Supporting line

The notion of supporting line is also discussed for planar shapes.

[2] The notion of a supporting line to a planar curve or convex shape can be generalized to n dimension as a supporting hyperplane.

If two bounded connected planar shapes have disjoint convex hulls that are separated by a positive distance, then they necessarily have exactly four common lines of support, the bitangents of the two convex hulls.

[2] Without the assumption of convexity, there may be more or fewer than four lines of support, even if the shapes themselves are disjoint.

For instance, if one shape is an annulus that contains the other, then there are no common lines of support, while if each of two shapes consists of a pair of small disks at opposite corners of a square then there may be as many as 16 common lines of support.