Local feature size: Difference between revisions

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Line 1: '''Local feature size''' refers to several related concepts in [[computer graphics]] and [[computational geometry]] for measuring the size of a geometric object near a particular point. ~~{{unreferenced\|date=August 2010}}~~ ~~Local feature size is a computer graphics term. Before the exact definition, we should give another concept called medial axis.~~ 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> ~~Medial axis of a manifold M is a point set such that each point in the set at least has two closest points in M.~~ 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> ~~The local feature size at x in M, denoted as LFS(x), is the distance from x to the medial axis of M.~~ {{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]]