Inner and outer j-radii of convex bodies in finite-dimensional normed spaces
Discrete & Computational Geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Generalized self-approaching curves
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Lower bounds for computing geometric spanners and approximate shortest paths
Discrete Applied Mathematics
Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A fast algorithm for approximating the detour of a polygonal chain
Computational Geometry: Theory and Applications
The Geometric Dilation of Finite Point Sets
Algorithmica
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
Discrete & Computational Geometry
The density of iterated crossing points and a gap result for triangulations of finite point sets
Proceedings of the twenty-second annual symposium on Computational geometry
On the geometric dilation of closed curves, graphs, and point sets
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Geometric dilation of closed curves in normed planes
Computational Geometry: Theory and Applications
Embedding point sets into plane graphs of small dilation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On geometric dilation and halving chords
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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Given two points on a closed planar curve, C, we can divide the length of a shortest connecting path in C by their Euclidean distance. The supremum of these ratios, taken over all pairs of points on the curve, is called the geometric dilation of C. We provide lower bounds for the dilation of closed curves in terms of their geometric properties, and prove that the circle is the only closed curve achieving a dilation of @p/2, which is the smallest dilation possible. Our main tool is a new geometric transformation technique based on the perimeter halving pairs of C.