# Reporting all intersection points, generalized segments (Line segment intersection)

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## Description

In this case, the segments are generalized (i.e. have algebraic degree ≥1); we still wish to report all points of intersection.

## Related Problems

Subproblem: Reporting all intersection points, line segments

Related: Reporting all intersection points, convex polygons, Reporting all intersection points, general polygons, Counting number of intersection points, line segments

## Parameters

$n$: number of line segments

$k$: number of points of intersection

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Jean-Daniel Boissonnat and Franco P. Preparata. | 1997 | $O(n \log n + k \log n)$ | $O(n)$ | Exact | Deterministic | Time & Space |

Balaban. | 1995 | $O(n \log n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |

Boissonnat; Snoeyink | 1999 | $O(n \log n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |