Is there an efficient algorithm for finding all intersections of a set of infinite lines?

Question

There are efficient (compared to O(n²) pairwise testing) algorithms for finding all intersections in a set of line segments, like the Bentley-Ottmann algorithm. However, I want to find all intersections in a set of infinite lines. When the region of interest is something finite like a rectangle, the line-segment intersection algorithms can be applied after clipping the lines. But

• Is there a simpler or more efficient way than just clipping the lines and applying line-segment intersection algorithms?
• Is there an efficient algorithm for all intersections over the entire plane for a set of lines?

Answer 1

In general case (not all lines are parallel) there are O(n^2) intersections, so simple loop with intersection calculation is the best approach
(there is no way to get n*(n-1)/2 points without calculations)

For the case of existence a lot of parallel lines make at first grouping lines by direction and check only intersections between lines in diffferent groups