- y0 x)]
   [(+ x0 y) (- y0 x)]
   [(+ x0 x) (- y0 y)]])

(defn circle [x0 y0 radius]
  "Return a seq of [x y] points of a circle of given radius centred on [x0 y0]"
  (loop [x radius, y 0, err 0, result []]
    (if (>= x y)
      (let [p (mirror-point x0 y0 x y)
            y (inc y)
            err (+ err (inc (* 2 y)))]
        (if (pos? (inc (* 2 (- err x))))
          (recur (dec x) y (+ err (- 1 (* 2 x))) (concat result p))
          (recur x       y err                   (concat result p))))
      result)))

(->>
  (circle 0 0 200)
  (map #(let [[a b] %] (format "%d, %d" a b)))
  (clojure.string/join "\n")
  (spit "/tmp/circle-200.csv"))