Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Computing a face in an arrangement of line segments and related problems
SIAM Journal on Computing
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The area bisectors of a polygon and force equilibria in programmable vector fields
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Constructing cuttings in theory and practice
Proceedings of the fourteenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
The CGAL Kernel: A Basis for Geometric Computation
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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Given a finite set L of lines in the plane we wish to compute the zone of an additional curve γ in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by γ, where γ is not given in advance but rather provided on-line portion by portion. This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). We implemented the four algorithms. We present implementation details, comparison of performance, and a discussion of the advantages and shortcomings of each of the proposed algorithms.