How can I detect whether a line (direction d and -d from point p) and a line segment (between points p1 and p2) intersects in 2D? If they do, how can I get their intersection point.
There are lots of example how to detect whether two line segments intersects but this should be even simpler case.
I found this but I do not understand what is a side-operator: http://www.loria.fr/~lazard//ARC-Visi3D/Pant-project/files/Line_Segment_Line.html
If this is a 2D task (the line and the segment lie in the same plane and they are specified by 2-dimensional coordinates), it's easy.
Construct a vector that is normal to d (the direction of the line) called n.
Compute dot products n.(p1-p) and n.(p2-p). If they have the same sign, there's no intersection. If they have opposite signs, there is an intersection. With a little bit of thought, you can figure out how to compute the location of the intersection in terms of p, p1-p and p2-p.