| Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory |
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| 引用本文： | CHENG Min & WANG GuojinInstitute of Images and Graphics,State Key Laboratory of CAD & CG,Zhejiang University,Hangzhou 310027,China. Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory[J]. 中国科学F辑(英文版), 2004, 47(1): 44-54. DOI: 10.1360/02yf0229 |
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| 作者姓名： | CHENG Min & WANG GuojinInstitute of Images and Graphics State Key Laboratory of CAD & CG Zhejiang University Hangzhou 310027 China |
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| 作者单位： | CHENG Min & WANG GuojinInstitute of Images and Graphics，State Key Laboratory of CAD & CG，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | 国家自然科学基金，国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 摘 要： | NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design.
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Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory |
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| Cheng Min,Wang Guojin. Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory[J]. Science in China(Information Sciences), 2004, 47(1): 44-54. DOI: 10.1360/02yf0229 |
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| Authors: | Cheng Min Wang Guojin |
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| Affiliation: | Institute of Images and Graphics, State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China |
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| Abstract: | NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design. |
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| Keywords: | NURBS curves matrix representation multi-degree reduction Chebyshev polynomials. |
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