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...

In this paper the problem of geometric interpolation of planar data by parametric polynomial curves is revisited. The conjecture that a parametric polynomial curve of degree ≤ n can interpolate 2n given points in R2 is confirmed for n ≤ 5 under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the optimal order 2n can be achie...

A method for automatic assessment of singing voice is proposed. Such method quantifies in a meaningful way the similarity between the user performance and a reference melody. A set of melodic similarity measures comprising intonation and rhythmic aspects have been implemented for this goal. Such measure implement different MIR techniques, such as melodic transcription or score alignment. The re...

This report describes a technique to detect curvature. The technique uses local polynomial fitting on a local orientation description of an image. The idea is based on the theory of rotational symmetries which describes curvature, circles, starpatterns etc. The local polynomial fitting is shown to be equivalent to calculating partial derivatives on a lowpass version of the local orientation. Th...

in x and y. The degree of the curve is the degree of the polynomial f(x, y). A parametric curve α(t) = (p(t), q(t)), where p(t) and q(t) are polynomials in t, is an algebraic curve. This is because we can eliminate t from the two polynomial equations x = p(t) and y = q(t) using the resultant technique, and obtain a polynomial equation, called their resultant, in x and y. The resultant has a deg...

We prove two formulae that express the Alexander polynomial 1C of several variables of a plane curve singularity C in terms of the ring OC of germs of analytic functions on the curve. One of them expresses1C in terms of dimensions of some factors corresponding to a (multi-indexed) filtration on the ring OC . The other one gives the coefficients of the Alexander polynomial 1C as Euler characteri...

throughout the current study, the appropriate function for a description of egg production curve in a commercial broiler dam line was determined through fittings of a number of six mathematical models, namely: incomplete gamma function (wm): modified incomplete gamma function (mwm): compartmental function (cm): modified compartmental function )mcm): polynomial regression function of ali and sch...

A polynomial map F = (P,Q) ∈ Z[x, y]2 with Jacobian JF := PxQy −PyQx ≡ 1 has polynomial inverse of integer coefficients if the complex plane curve P = 0 has infinitely many integer points. 2000 Mathematical Subject Classification: 14R15.

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basi...