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Proceedings of CAD'14, 2014, 129-131
An Extension Algorithm for Disk B-Spline Curve with G2 Continuity

Ting Zhang, Xingce Wang, Qianqian Jiang, Zhongke Wu, Mingquan Zhou, Beijing Normal University
Hock Soon Seah, Nanyang Technological University

Abstract. Disk B-Spline curve has its distinct advantages in representing a 2D region. In 2004, Wu and Seah first proposed the disk B-Spline curve through extending disk Bezier curve, which is defined in B-Spline form and describes not only a 2D region, but also the center curve (skeleton) of the region explicitly. Furthermore, DBSC is used for representing artistic brushstrokes and applications in 2D animation. Curve extension is a general problem in curve design. A given curve usually needs to be extended in order to meet some geometric shape conditions or engineering requirements. Ting et al. proposed a DBSC extension algorithm based on curve unclamping. With their method, the unclamped knot vector of the extended DBSC is computed according to the accumulated chord length method. The original DBSC and the extending segment satisfy C2-continuity at the joint disk. However, the extended DBSC is exclusive and in some cases is not a desired result. Geometric continuity plays an important role in depicting curves’ fairness and can supply additional degrees of freedom for adjustment. In this paper, we propose a G2-continuity extension algorithm for DBSC. The shape of the extended DBSC is determined by minimizing its strain energy. The unclamped knot vector is determined by the optimal degree of freedom acquired.

Keywords. Curve extension, disk B-Spline curve, G2 continuity, minimal energy method

DOI: 10.14733/cadconfP.2014.129-131