Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors

Authors:
Shoichi Okaniwa;Ahmad Nasri;Hongwei Lin;Abdulwahed Abbas;Yuki Kineri;Takashi Maekawa
Affiliations:
Casio Computer Co., Ltd., Shibuya;American University of Beirut, Riad El-Solh;Zhejiang University, Hangzhou;The University of Balamand, Tripoli;Yokohama National University, Yokohama;Yokohama National University, Yokohama
Venue:
IEEE Transactions on Visualization and Computer Graphics
Year:
2012

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Abstract

This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.