Computation of the shortest path between two curves on a parametric surface by geodesic-like method

In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in $\mathbb{R}^3$. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.