'---------------------------------------------------------------------------------------------------------
'************************************ Routine LinesSegmentsIntersect *************************************
'---------------------------------------------------------------------------------------------------------
'VBA implementation of the theory provided by Paul Bourke (http://paulbourke.net/geometry/pointlineplane/)
'author: ing. Giuseppe Iaria - rev. 07/08/2014
'---------------------------------------------------------------------------------------------------------
'Routine determines the intersection point of two line segments
'defined by their respective end points P1-P2 and P3-P4
'If exsists, actual point P of intersection is returned, otherwise point P is set to (0,0)
'Both conditions of lines and segments intersection are valued and returned
'Routine arguments are defined as follows:
'Points P1 (x1 ; y1), P2 (x2 ; y2), P3 (x3 ; y3), P4 (x4 ; y4), P (xP ; yP)
'Condition of lines intersection: LinesIntersection
'Condition of segments intersection: SegmentsIntersection
'---------------------------------------------------------------------------------------------------------
Public Sub LinesSegmentsIntersect(ByVal x1 As Double, ByVal y1 As Double, _
                        ByVal x2 As Double, ByVal y2 As Double, _
                        ByVal x3 As Double, ByVal y3 As Double, _
                        ByVal x4 As Double, ByVal y4 As Double, _
                        ByRef xP As Double, ByRef yP As Double, _
                        ByRef LinesIntersection As Boolean, ByRef SegmentsIntersection As Boolean)
Dim NumA As Double, NumB As Double, DeNom As Double
Dim uA As Double, uB As Double
Const EPS As Single = 0.0001
NumA = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)
NumB = (x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3)
DeNom = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1)
'Verify if lines are coincident
'if they do, the poit P is given back as midpoint of midpoints of both segments
If Abs(NumA) < EPS And Abs(NumB) < EPS And Abs(DeNom) < EPS Then
    LinesIntersection = True
    xP = (x1 + x2 + x3 + x4) / 4
    yP = (y1 + y2 + y3 + y4) / 4
    Exit Sub
End If
'Verify if lines are parallel
'if they do, no intersection occurs, the point P is given back as (0,0)
If Abs(DeNom) < EPS Then
    LinesIntersection = False
    xP = 0
    yP = 0
    Exit Sub
End If
'An intersection between the lines exists
'and the coordinates of point of intersection P are given back
LinesIntersection = True
uA = NumA / DeNom
uB = NumB / DeNom
xP = x1 + uA * (x2 - x1)
yP = y1 + uA * (y2 - y1)
'Verify if the point P is inside both segments
If uA < 0 Or uA > 1 Or uB < 0 Or uB > 1 Then SegmentsIntersection = False Else SegmentsIntersection = True
End Sub