A new extension algorithm for cubic B-splines based on minimal strain energy

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 GC^2-continuous with the original one, a family of cubic polynomial interp...

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Bibliographic Details
Published in:Journal of Zhejiang University. A. Science Vol. 7; no. 12; pp. 2043 - 2049
Main Authors: Mo, Guo-liang, Zhao, Ya-nan
Format: Journal Article
Language:English
Published: Department of Information and Computational Science, Zhejiang University City College, Hangzhou 310015, China 01.12.2006
Subjects:
GC^2连续
再参量化
最小应变能量
Extension
Knot removal
Reparametrization
GC2-continuous
Minimal strain energy
ISSN:1673-565X, 1862-1775
Online Access:Get full text
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Summary: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 GC^2-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 GC^2 parameter to be zero and determining the second GC^2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C-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.
Bibliography:TP391.72
GC^2-continuous, Extension, Minimal strain energy, Knot removal, Reparametrization
33-1236/O4
ISSN:1673-565X
1862-1775
DOI:10.1631/jzus.2006.a2043