Planar Transition Curves Using Quartic Bezier Spiral

Abstract

A method to construct the transition curves by using a family of the quartic Bezier spiral is described. The applications of quartic spiral discussed are G2 transition curve joining a straight line and a circle, and joining two straight lines with a pair of spiral segment. 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 was introduced has more degrees of freedom and will give a better approximation to clothoid spiral. These methods of constructing transition curves can be simplified by transformation process which extends the application area, and it gives a family of transition curves that allow more flexible curve designs.