Total least squares fitting of Bézier and B-spline curves to ordered data

Pii: S0167-8396(02)00088-2

We begin by considering the problem of fitting a single Bézier curve segment to a set of ordered data so that the error is minimized in the total least squares sense. We develop an algorithm for applying the Gauss–Newton method to this problem with a direct method for evaluating the Jacobian based on implicitly differentiating a pseudo-inverse. We then demonstrate the simple extension of this a...

TENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE

In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...

Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree

In this paper, we propose a method to obtain a constrained approximation of a rational Bézier curve by a polynomial Bézier curve. This problem is reformulated as an approximation problem between two polynomial Bézier curves based on weighted least-squares method, where weight functions ρ(t) = ω(t) and ρ(t) = ω(t) are studied respectively. The efficiency of the proposed method is tested using so...

Least-Squares Fitting of Data with B-Spline Curves

LP fitting approach for reconstructing parametric surfaces from points clouds

We present a method to reconstruct a surface from a group of points, each provided with two parameters. The kind of reconstructed surface can be a Bezier surface, a B-spline surface or any surface generated by a basis of functions. The usual method involved in such a reconstruction is the least squares approach. Our original fitting method called LP-fitting uses a linear program for minimizing ...