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.

*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><ref>{{cite journal | doi=10.1007/PL00009475 | first1=Nina | last1=Amenta | first2=Marshall | last2=Bern | title=Surface reconstruction by Vornonoi filtering | journal=Discrete and Computational Geometry | year=1999 | issue=4 | pages= 481–504 | volume=22}}</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

| width = 350

| 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

| alt1 = Medial axis-base definition.

| caption1 = Local feature size for smooth a smooth manifold (black) with medial axis (red).

| image2 = Ruppert_lfs.svg

| alt2 = Planar straight line graph-based definition.

| caption2 = Local feature size for a planar straight-line graph.

}}

== References ==