G2-Continuity Blending of Ball B-Spline Curve Using Extension

Curve blending is an essential task in geometric modeling, while a ball B-spline curve (BBSC) has its advantages in representing freeform tubular objects. This paper proposes a blending algorithm for ball B-Spline curve with G2 continuity, which is used to describe the smoothness of the joint point. An original BBSC is extended smoothly to join another one, such that no additional blending curve is created and the two original curves are not changed. The shape of the extended curve is then determined by minimizing strain energy. The corresponding scalar function of the control balls is determined through applying G2-continuity conditions to the 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. The experiment results demonstrate our method for blending BBSC is effective. Moreover, some G2 blending results of the BBSC in simulating the tubular objects are given.