Ramer-Douglas-Peucker line simplification: Difference between revisions
Ramer-Douglas-Peucker line simplification (view source)
Revision as of 10:36, 16 June 2017
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=={{header|Racket}}==
<lang racket>#lang racket
(require math/flonum)
;; points are lists of x y (maybe extensible to z)
;; x+y gets both parts as values
(define (x+y p) (values (first p) (second p)))
;; https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line
(define (⊥-distance P1 P2)
(let*-values
([(x1 y1) (x+y P1)]
[(x2 y2) (x+y P2)]
[(dx dy) (values (- x2 x1) (- y2 y1))]
[(h) (sqrt (+ (sqr dy) (sqr dx)))])
(λ (P0)
(let-values (((x0 y0) (x+y P0)))
(/ (abs (+ (* dy x0) (* -1 dx y0) (* x2 y1) (* -1 y2 x1))) h)))))
(define (douglas-peucker points-in ϵ)
(let recur ((ps points-in))
;; curried distance function which will be applicable to all points
(let*-values
([(p0) (first ps)]
[(pz) (last ps)]
[(p-d) (⊥-distance p0 pz)]
;; Find the point with the maximum distance
[(dmax index)
(for/fold ((dmax 0) (index 0))
((i (in-range 1 (sub1 (length ps))))) ; skips the first, stops before the last
(define d (p-d (list-ref ps i)))
(if (> d dmax) (values d i) (values dmax index)))])
;; If max distance is greater than epsilon, recursively simplify
(if (> dmax ϵ)
;; recursive call
(let-values ([(l r) (split-at ps index)])
(append (drop-right (recur l) 1) (recur r)))
(list p0 pz))))) ;; else we can return this simplification
(module+ main
(douglas-peucker
'((0 0) (1 0.1) (2 -0.1) (3 5) (4 6) (5 7) (6 8.1) (7 9) (8 9) (9 9))
1.0))
(module+ test
(require rackunit)
(check-= ((⊥-distance '(0 0) '(0 1)) '(1 0)) 1 epsilon.0))</lang>
{{out}}
<pre>'((0 0) (2 -0.1) (3 5) (7 9) (9 9))</pre>
=={{header|Sidef}}==
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