Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A Fast Algorithm for Polygon Containment by Translation (Extended Abstract)
Proceedings of the 12th Colloquium on Automata, Languages and Programming
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
A simple entropy-based algorithm for planar point location
ACM Transactions on Algorithms (TALG)
Optimal Expected-Case Planar Point Location
SIAM Journal on Computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Entropy, triangulation, and point location in planar subdivisions
ACM Transactions on Algorithms (TALG)
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Let $\mathcal{S}$ be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in $\mathcal{S}$ where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time $O(1+\min(\log \frac{1}{\Delta_{p}}, \log n))$, where Δp is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p∈P, the quadrilateral containing p has area $\Omega(\Delta_{p}^2)$.