Local feature size: Difference between revisions

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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.

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*Given a 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>.

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*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>.

Local feature size is a computer graphics term. Before the exact definition, we should give another concept called medial axis.

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.

The local feature size at x in M, denoted as LFS(x), is the distance from x to the medial axis of M.

== References ==

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{{Reflist}}

[[Category:Geometric algorithms]]