Line Intersecting a Point

[racingpsider]

Hi all!
I have an easy question for you math buffs (which I have started studying once again... math... not buffs):
What is the equation to determine if a line intersects a given point? For example:
Consider Line(x1,y1)-(x2,y2)
Does this line intersect point xy?

As far as how I plan on using it:
A user may draw a line, then they may move that line by selecting it with a mouseup on the picture. I need to know if the user clicked the line, or clicked the background.

Thanks!

[Jotaf98]

Aww man!!! I'm on holydays and now geometry has come to torture me again! You're really lucky that I learned that this year... hmm... Here's the equation:

(x2-x1)/x = (y2-y1)/y

If that doesn't work try switching the x and y (the ones without the numbers right after them). That should work

[racingpsider]

Thanks for your quick response, but that doesn't seem to work, with any of the numbers rearranged. Hmmn... let me try this:

Public Sub DrawPoint(byval Pnt as XYPoint)
'// draw a dot, green or red. Green if it is on the provided line.
Dim Ln as ALine '// with x1,y1,x2,y2
Dim RGBCol as RGBColor '// with R,G,B values

Ln.x1 = 50
Ln.y1 = 125
Ln.x2 = 139
Ln.y2 = 420

If IsOnThisLine(Pnt,Ln)
RGBCol.R = 0
RGBCol.G = 255
Else
RGBCol.R = 255
RGBCol.G = 0
End If

PictureTarget.PSet (Pnt.x,Pnt.y),RGB(RGBCol.R, RGBCol.G,0)

End Sub

Private Function IsOnThisLine(ByVal Pnt as XYPoint, ByVal Ln as ALine) As Boolean
Dim Res1 as Single
Dim Res2 as Single

'.... super code here....

End Function

[Jotaf98]

Oh ok, sorry. You're right, the right formula is:

(X - X1) / (X2 - X1) = (Y - Y1) / (Y2 - Y1)

Don't bother testing it, it doesn't work - you always get False. I think it's because VB always rounds the result of the divisions to fit in a Double or Single or whatever, so the comparison doesn't work... sorry, can't help

Search the internet or something... I'm sure this has been used before, they must have used another method based on Bresenham's algorythm or something complicated like that

[racingpsider]

Actually, I did test it and with a little bit of modification it works well enough!

result1 = (x - x1) / (x2 - x1)
result2 = (Y - y1) / (y2 - y1)

result1 = Round(result1, 1)
result2 = Round(result2, 1)

If result1 = result2 Then
IsOnThisLine = True
Else
IsOnThisLine = False
End If

With a little additional logic (since its actually a line segment, not an infinite line) I will be now be able to determine if a user clicks close to the line! Yay!

Thanks man!

[Jotaf98]

Heh you're welcome

You're right it's for an infinite line sorry... I never tought of rounding the 2 members of the equation because I thought that each one was the slope of the line (a small fractional number)
Heh anyways it's working so no problem