An Extension Algorithm for Ball B-Spline Curves with G2 Continuity

Curve extension is a useful function in shape modeling for cyber worlds, while a ball B-spline curve (BBSC) has its advantages in representing freeform tubular objects. In this paper, an extension algorithm for ball B-Spline curve with G²-continuity is investigated. We apply the extending method of B-Spline curves to the center curve of BBSC through generalizing a minimal strain energy method from 2D to 3D. And the initial value of G²-continuity parameter was selected by minimizing the approximate energy function which is a problem with O(1) time complexity. The corresponding scalar function of control balls is determined through applying G²-continuity condition to scalar function. In order to ensure the radii of the control balls are positive, we make a decision about the range of the G²-continuity parameter and then determine it by minimizing the strain energy in the affected area. Some experiments for comparing our method with other methods are given. The results show our method for extending BBSC is effective.