X = X1 + t * (X2 - X1), Y = Y1 + t * (Y2 - Y1)
    X = A1 + s * (A2 - A1), Y = B1 + s * (B2 - B1)

where the parameters s and t vary from 0 to 1. It solves these equations for s and t to see where the lines intersect. If the segments intersect, then s and t are both between 0.0 and 1.0.

' Return True if the segments intersect.
Private Function SegmentsIntersect(ByVal X1 As Single, _
    ByVal Y1 As Single, ByVal X2 As Single, ByVal Y2 As _
    Single, ByVal A1 As Single, ByVal B1 As Single, ByVal _
    A2 As Single, ByVal B2 As Single) As Boolean
Dim dx As Single
Dim dy As Single
Dim da As Single
Dim db As Single
Dim t As Single
Dim s As Single

    dx = X2 - X1
    dy = Y2 - Y1
    da = A2 - A1
    db = B2 - B1
    If (da * dy - db * dx) = 0 Then
        ' The segments are parallel.
        SegmentsIntersect = False
        Exit Function
    End If
    
    s = (dx * (B1 - Y1) + dy * (X1 - A1)) / (da * dy - db * _
        dx)
    t = (da * (Y1 - B1) + db * (A1 - X1)) / (db * dx - da * _
        dy)
    SegmentsIntersect = (s >= 0# And s <= 1# And _
                         t >= 0# And t <= 1#)

    ' If it exists, the point of intersection is:
    ' (x1 + t * dx, y1 + t * dy)
End Function