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Undid revision 1024722084 by Fgnievinski (talk) There is in MOS:FIRST nothing that says we have to invert the usual of prepositions and main clauses order and with the context before even naming the main topic start. |
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'''Local feature size'''
*Given a [[differentiable manifold|smooth manifold]] <math>M</math>, the local feature size at any point <math>x \in M</math> is the distance between <math>x</math> and the [[medial axis]] of <math>M</math>.<ref>{{cite journal | doi=10.1007/PL00009475 | first1=Nina | last1=Amenta | author1-link = Nina Amenta | first2=Marshall | last2=Bern | title=Surface reconstruction by Voronoi filtering | journal=Discrete and Computational Geometry | year=1999 | issue=4 | pages= 481–504 | volume=22| url=https://escholarship.org/content/qt4rc7z0d1/qt4rc7z0d1.pdf?t=ptt31s | doi-access=free }}</ref>
*Given a [[planar straight-line graph]], the local feature size at any point <math>x</math> is the radius of the smallest closed ball centered at <math>x</math> which intersects any two disjoint features (vertices or edges) of the graph.<ref>{{cite journal | doi=10.1006/jagm.1995.1021 | first=Jim | last=Ruppert | title=A Delaunay refinement algorithm for quality 2-dimensional mesh generation | journal=Journal of Algorithms | year=1995 | issue=3 | pages= 548–585 | volume=18}}</ref>
{{multiple image
| direction = horizontal
| align = center
| header = Definitions of local feature size. In each case, the local feature size at the blue points is the radius of the associated blue circle.
| image1 = Medial_lfs.svg
| width1 = {{#expr: (250 * 1276 / 886) round 0}}
| alt1 = Medial axis-base definition.
| caption1 = Local feature size for a smooth manifold (black) with medial axis (red).
| image2 = Ruppert_lfs.svg
| width2 = {{#expr: (250 * 1205 / 780) round 0}}
| alt2 = Planar straight line graph-based definition.
| caption2 = Local feature size for a planar straight-line graph.
}}
==See also==
*[[Nearest neighbour function]]
== References ==
{{Reflist}}
[[Category:Geometric algorithms]]
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