| A matrix method for degree-raising of B-spline curves |
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| 引用本文： | 秦开怀. A matrix method for degree-raising of B-spline curves[J]. 中国科学E辑(英文版), 1997, 40(1): 71-81. DOI: 10.1007/BF02916592 |
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| 作者姓名： | 秦开怀 |
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| 作者单位： | Department of |
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| 基金项目： | Project supported by the National Natural Science Foundation of China. |
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| 摘 要： | A new identity is proved that represents the kth 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 degree k - 1, it can help obtain a segment of curve of degree k 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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A matrix method for degree-raising of B-spline curves |
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| Kaihuai Qin. A matrix method for degree-raising of B-spline curves[J]. Science in China(Technological Sciences), 1997, 40(1): 71-81. DOI: 10.1007/BF02916592 |
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| Authors: | Kaihuai Qin |
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| Affiliation: | (1) Department of Computer Science and Technology, Tsinghua University, 100084 Beijing, China |
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| Abstract: | A new identity is proved that represents the kth 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 degree k - 1, it can help obtain a segment of curve of degree k 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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| Keywords: | B-spline curve degree-raising control polygon. |
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