#lang racket

(module pip racket
  (require racket/contract)

  (provide point)
  (provide seg)
  (provide (contract-out [point-in-polygon? (->
                                             point?
                                             list?
                                             boolean?)]))

  (struct point (x y) #:transparent)
  (struct seg (Ax Ay Bx By))
  (define ε 0.000001)
  (define (neq? x y) (not (eq? x y)))

  (define (ray-cross-seg? r s)
    (let* ([Ax (seg-Ax s)] [Ay (seg-Ay s)]
           [Bx (seg-Bx s)] [By (seg-By s)]
           [Px (point-x r)] [Pyo (point-y r)]
           [Py (+ Pyo (if (or (eq? Pyo Ay)
                              (eq? Pyo By))
                          ε 0))])

      (cond [(or (< Py Ay) (> Py By)) #f]
            [(> Px (max Ax Bx)) #f]
            [(< Px (min Ax Bx)) #t]
            [else
             (let ([red (if (neq? Ax Px)
                            (/ (- By Ay) (- Bx Ax))
                            +inf.0)]
                   [blue (if (neq? Ax Px)
                             (/ (- Py Ax) (- Px Ax))
                             +inf.0)])
               (if (>= blue red) #t #f))])))

  (define (point-in-polygon? point polygon)
    (odd?
     (for/fold ([c 0]) ([seg polygon])
       (+ c (if (ray-cross-seg? point seg) 1 0))))))

(require 'pip)

(define test-point-list
  (list
   (point 5.0    5.0)
   (point 5.0    8.0)
   (point -10.0  5.0)
   (point  0.0   5.0)
   (point 10.0   5.0)
   (point  8.0   5.0)
   (point 10.0  10.0)))

(define square
  (list (seg 0.0   0.0  10.0   0.0)
        (seg 10.0  0.0  10.0  10.0)
        (seg 10.0  10.0  0.0  10.0)
        (seg 0.0   0.0  0.0   10.0)))

(define exagon
  (list (seg  3.0   0.0   7.0   0.0)
        (seg  7.0   0.0  10.0   5.0)
        (seg 10.0   5.0   7.0  10.0)
        (seg  7.0  10.0   3.0  10.0)
        (seg  0.0   5.0   3.0   10.0)
        (seg  3.0   0.0 0.0   5.0)))

(define (test-figure fig name)
  (printf "\ntesting ~a: \n" name)
  (for ([p test-point-list])
    (printf "testing ~v: ~a\n"  p (point-in-polygon? p fig))))

(test-figure square "square")
(test-figure exagon "exagon")