Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, PR China

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Abstract—The shape features of planar C-B-spline segments are analyzed. The necessary and sufficient conditions are derived for the curve having one or two inflection points, a loop or a cusp, or be locally or globally convex. All conditions are completely characterized by the relative position of the control polygon’s side vectors, and are summarized in three kinds of shape diagrams in terms of the linear independence of the three side vectors. Moreover, it is proved that a spatial C-B-spline segment has no singularities and generalized inflection points.

Index Terms—C-B-spline, Singularity, Inflection point, Convexity, Shape diagram

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Cite: Rongjun Wu, Guohua Peng, "Shape Analysis of C-B-splines," Journal of Computers vol. 9, no. 3, pp. 750-757, 2014.