Local feature size
Encyclopedia
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.
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
and computational geometry
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...
for measuring the size of a geometric object near a particular point.
- Given a smooth manifoldDifferentiable manifoldA differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since...
, the local feature size at any point 
is the distance between 
and the medial axisMedial axisThe medial axis of an object is the set of all points having more than one closest point on the object's boundary. Originally referred to as the topological skeleton, it was introduced by Blum as a tool for biological shape recognition....
of
. - Given a planar straight-line graphPlanar straight-line graphPlanar straight-line graph is a term used in computational geometry for an embedding of a planar graph in the plane such that its edges are mapped into straight line segments...
, the local feature size at any point
is the radius of the smallest closed ball centered at 
which intersects any two disjoint features (vertices or edges) of the graph.