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 ${\displaystyle M}$, the local feature size at any point ${\displaystyle x\in M}$ is the distance between ${\displaystyle x}$ and the medial axis of ${\displaystyle M}$.[1]
• Given a planar straight-line graph, the local feature size at any point ${\displaystyle x}$ is the radius of the smallest closed ball centered at ${\displaystyle x}$ which intersects any two disjoint features (vertices or edges) of the graph.[2]

Definitions of local feature size. In each case, the local feature size at the blue points is the radius of the associated blue circle.

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

Local feature size for a planar straight-line graph.

See also

• Nearest neighbour function

References

1. Amenta, Nina; Bern, Marshall (1999). "Surface reconstruction by Voronoi filtering" (PDF). Discrete and Computational Geometry. 22 (4): 481–504. doi:10.1007/PL00009475.
2. Ruppert, Jim (1995). "A Delaunay refinement algorithm for quality 2-dimensional mesh generation". Journal of Algorithms. 18 (3): 548–585. doi:10.1006/jagm.1995.1021.