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Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors
Sept. 2012 (vol. 18 no. 9)
pp. 1474-1487
A. Abbas, Dept. of Comput. Sci., Univ. of Balamand, Tripoli, Lebanon
Hongwei Lin, Zhejiang Univ., Hangzhou, China
A. Nasri, American Univ. of Beirut, Beirut, Lebanon
S. Okaniwa, Digital Imaging Div., Casio Comput. Co., Ltd., Shibuya, Japan
Y. Kineri, Dept. of Mech. Eng., Yokohama Nat. Univ., Yokohama, Japan
T. Maekawa, Dept. of Mech. Eng., Yokohama Nat. Univ., Yokohama, Japan
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.

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Index Terms:
splines (mathematics),computational geometry,interpolation,shape design,uniform B-spline curve interpolation,prescribed tangent,curvature vectors,geometric algorithm,data point sequence,curvature vectors constraints,knot insertion,handling plane,space curves,linear system,NC machining,Spline,Interpolation,Equations,Aerospace electronics,Vectors,Educational institutions,Electronic mail,parametric curve.,B-spline curve,interpolation,tangent,curvature vector
Citation:
A. Abbas, Hongwei Lin, A. Nasri, S. Okaniwa, Y. Kineri, T. Maekawa, "Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 9, pp. 1474-1487, Sept. 2012, doi:10.1109/TVCG.2011.262
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