Local feature size

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 $M$, the local feature size at any point $x\; \backslash in\; M$ is the distance between $x$ and the medial axis of $M$.{{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 }}
• Given a planar straight-line graph, the local feature size at any point $x$ is the radius of the smallest closed ball centered at $x$ which intersects any two disjoint features (vertices or edges) of the graph.{{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}}

{{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.

}}