The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
New methods for computing visibility graphs
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Skewed projections with an application to line stabbing in R3
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Arrangements of lines in 3-space: a data structure with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Verifiable implementations of geometric algorithms using finite precision arithmetic
Verifiable implementations of geometric algorithms using finite precision arithmetic
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Combinatorial structure of rigid transformations in 2D digital images
Computer Vision and Image Understanding
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We consider arrangements of curves that intersect pairwise in at most k points. We show that a curve can sweep any such arrangement and maintain the k-intersection property if and only if k equals 1 or 2. We apply this result to an eclectic set of problems: finding Boolean formulae for polygons with curved edges, counting triangles and digons in arrangements of pseudocircles, and finding extension curves for arrangements. We also discuss implementing the sweep.