Geometric dilation of closed planar curves: New lower bounds

DOI10.1016/j.comgeo.2004.12.009zbMath1121.65020OpenAlexW2058888466MaRDI QIDQ883237

Rolf Klein, Annette Ebbers-Baumann, Ansgar Grüne

Publication date: 4 June 2007

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2004.12.009

zbMATH Keywords

dilationcomputational geometryconvex geometryconvex curvesdetourhalving pair transformation

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items

Classical curve theory in normed planes ⋮ Observation routes and external watchman routes ⋮ On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces ⋮ Most finite point sets in the plane have dilation \(>1\) ⋮ Geometric dilation of closed curves in normed planes

Cites Work

• Homotopical effects of dilatation
• Inner and outer \(j\)-radii of convex bodies in finite-dimensional normed spaces
• A fast algorithm for approximating the detour of a polygonal chain.
• The geometric dilation of finite point sets
• Quadrisecants give new lower bounds for the ropelength of a knot
• On Distortion and Thickness of Knots
• Self-approaching curves
• Generalized self-approaching curves
• Lower bounds for computing geometric spanners and approximate shortest paths
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