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» Geometric dilation of closed planar curves: New lower bounds
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COMGEO
2007
ACM
13 years 4 months ago
Geometric dilation of closed planar curves: New lower bounds
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...
Annette Ebbers-Baumann, Ansgar Grüne, Rolf Kl...
WADS
2005
Springer
111views Algorithms» more  WADS 2005»
13 years 10 months ago
On Geometric Dilation and Halving Chords
Let G be an embedded planar graph whose edges may be curves. The detour between two points, p and q (on edges or vertices) of G, is the ratio between the shortest path in G between...
Adrian Dumitrescu, Annette Ebbers-Baumann, Ansgar ...
COMPGEOM
2004
ACM
13 years 8 months ago
Continuous path verification in multi-axis NC-machining
We introduce a new approach to the problem of collision detection between a rotating milling-cutter of an NC-machine and a model of a solid workpiece, as the rotating cutter conti...
Ron Wein, Oleg Ilushin, Gershon Elber, Dan Halperi...