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Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 78702, 11 pages
Research Article

Least Squares Fitting of Piecewise Algebraic Curves

Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 25 March 2007; Revised 4 June 2007; Accepted 18 October 2007

Academic Editor: T. Zolezzi

Copyright © 2007 Chun-Gang Zhu and Ren-Hong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A piecewise algebraic curve is defined as the zero contour of a bivariate spline. In this paper, we present a new method for fitting C1 piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data. By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is also considered in the method. Moreover, some examples are presented.