Efficient algorithms for common transversals
Information Processing Letters
Algorithms for line transversals in space
SCG '87 Proceedings of the third annual symposium on Computational geometry
Polyhedral line transversals in space
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
On the detection of a common intersection of k convex objects in the plane
Information Processing Letters
An on-line algorithm for fitting straight lines between data ranges
Communications of the ACM
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Hierarchical decomposition of polygons with applications
Hierarchical decomposition of polygons with applications
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We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width &sgr;. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are &THgr;(n) when &sgr; ≤ &pgr; or &sgr; = 2&pgr;, but require &OHgr;(n log n) time (at least), when &pgr;