Public Function IntersectComplex(x1 As Double, y1 As Double, x2 As Double, y2 As Double, LineCoordinates As Range, Axis As Boolean) As Variant
'
' Complex Intersect.
' Because the line segments are not uniformly spaced the (xy,y1)(x2,y2) could cross
' at any point along the other line
'
' Return
' If intersection
' requested coordinate
' else
' nothing
' endif
' Axis=True returns X value
' Axis=False returns Y value
'
Dim dblCrossX As Double
Dim dblCrossY As Double
Dim dblTestx1 As Double
Dim dblTesty1 As Double
Dim dblTestx2 As Double
Dim dblTesty2 As Double
Dim intSegment As Integer
With LineCoordinates
For intSegment = 1 To .Rows.Count - 1
dblTestx1 = .Cells(intSegment, 1)
dblTesty1 = .Cells(intSegment, 2)
dblTestx2 = .Cells(intSegment + 1, 1)
dblTesty2 = .Cells(intSegment + 1, 2)
If m_CalculateIntersecti0n(x1, y1, x2, y2, dblTestx1, dblTesty1, dblTestx2, dblTesty2, dblCrossX, dblCrossY) Then
If Axis Then
IntersectComplex = dblCrossX
Else
IntersectComplex = dblCrossY
End If
Exit Function
End If
Next
' Special check for last pairing
intSegment = .Rows.Count
dblTestx1 = .Cells(intSegment, 1)
dblTesty1 = .Cells(intSegment, 2)
dblTestx2 = .Cells(intSegment, 1)
dblTesty2 = .Cells(intSegment, 2)
If m_CalculateIntersecti0n(x1, y1, x2, y2, dblTestx1, dblTesty1, dblTestx2, dblTesty2, dblCrossX, dblCrossY) Then
If Axis Then
IntersectComplex = dblCrossX
Else
IntersectComplex = dblCrossY
End If
Exit Function
End If
End With
IntersectComplex = CVErr(xlErrNA) ' Null
End Function
Private Function m_CalculateIntersecti0n(x1 As Double, y1 As Double, x2 As Double, y2 As Double, _
x3 As Double, y3 As Double, x4 As Double, y4 As Double, _
ByRef CrossX As Double, ByRef CrossY As Double) As Variant
'Call with x1,y1,x2,y2,x3,y3,x4,y4 and returns intersect,x,y
'
'Where:
' x1,y1,x2,y2,x3,y3,x4,y4 are the end points of two line segments
'Returns:
' intersect is true/false, and x,y is the interecting point if intersect is true
'
'Description:
'
'Equations for the lines are:
' Pa = P1 + Ua(P2 - P1)
' Pb = P3 + Ub(P4 - P3)
'
'Solving for the point where Pa = Pb gives the following equations for ua and ub
'
' Ua = ((x4 - x3) * (y1 - y3) - (y4 - y3 ) * (x1 - x3)) / ((y4 - y3) * (x2 - x1)
' - (x4 - x3) * (y2 - y1))
' Ub = ((x2 - x1) * (y1 - y3) - (y2 - y1 ) * (x1 - x3)) / ((y4 - y3) * (x2 - x1)
' - (x4 - x3) * (y2 - y1))
'
'Substituting either of these into the corresponding equation for the line gives
' the intersection point.
'For example the intersection point (x,y) is
' x = x1 + Ua(x2 - x1)
' y = y1 + Ua(y2 - y1)
'
'Notes:
' - The denominators are the same.
'
' - If the denominator above is 0 then the two lines are parallel.
'
' - If the denominator and numerator are 0 then the two lines are coincident.
'
' - The equations above apply to lines,
' if the intersection of line segments is
' required then it is only necessary to test if ua and ub lie between 0 and 1.
' Whichever one lies within that range then the corresponding line segment
' contains the intersection point. If both lie within the range of 0 to 1 then
' the intersection point is within both line segments.
'
Dim dblDenominator As Double
Dim dblUa As Double
Dim dblUb As Double
'Pre calc the denominator, if zero then
' both lines are parallel and there is no
' intersection
dblDenominator = ((y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1))
If dblDenominator <> 0 Then
'Solve for the simultaneous equations
dblUa = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)) / dblDenominator
dblUb = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3)) / dblDenominator
Else
If (x1 = x3) And (y1 = y3) Then
CrossX = x1
CrossY = y1
m_CalculateIntersection = True
Else
m_CalculateIntersection = False
End If
Exit Function
End If
'Could the lines intersect?
If dblUa > 0 And dblUa < 1 And dblUb > 0 And dblUb < 1 Then
'Calculate the intersection point
CrossX = x1 + dblUa * (x2 - x1)
CrossY = y1 + dblUa * (y2 - y1)
'Yes, they do
m_CalculateIntersection = True
ElseIf dblUa = 0 And dblUb = 0 Then
' cross at a segment start
CrossX = x1
CrossY = y1
'Yes, they do
m_CalculateIntersection = True
ElseIf dblUa = 1 And (dblUb > 0 And dblUb < 1) Then
' cross at right angles or ends on other line
CrossX = x2
CrossY = y1
'Yes, they do
m_CalculateIntersection = True
ElseIf dblUb = 1 And (dblUa > 0 And dblUa < 1) Then
' cross at right angles or ends on other line
CrossX = x1
CrossY = y3
'Yes, they do
m_CalculateIntersection = True
ElseIf dblUa = 1 And dblUb = 1 Then
' cross at a segment end
CrossX = x2
CrossY = y2
m_CalculateIntersection = True
Else
'No, they do not
m_CalculateIntersection = False
End If
End Function