  A method to construct transition curves using a family of the quartic Bezier
spiral is described. The transition curves discussed are S-shape and C-shape of
contact, between two separated circles. A spiral is a curve of monotone
increasing or monotone decreasing curvature of one sign. Thus, a spiral cannot
have an inflection point or curvature extreme. The family of quartic Bezier
spiral form which is introduced has more degrees of freedom and will give a
better approximation. It is proved that the methods of constructing transition
curves can be simplified by the transformation process and the ratio of two
radii has no restriction, which extends the application area, and it gives a
family of transition curves that allow more flexible curve designs.
