  The minimum feature size of a crossing-free straight line drawing is the
minimum distance between a vertex and a non-incident edge. This quantity
measures the resolution needed to display a figure or the tool size needed to
mill the figure. The spread is the ratio of the diameter to the minimum feature
size. While many algorithms (particularly in meshing) depend on the spread of
the input, none explicitly consider finding a mesh whose spread is similar to
the input. When a polygon is partitioned into smaller regions, such as
triangles or quadrangles, the degradation is the ratio of original to final
spread (the final spread is always greater).
  Here we present an algorithm to quadrangulate a simple n-gon, while achieving
constant degradation. Note that although all faces have a quadrangular shape,
the number of edges bounding each face may be larger. This method uses Theta(n)
Steiner points and produces Theta(n) quadrangles. In fact to obtain constant
degradation, Omega(n) Steiner points are required by any algorithm.
  We also show that, for some polygons, a constant factor cannot be achieved by
any triangulation, even with an unbounded number of Steiner points. The
specific lower bounds depend on whether Steiner vertices are used or not.
