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CLC number: TP391.72
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Received: 2006-03-28
Revision Accepted: 2006-07-03
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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 A, 2006, 7(12): 2043-2049.
@article{title="A new extension algorithm for cubic B-splines based on minimal strain energy",
author="MO Guo-liang, ZHAO Ya-nan",
journal="Journal of Zhejiang University Science A",
volume="7",
number="12",
pages="2043-2049",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A2043"
}
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DOI - 10.1631/jzus.2006.A2043
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 minimizing 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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