The family of biarcs that matches planar, two-point Hermite data

The biarc is a curve made by joining two circular arcs in a G 1 fashion. There is a one-parameter family of biarcs that can match given planar, two-point G 1 Hermite data. This note considers the range of G 1 Hermite data that can be matched, identifies the region in which the members of the family of biarcs lie, and shows that there is exactly one member biarc passing through each point in that region.