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A matrix method for degree-raising of B-spline curves

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Abstract

A new identity is proved that represents thekth order B-splines as linear combinations of the (k+1) th order B-splines. A new method for degree-raising of B-spline curves is presented based on the identity. The new method can be used for all kinds of B-spline curves, that is, both uniform and arbitrarily nonuniform B-spline curves. When used for degree-raising of a segment of a uniform B-spline curve of degreek−1, it can help obtain a segment of curve of degreek that is still a uniform B-spline curve without raising the multiplicity of any knot. The method for degree-raising of Bezier curves can be regarded as the special case of the new method presented. Moreover, the conventional theory for degree-raising, whose shortcoming has been found, is discussed.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, 100084, Beijing, China

    Qin Kaihuai

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  1. Qin Kaihuai
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Project supported by the National Natural Science Foundation of China.

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Qin, K. A matrix method for degree-raising of B-spline curves. Sci. China Ser. E-Technol. Sci. 40, 71–81 (1997). https://doi.org/10.1007/BF02916592

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  • DOI: https://doi.org/10.1007/BF02916592

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