| A new extension algorithm for cubic B-splines based on minimal strain energy |
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| 作者姓名： | MO Guo-liang ZHAO Ya-nan |
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| 作者单位： | Department of Information and Computational Science，Zhejiang University City College，Hangzhou 310015，China |
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| 摘 要： | INTRODUCTION B-spline curves and surfaces have been widely used in Computer Graphics (CG) and Computer Aided Design (CAD) (Hoschek and Lasser, 1993; Piegl and Tiller, 1997). Many practical algorithms, such as those for position and derivatives evaluation, knot insertion, knot deletion and degree elevation, are usually implemented in a CAD system that uses B-spline as a shape design tool. In curve and surface design, a given B-spline curve or surface usually needs to be extended in …
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| 关 键 词： | GC^2连续 扩展 最小应变能量 再参量化 |
| 收稿时间： | 2006-03-08 |
| 修稿时间： | 2006-07-03 |
A new extension algorithm for cubic B-splines based on minimal strain energy |
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| MO Guo-liang ZHAO Ya-nan.A new extension algorithm for cubic B-splines based on minimal strain energy[J].Journal of Zhejiang University Science,2006,7(12):2043-2049. |
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| Authors: | Guo-liang Mo Ya-nan Zhao |
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| Institution: | (1) Department of Information and Computational Science, Zhejiang University City College, Hangzhou, 310015, China |
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| Abstract: | Extension of a B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC2 parameter to be zero and determining the second GC2 parameter by mini- mizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C2-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given. |
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| Keywords: | GC~2-continuous Extension Minimal strain energy Knot removal Reparametrization |
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