Least-squares fitting of algebraic spline curves via normal vector estimation. (English) Zbl 0967.65011

Jüttler, Bert

Cipolla, Roberto (ed.) et al., The mathematics of surfaces IX. Proceedings of the 9th IMA conference, Cambridge, GB, September 4-7, 2000. London: Springer. 263-280 (2000).

Summary: We describe an algorithm for fitting implicitly defined algebraic spline curves to given planar data. By simultaneously approximating points and associated normal vectors, we obtain a method which is both computationally simple, as the result is obtained by solving a system of linear equations, and geometrically invariant. The initial result of the curve fitting procedure is improved by iteratively adjusting the associated field of normal vectors. It is planned to generalize the approach to algebraic spline surfaces.
For the entire collection see [Zbl 0946.00021].

MSC:

65D10	Numerical smoothing, curve fitting
65D17	Computer-aided design (modeling of curves and surfaces)

Keywords:

curve fitting; algorithm; algebraic spline curves; algebraic spline surfaces