Qnintic G~2 Interpolating Fair Curves Via Curvature Variation Minmization

The construction of fair curves has significant application requirements in route design, trajectory planning and related fields. In general, fair curves are usually constructed by optimizing a certain energy functional. This paper proposes a construction method for quintic G2 interpolating curves by minimizing curvature variation. After replacing curvature variation with the approximate jerk energy, it is quite efficient to obtain the solution of fair curves. Besides the jerk energy, the objective function is regulated by a term of curve length, such that the objective function becomes convex and has the effect to restrict the lengths of resulting curves. Because the objective function is expressed as a quartic function in two unknowns, it is able to satisfy the requirement of real-time curve construction. Experiments demonstrate that the proposed method can produce interpolating curves with smaller of curvature variation.