Input | Output |
Input Description: A set of lines and line segments \(l_1,...,\l_n\).
Problem: What is the decomposition of the plane defined by \(l_1,...,\l_n\)?
Excerpt from The Algorithm Design Manual: One of the most fundamental problems in computational geometry is constructing arrangements of lines, that is, explicitly building the regions formed by the intersections of a set of \(n\) lines. Algorithms for a surprising number of problems are based on constructing and analyzing the arrangement of a specific set of lines:
cgal (rating 10) |
Topological Sweep in Degenerate Cases (rating 9) |
CGAL (rating 8) |
Arrange (rating 7) |
LEDA (rating 4) |
Davenport-Schinzel sequences and their geometric applications by M. Sharir and P. Agarwal | Computational Geometry in C by Joseph O'Rourke | Algorithms in Combinatorial Geometry by Herbert Edelsbrunner |