155 lines
7.4 KiB
Racket
155 lines
7.4 KiB
Racket
#lang racket/base
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;; Small library for clipping points, rectangles, lines and polygons against axial planes.
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(require racket/match racket/list)
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(provide point-in-bounds? clip-line clip-lines clip-polygon)
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;; ===================================================================================================
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;; Point clipping
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(define (point-in-bounds? v x-min x-max y-min y-max)
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(match-define (vector x y) v)
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(and (<= x-min x x-max) (<= y-min y y-max)))
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;; ===================================================================================================
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;; Line clipping
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(define (clip-line-x start-in-bounds? x x1 y1 x2 y2)
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(define t (/ (- x x1) (- x2 x1)))
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(cond [start-in-bounds? (values x1 y1 x (+ y1 (* t (- y2 y1))))]
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[else (values x (+ y1 (* t (- y2 y1))) x2 y2)]))
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(define (clip-line-y start-in-bounds? y x1 y1 x2 y2)
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(define t (/ (- y y1) (- y2 y1)))
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(cond [start-in-bounds? (values x1 y1 (+ x1 (* t (- x2 x1))) y)]
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[else (values (+ x1 (* t (- x2 x1))) y x2 y2)]))
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(define (clip-line-x-min x-min x1 y1 x2 y2)
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(cond [(and (x1 . >= . x-min) (x2 . < . x-min)) (clip-line-x #t x-min x1 y1 x2 y2)]
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[(and (x2 . >= . x-min) (x1 . < . x-min)) (clip-line-x #f x-min x1 y1 x2 y2)]
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[else (values x1 y1 x2 y2)]))
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(define (clip-line-x-max x-max x1 y1 x2 y2)
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(cond [(and (x1 . <= . x-max) (x2 . > . x-max)) (clip-line-x #t x-max x1 y1 x2 y2)]
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[(and (x2 . <= . x-max) (x1 . > . x-max)) (clip-line-x #f x-max x1 y1 x2 y2)]
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[else (values x1 y1 x2 y2)]))
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(define (clip-line-y-min y-min x1 y1 x2 y2)
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(cond [(and (y1 . >= . y-min) (y2 . < . y-min)) (clip-line-y #t y-min x1 y1 x2 y2)]
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[(and (y2 . >= . y-min) (y1 . < . y-min)) (clip-line-y #f y-min x1 y1 x2 y2)]
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[else (values x1 y1 x2 y2)]))
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(define (clip-line-y-max y-max x1 y1 x2 y2)
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(cond [(and (y1 . <= . y-max) (y2 . > . y-max)) (clip-line-y #t y-max x1 y1 x2 y2)]
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[(and (y2 . <= . y-max) (y1 . > . y-max)) (clip-line-y #f y-max x1 y1 x2 y2)]
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[else (values x1 y1 x2 y2)]))
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(define (clip-line v1 v2 x-min x-max y-min y-max)
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(let/ec return
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(match-define (vector x1 y1) v1)
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(match-define (vector x2 y2) v2)
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;; early accept: both endpoints in bounds
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(when (and (<= x-min x1 x-max) (<= y-min y1 y-max)
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(<= x-min x2 x-max) (<= y-min y2 y-max))
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(return v1 v2))
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;; early reject: both endpoints on the outside of the same plane
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(when (or (and (x1 . < . x-min) (x2 . < . x-min)) (and (x1 . > . x-max) (x2 . > . x-max))
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(and (y1 . < . y-min) (y2 . < . y-min)) (and (y1 . > . y-max) (y2 . > . y-max)))
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(return #f #f))
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(let*-values ([(x1 y1 x2 y2) (clip-line-x-min x-min x1 y1 x2 y2)]
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[(x1 y1 x2 y2) (clip-line-x-max x-max x1 y1 x2 y2)]
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[(x1 y1 x2 y2) (clip-line-y-min y-min x1 y1 x2 y2)]
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[(x1 y1 x2 y2) (clip-line-y-max y-max x1 y1 x2 y2)])
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(values (vector x1 y1) (vector x2 y2)))))
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;; ===================================================================================================
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;; Polygon clipping
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(define-syntax-rule (make-clip-polygon in-bounds? clip-line)
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(λ (val xs ys)
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(cond [(empty? xs) (values empty empty)]
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[else
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(for/fold ([res-xs empty] [res-ys empty]) ([x1 (in-list (cons (last xs) xs))]
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[x2 (in-list xs)]
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[y1 (in-list (cons (last ys) ys))]
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[y2 (in-list ys)])
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(define v1-in-bounds? (in-bounds? x1 y1 val))
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(define v2-in-bounds? (in-bounds? x2 y2 val))
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(cond [(and v1-in-bounds? v2-in-bounds?) (values (cons x2 res-xs)
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(cons y2 res-ys))]
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[(and (not v1-in-bounds?) (not v2-in-bounds?)) (values res-xs res-ys)]
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[else (let-values ([(x1 y1 x2 y2) (clip-line v1-in-bounds? val x1 y1 x2 y2)])
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(cond [v2-in-bounds? (values (list* x2 x1 res-xs)
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(list* y2 y1 res-ys))]
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[else (values (cons x2 res-xs) (cons y2 res-ys))]))]))])))
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(define-syntax-rule (x-min-in-bounds? x y x-min) (x . >= . x-min))
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(define-syntax-rule (x-max-in-bounds? x y x-max) (x . <= . x-max))
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(define-syntax-rule (y-min-in-bounds? x y y-min) (y . >= . y-min))
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(define-syntax-rule (y-max-in-bounds? x y y-max) (y . <= . y-max))
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(define clip-polygon-x-min (make-clip-polygon x-min-in-bounds? clip-line-x))
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(define clip-polygon-x-max (make-clip-polygon x-max-in-bounds? clip-line-x))
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(define clip-polygon-y-min (make-clip-polygon y-min-in-bounds? clip-line-y))
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(define clip-polygon-y-max (make-clip-polygon y-max-in-bounds? clip-line-y))
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(define (clip-polygon vs x-min x-max y-min y-max)
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(let/ec return
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;; early reject: no polygon
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(when (empty? vs) (return empty))
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(match-define (list (vector xs ys) ...) vs)
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;; early accept: all endpoints in bounds
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(when (and (andmap (λ (x) (<= x-min x x-max)) xs)
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(andmap (λ (y) (<= y-min y y-max)) ys))
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(return vs))
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;; early reject: all endpoints on the outside of the same plane
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(when (or (andmap (λ (x) (x . < . x-min)) xs) (andmap (λ (x) (x . > . x-max)) xs)
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(andmap (λ (y) (y . < . y-min)) ys) (andmap (λ (y) (y . > . y-max)) ys))
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(return empty))
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(let*-values ([(xs ys) (clip-polygon-x-min x-min xs ys)]
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[(xs ys) (clip-polygon-x-max x-max xs ys)]
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[(xs ys) (clip-polygon-y-min y-min xs ys)]
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[(xs ys) (clip-polygon-y-max y-max xs ys)])
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(map vector xs ys))))
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;; ===================================================================================================
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;; Lines clipping
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(define (join-lines lines)
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(let loop ([lines lines] [current-line empty])
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(cond [(empty? lines) (list (reverse current-line))]
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[(empty? current-line) (loop (rest lines) (reverse (first lines)))]
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[else
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(match-define v (first current-line))
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(match-define (list v1 v2) (first lines))
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(cond [(equal? v v1) (loop (rest lines) (cons v2 current-line))]
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[else (cons (reverse current-line) (loop lines empty))])])))
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#;
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(join-lines
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'((#(1 2) #(3 4))
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(#(3 4) #(5 6))
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(#(5 7) #(7 8))
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(#(7 8) #(9 10))))
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(define (clip-lines vs x-min x-max y-min y-max)
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(let/ec return
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;; early reject: no lines
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(when (empty? vs) (return empty))
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(match-define (list (vector xs ys) ...) vs)
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;; early accept: all endpoints in bounds
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(when (and (andmap (λ (x) (<= x-min x x-max)) xs) (andmap (λ (y) (<= y-min y y-max)) ys))
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(return (list vs)))
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;; early reject: all endpoints on the outside of the same plane
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(when (or (andmap (λ (x) (x . < . x-min)) xs) (andmap (λ (x) (x . > . x-max)) xs)
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(andmap (λ (y) (y . < . y-min)) ys) (andmap (λ (y) (y . > . y-max)) ys))
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(return empty))
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(join-lines
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(reverse
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(for/fold ([res empty]) ([v1 (in-list vs)] [v2 (in-list (rest vs))])
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(let-values ([(v1 v2) (clip-line v1 v2 x-min x-max y-min y-max)])
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(cond [(and v1 v2) (cons (list v1 v2) res)]
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[else res])))))))
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