Line intersection calculus

The following script is a demo demonstrating using Rebol for analytical geometry: line intersection calculus. The function wrote in the script calculate is lines intersect, don't intersect or are parallel.

Here is the source:

REBOL [
    File: %line-intersection-demo.r
    Date: 10-Jan-2004
    Title: "Line Intersection Demo"
    Purpose: {Demonstrate an algorithm used to detect an intersection between two line segments.}
    Version: 1.0.1
    Author: "Claude Precourt"
    Acknowledgements: ["Paul Bourke"]
    Web: http://astronomy.swin.edu.au/~pbourke/geometry/lineline2d/
]
line-intersect?: func [
        "It determines if lines intescet"
        pt1 [pair!]   "First line start point"
        pt2 [pair!] "First line end point"
        pt3 [pair!]   "Second line stard point"
        pt4 [pair!]   "Second line end point"
        /local denom ua ub
    ][
        denom: ((pt4/y - pt3/y) * (pt2/x - pt1/x)) - ((pt4/x - pt3/x) * (pt2/y - pt1/y))
        if denom = 0 [print "lines are parallel" return false] ;; lines are parallel
        ua: (((pt4/x - pt3/x) * (pt1/y - pt3/y)) - ((pt4/y - pt3/y) * (pt1/x - pt3/x))) / denom
        ub: (((pt2/x - pt1/x) * (pt1/y - pt3/y)) - ((pt2/y - pt1/y) * (pt1/x - pt3/x))) / denom
        either   all [
            ua >= 0
            ua <= 1
            ub >= 0
            ub <= 1
            ] [return true][return false]
]
img-data: to-image layout [origin 0x0 box black 512x512]
view layout [
    img: image img-data
    across
    button "Test" [
        pt1: to-pair reduce [random 512 random 512]
        pt2: to-pair reduce [random 512 random 512]
        pt3: to-pair reduce [random 512 random 512]
        pt4: to-pair reduce [random 512 random 512]
        either line-intersect? pt1 pt2 pt3 pt4 [
            pen-color: red
            status-text/text: "YES"
        ][
            pen-color: white
            status-text/text: "NO"
        ]
        img-data: to-image layout [origin 0x0
            box black 512x512 effect [
                draw [pen pen-color line pt1 pt2 line pt3 pt4]  
            ]
        ]
        img/image: img-data
        show [img status-text]
    ]
    button "Quit" [quit]
    text bold "   Intersection?"
    status-text: text 150x24 "-"
]