~F84. SMOOTHING.


	In CRE  the term "smoothing"  refers more  to the problem  of
breaking a  manifold (polygon) into functions  (arcs), rather than to
the problem  of fitting  functions to  measured  data. The  smoothing
step, converts the  polygons of vertical and  horizontal vectors into
polygons of  arcs.  For the present the term "arc" means "linear arc"
which is  a line  segment. Fancier  arcs: circular  and cubic  spline
were implemented  and thrown out mostly  because they were  of no use
to higher processes  such as  the polygon compare  which would  break
the fancier arcs back  down into linear vectors for  computing areas,
inertia tensors or mere display buffers.


	Smoothing  is applied to each  polygon of a level.   To start
the smoothing, a ring of two  arcs is formed (a bi-gon) with one  arc
at the  uppermost left and  the other at  the lowermost right  of the
given vector  polygon. Next a recursive make arc operation, MKARC, is
is appled to the  two initial arcs. Since  the arc given to  MKARC is
in a one  to one correspondece with a doubly  linked list of vectors;
MKARC checks to  see whether  each point on  the list  of vectors  is
close enough to the  approximating arc.  MKARC returns  the given arc
as  good enough when all  the sub vectors fall  within a given width;
otherwise MKARC splits the arc in two and places a new arc  vertex on
the vector vertex that was furthest away from the original arc.


	The  two large  images  in figure-7,    illustrate a  polygon
smoothed  with arc  width tolerances set  at two  different widths in
order to  show one  recursion of  MKARC.   The  eight smaller  images
illustrate  the results  of setting  the arc  width tolerance  over a
range of values. Because of  the dekinking mentioned earlier the  arc
width tolerance  can be equal  to or less  than 1.0 pixels  and still
expect a  substantial reduction in the number  of vectors it takes to
describe a contour polygon.


	A  final  important  smoothing detail is  that the arc  width
tolerance is  actually taken  as a function  of the  highest contrast
vector  found along the arc; so that  high contrast arcs are smoothed
with much smaller  arc width tolerances  than are low contrast  arcs.
After smoothing, the  contrast across  each arc  is computed  and the
ring of  arcs replaces  the ring  of vectors  of the  given  polygon.
(Polygons that would be expressed as only two arcs are deleted).
~I1973,800;F8- 30 -