Traditionally, transition curves used in railway and highway design are developed from spirals which graduate from a large radius at the point of entry into the curve down to a desired smaller radius with the intent of making a continuous change from the zero curvature (infinite radius) of straight line travel to the curvature required to follow the necessary route of travel. Unfortunately, even though spirals can be selected with nearly zero curvature, there is still some discontinuity in the curvature at the point of entry. In order to develop a more continuous curvature through the transition from straight line travel into the curve, functions that contained points of zero curvature (inflection points) were investigated. At this time, equations have been developed which allow for exact computation of quartic and cosine function transition curves given either the angle of turn and the minimums radius of the curve, or the angle of turn and the distance between the points of entry and exit. These curves not only provide an absolutely continuous change in curvature from straight line travel into the curve, but the calculations can be performed in closed form with no iteration in a matter of minutes. I would like the opportunity to try this method in a real case to compare to the results obtained with the traditional methods.