When does two line segments intercept?

[Math Tutor]

Suppose you have two line segments.
Every segment is defined by start and end point coordinates.

What is the formula that shows whether the two line segments intercept.

[Guest]

If they are not parallel then they will intesect somewhere.
I assume you mean intersect rather than intercept.
If they are parallel then both have the same slope and they will not intersect

[Guest]

For line 1....x1,y1 is start and x2,y2 is end
For line2.....x3,y3 is start and x4,y4 is end

For line 1....slope is m1= (y2-y1)/(x2-x1)
For line 2....slope is m2= (y4-y3)/(x4-x3)
The lines will intersect when m1 is different from m2.....when (m2 - m1) <> 0 or ( m1/m2) <> 1
The lines are parallel when m1=m2 or [(m2 - m1) = 0] or when m1/m2 = 1 and they won't intersect.
If m1 = -(1/m2) the lines intersect at right angles (90 degrees) so in this case they are perpendicular.

[Math Tutor]

Here we do not talk about lines and segments.

Suppose you have to write a program.
How will you define that 2 segments intercepts?

[Guest]

Give an example of your syntax for defining lines.
How do you define a line in your syntax.......Doesnt matter whether it intercepts or not
All lines will intercept, only parallel ones will not intercept.

Is it with start and end points....x1,y1 is start and x2,y2 is end

[Math Tutor]

It is true for lines and not for segments.

Segments are defined by start and end points.
x1,y1 is start and x2,y2 is the end for the first segment.

[Guest]

Well then.....What is the question.??

[Math Tutor]

When does two line segments(by given coordinates) intercept?

[Guest]

You can use the separating axis theorem, see
http://en.wikipedia.org/wiki/Hyperplane ... on_theorem
There are three "separating axis" (not to be confused with the "separating line") you have to check in 2D space:
the axis perpendicular to segment 1
the axis perpendicular to segment 2
the axis parallel to segment 1 (or 2)

R. Baber.

[leesajohnson]

If the lines are not parallel to each other they will intercept somewhere.

[Guest]

Good thinking , leesa

and...... no one mentioned straight lines yet..... just start and end point......segments of lines ......are the long enough to intersect ?? ..... If they were longer they may intersect.....????

..... or are they crooked and intersect several times......??????