Finding common tangents
Common tangents are simply lines that are tangent to both polygons at the same time, and so that the both polygons lie to one side of that line. In other words, a common tangent is a line of support for both polygons. An example is illustrated below:
Two disjoint convex polygons and a common tangent line between them.
In fact, common tangents are determined by the same pairs of points between the polygons that determine the bridges. Hence,
given two disjoint polygons, there exist two common tangents between the polygons, and when the polygons intersect, there may be as many as there are vertices.
The same algorithm computing the bridges between two convex polygons (i.e. the merge algorithm) can therefore be used to determine common tangents.
Another "version" of lines tangent to both polygons are critical support lines. In that case the polygons lie on opposite sides of the line.
Bridges can also be used in computing the intersection of two convex polygons.
December 17th, 1998