graphics - time complexity of line segment or edge intersection finding algorithms -

i briefly reviewed literature on line intersection , line arrangement problems in computational geometry. of them based on plane sweep algorithm. angle of computational complexity, seeems me asymptotic algorithmic bounds function of number of line segments , term "k" "k" number of intersections among edges. example, 1 of best known algorithms has time complexity of o(nlogn + "k") output sensitive. problem difficulty in understanding fact why cannot rid of term "k" while providing time complexity. because if @ other algorithms e.g sorting problems, complexity not function of how many swaps or comparisons done. function of number of inputs. insights helpful.

if you'd express worst-case complexity strictly in terms of number of line segments in input, have assume k largest possible number of intersections (namely n²). algorithm o(n log n + k) time complexity (such balaban's) called o(n² + n log n) or o(n * (n + log n)) if prefer.