Question

Bentley-Ottmann Algorithm is used to determined the intersection point of a list of lines. However as mentioned here in Wiki, there are a few drawbacks:

The algorithm assumes that line
segments are not vertical, that line
segment endpoints do not lie on other
line segments, that crossings are
formed by only two line segments, and
that no two event points have the same
x-coordinate. However, these general
position assumptions are not
reasonable for most applications of
line segment intersection.

My question is is there a generalization of this algorithm can overcome/overcome the above difficulties?

Answer 1

The Wikipedia article you linked to has a section on handling these special positions, which suggests these modifications to the basic algorithm:

• By convention, a point is to the “left” of a point vertically above it; thus the “left” endpoint of a vertical line is its lower endpoint.
• Events may consist of the crossings of two or more lines.
• When an event point is reached, its incident segments must be reversed in the sweep line (not just swapped, as there may be more than two).
• After a crossing is handled, there may be more than two old event points to be removed or more than two new event points to be inserted.