Create line segment from two points in Clojure

Question

What's the best way to go about doing this? Here's what I've got so far

(defn line-segment [start end]
  (let [x-direction (abs (- (first end) (first start)))
        y-direction (abs (- (last end) (last start)))]
    (cond
      (= 0 x-direction) (something ...)
      (= 0 y-direction) (something ...))))

Here's my end goal

user=> (line-segment [5 6] [5 8])
([5 6] [5 7] [5 8])

And yes, there are no diagonals, only x or y movement.

Thanks.

Answer 1

I think this is a pretty elegant solution:

(defn line-segment [start end]
  (let [x1 (first start) x2 (first end)
        y1 (last start)  y2 (last end)
        dx (if (> x1 x2) -1 1)
        dy (if (> y1 y2) -1 1)]
    (for [x (range x1 (+ dx x2) dx)
          y (range y1 (+ dy y2) dy)]
      [x y])))

REPL session:

user> (line-segment [5 6] [5 8])
([5 6] [5 7] [5 8])
user> (line-segment [5 8] [5 6])
([5 8] [5 7] [5 6])
user> (line-segment [-2 7] [1 7])
([-2 7] [-1 7] [0 7] [1 7])
user> (line-segment [1 7] [-2 7])
([1 7] [0 7] [-1 7] [-2 7])

This function returns a LazySeq even though your sample output was formatted as a vector. I figured this wasn't important.

Answer 2

Here's a simple solution that also allows diagonals:

(use 'clojure.contrib.math)

(defn line-segment [start end]
  (let [x1 (first start) x2 (first end)
        y1 (last start)  y2 (last end)
        xdiff (- x2 x1)
        ydiff (- y2 y1)
        maxdiff (max (abs xdiff) (abs ydiff))
        dx (/ xdiff maxdiff)
        dy (/ ydiff maxdiff)]
    (for [i (range (inc maxdiff))]
      [(round (+ x1 (* i dx))) (round (+ y1 (* i dy)))])))

As with dbryne's solution, this returns a lazy sequence of points rather than a vector: I think this is the most useful form assuming that you subsequently want to do something with each of the points on the line segment in turn.