On Local Fairing Algorithm for Cubic B-spline with the Second Discrete Curvature

In this paper, a new discrete curvature-the second discrete curvature is introduced. It is obtained that the curvatures of a cubic B-spline curve at its joining points are "proportional to" the second discrete curvatures of its corresponding control points about the node vector, and the second discrete curvature has similar properties but be more accurate than discrete curvature. The fairing algorithm for cubic B-spline based on the second discrete curvature is given. With this algorithm curves are faired through adjusting the second discrete curvature of the corresponding control points directly, thus the fairing process is more concise and has stronger geometrical intuition. It is showed that the algorithm can get better fairing effects through experiment examples.