In this paper, we propose a linear method for C approximation of rational Bézier curve with arbitrary degree polynomial curve. Based on weighted least-squares, the problem be converted to an approximation between two polynomial curves. Then applying Bernstein-Jacobi hybrid polynomials, we obtain the resulting curve. In order to reduce error, degree reduction method for Bézier curve is used. A e...

Keywords: Arbitrary order derivative Derivative formula Rational Bézier curve a b s t r a c t In this paper, we develop the exact arbitrary order derivative formula of a rational Bézier curve at its corner. Some examples are presented to demonstrate the computation of the exact derivatives. Derivative formula of a parametric curve has important applications in geometric design and applied mathe...

In order to tackle the problem of shape design and shape adjustment of complex surfaces in engineering, continuity conditions between generalized Bézier-like surfaces with multiple shape parameters are studied in this paper. Firstly, the geometric model of the generalized Bézier-like surfaces is built by blending a number of Bézier-like curves with independent shape parameters. Secondly, based ...

The main goal of the paper is to introduce methods which compute Bézier curves faster than Casteljau’s method does. These methods are based on the spectral factorization of a n×n Bernstein matrix, B n(s) = PnGn(s)P −1 n , where Pn is the n×n lower triangular Pascal matrix. So we first calculate the exact optimum positive value t in order to transform Pn in a scaled Toeplitz matrix, which is a p...

Most shapes are simply too complicated to define using a single Bézier curve. A spline curve is a sequence of curve segments that are connected together to form a single continuous curve. For example, a piecewise collection of Bézier curves, connected end to end, can be called a spline curve. Overhauser curves are another example of splines. The word “spline” can also be used as a verb, as in “...

By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.

This paper considers the shape control of the cubic H-Bézier curve, which can represent hyperbolas and catenaries accurately. We fix all the control points while let one vary. The locus of the moving control point that yields a cusp on the cubic H-Bézier curve is a planar curve; The tangent surface of the planar curve is the locus of the positions of the moving control point that yield inflecti...

In this paper a class of quartic trigonometric Bézier curve, called QT Bézier curve, with two shape parameters is presented. These curves not only inherit most properties of the usual quartic Bézier curves in the polynomial space, but also enjoy some other advantageous properties for shape modelling. The shape of the curve can be adjusted by altering the values of shape parameters while the con...

An optimal curve fitting technique has been developed which is meant to automatically provide a fit to any ordered digital data in plane. A more flexible class of rational cubic functions is the basis of this technique. This class of functions involves two control parameters, which help to produce optimal curve fit. The curve technique has used various ideas for curve design. These ideas includ...