Transition between concentric or tangent circles with a single segment of PH quintic curve

The paper describes a method to join two circles with a C-shaped and an S-shaped transition curve, composed of a Pythagorean hodograph quintic segment, preserving G² continuity. It is considered desirable to have such a curve in satellite path planning, highway or railway route designing, or non-holonomic robot path planning. As an extension of our previous work, we show that a single quintic curve can be used for blending or for a transition curve between two circles, including the previously unsolved cases of concentric and tangential circles.