Graphics Reference
In-Depth Information
Self-intersection
Edge
Interior
Vertex
Diagonal
Exterior
(a)
(b)
Figure 3.13
The components of a polygon. Polygon (a) is simple, whereas polygon (b) is
nonsimple due to self-intersection.
area covered by the polygon) and the
exterior
(the unbounded area outside the poly-
gon). Usually the term
polygon
refers to both the polygon boundary and the interior.
A polygon
diagonal
is a line segment that joins two polygon vertices and lies fully
inside the polygon. A vertex is a
convex vertex
if the interior angle (the angle between
the sides connected to the vertex, measured on the inside of the polygon) is less than
or equal to 180 degrees (Figure 3.14a). If the angle is larger than 180 degrees, it is
instead called a
concave
(or
reflex
)
vertex
(Figure 3.14b).
A polygon
P
is a
convex polygon
if all line segments between any two points of
P
lie
fully inside
P
. A polygon that is not convex is called a
concave polygon
. A polygon with
Convex
vertex
Concave
vertex
(a)
(b)
Figure 3.14
(a) For a convex polygon, the line segment connecting any two points of the
polygon must lie entirely inside the polygon. (b) If two points can be found such that the
segment is partially outside the polygon, the polygon is concave.
