The following text is an extract from a pdf found online, basically the technique doesn't seem to find the point of intersection, but it says to determine if the two line segments intersect using cross products.

enter image description here

Given the limited amount of description here, How does this technique work for determining if the two lines intersect?

  • $\begingroup$ Please include critical parts of your question as text instead of posting an image of it. Images are neither searchable nor accessible to screen readers, and your question is completely incomprehensible with images disable. You can find a quick reference for MathJax, which is used here for formatting mathematical expression, here. $\endgroup$ – amd Jun 12 at 19:22

The basic idea is that if the two line segments do not intersect then either

(a) the second is wholly to the right or wholly to the left of the first; or

(b) the first is wholly to the right or wholly to the left of the second.

[It is possible for both to be true]

It does this by locating the endpoints of each segment in relation (right or left) to the other segment.

  • $\begingroup$ um.... it does give me some hint, but, what relation does it have with cross product. I have only taken a course on linear algebra, and know to interpret it only in terms of area. $\endgroup$ – mathmaniage Jun 12 at 15:50
  • $\begingroup$ @mathmaniage The cross product has a sign which depends on the relative orientation of two lines which meet at a point. Really that represents the choice of one of the two normals to the plane containing the lines. Here the lines are defined by three points - two on the segment and one at the end of the other segment. The two vectors for the cross product in the first case are $PQ$ and $QR$. The sign of the cross product determines whether the path $PQR$ has a left turn or a right turn. $\endgroup$ – Mark Bennet Jun 12 at 16:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.