Computational geometry: an introduction
Computational geometry: an introduction
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Randomized optimal algorithm for slope selection
Information Processing Letters
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Off-line maintenance of planar configurations
Journal of Algorithms
An Expander-Based Approach to Geometric Optimization
SIAM Journal on Computing
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Separating objects in the plane by wedges and strips
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Efficient randomized algorithms for robust estimation of circular arcs and aligned ellipses
Computational Geometry: Theory and Applications
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A tight bound for the number of different directions in three dimensions
Proceedings of the nineteenth annual symposium on Computational geometry
Solution of Scott's problem on the number of directions determined by a point set in 3-space
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Farthest line segment Voronoi diagrams
Information Processing Letters
Farthest segments and extremal triangles spanned by points in R3
Information Processing Letters
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Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n log n) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum) area triangle with a vertex at q and the other two vertices in S\{q} in optimal O(n log n) time and O(n) space. Finally, we give an O(n log n) time, O(n) space algorithm to find the kth closest line from q and show how to find the k closest lines from q in O(n logn + k) time and O(n + k) space.