Circle shooting in a simple polygon
Journal of Algorithms
Randomized incremental construction of abstract Voronoi diagrams
Computational Geometry: Theory and Applications
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Casting a polyhedron with directional uncertainty
Computational Geometry: Theory and Applications
Ray shooting and stone throwing with near-linear storage
Computational Geometry: Theory and Applications
Voronoi diagrams with a transportation network on the euclidean plane
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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Given two sets A and B of m non-intersecting line segments in the plane, we show how to compute in O(m logm) time a data structure that uses O(m) space and allows to answer the following query in O(logm) time: Given a parabola γ: y = ax2 + bx + c, does γ separate A and B? This structure can be used to build a data structure that stores a simple polygon and allows ray-shooting queries along parabolic trajectories with vertical main axis. For a polygon with complexity n, we can answer such “stone throwing” queries in O(log2n) time, using O(n logn) space and O(n log2n) preprocessing time. This matches the best known bound for circular ray shooting in simple polygons.