位相幾何学と人工知能

最近ＡＡＡＩ（アソシエション・フォア・ザ・アドバンスメント・オブ・アーテイフィシャル・インテリジェンス）の論文に目を通しています。
The paper proposes an algorithm for determining topological relationships between complex polygons. The method is based on the use of circular strings to describe a topological relationship. Firstly, one must consider what topological relationships are to be defined. Basically, pairs of convex polygons are assigned relationships such as:
DC = disconnected
TPP = tangential proper part
NTPP = Non-tangential proper part
EQ = Equivalent
EC = Externally connected
The string is a set of characters which describe segments on the border of the intersection of the two regions, i.e. if the regions are a and b, the string describes segments on d(a intersect b).
I am wondering: 1. how polygons are represented in computer memory. 2. how the intersections and boundaries are determined. 3. how artificial intelligence is involved.
The algorithm given, which seems to be a one-step classification metric, is premised on the ability to compute the intersection of two regions in linear time. It also seems to assume the ability to easily determine angle measure and ray length.