G1 interpolation with a single Cornu spiral segment

摘要

Cornu spiral segments are used in applications such as the geometric design of highways and railways, robot path planning, and shape completion. For some applications, e.g. shape completion in computer vision, it is important to use a single visually pleasing curve segment to smoothly fill a gap, even though the gap may not be filled in a curvature continuous manner. An improved method for doing so using a Cornu spiral segment is discussed. The method is generally suitable for any application where it is required to smoothly fit a curve between two given points when the corresponding tangent directions, but not the curvatures, are also given or known.