Glossary

A simple polygon containing precisely two ears and one mouth [7].

A vertex *p _{i}* is concave if a left turn is made at

The convex hull *CH*(*P*) of a polygon
*P* is the
smallest convex polygon that contains *P*.

A polygon *P* is convex if and only if for any
pair of points *x*, *y* in *P* the line segment between
*x* and *y* lies entirely in *P*.

A vertex *p _{i}* is convex if a right turn is made at

The one edge of a good sub-polygon *GSP*
that is not in simple polygon
*P* (where *GSP* is a good sub-polygon of *P*).

A line segment lying entirely inside
polygon *P* and
joining two non-consecutive vertices *p _{i}* and

Given a triangulated simple polygon, the dual-tree is the graph generated by plotting a vertex at each triangle and edges joining vertices in adjacent triangles (triangles which share a diagonal).

A
principal vertex *p _{i}* of a
simple polygon

A good sub-polygon of a
simple polygon *P*, denoted by *GSP*,
is a sub-polygon whose
boundary differs from that of *P* by at most one edge. This edge,
if it exists, is called the cutting edge
[1].

A simple closed curve *C* in the plane divides the plane into exactly two
domains, an inside and an outside
[2].

A vertex in a graph with only 1 edge incident to it.

A principal vertex *p _{i}* of a
simple polygon

Except for convex polygons, every simple polygon has at least one mouth [7].

A closed chain of *n* line segments (*p _{i}*,

2 Polygons

A vertex *p _{i}* of
simple polygon

A proper ear of a good sub-polygon *GSP* is an
ear of *GSP* which is not an end-point of the
cutting edge of *P*
[1].

A polygon *P*
with no two non-consecutive edges intersecting. There is a
well-defined bounded interior and unbounded exterior for a simple polygon,
where the interior is surrounded by edges. When referring to *P*,
the convention is to include the interior of *P*.

A triangulation of a
simple polygon consists of *n*-3
non-intersecting diagonals or
*n*-2 triangles where *n* is the number of vertices in
the simple polygon.

Except for triangles every simple polygon has at least two non-overlapping ears [4].

`This page was last updated on Wednesday, December 10 ^{th},
1997.`

`©` `1997 Ian Inc.`