In this paper, we investigate how to topologically
and geometrically characterize the intersection relations between
a movable convex polygon and a set of possibly overlapping
polygons fixed in the plane. More specifically, a subset
is called an intersection relation if there exists a placement of
that intersects, and only intersects, . The objective of this paper
is to design an efficient algorithm that finds a finite and discrete
representation of all of the intersection relations between and
. Past related research only focuses on the complexity of the
free space of the configuration space between and and how
to move or place an object in this free space. However, there are
many applications that require the knowledge of not only the free
space, but also the intersection relations. Examples are presented
to demonstrate the rich applications of the formulated problem
on intersection relations.