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

• 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
• DOI: 10.1631/jzus.2006.a2043

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.