Results 221 to 230 of about 129,549 (262)

Algebraically rectifiable parametric curves

Computer Aided Geometric Design, 1993
A differentiable parametric curve \((x(t),y(t))\) is said to be a polynomial parametric one, if \(x(t)\), \(y(t)\) both are polynomials. In this paper sufficient and necessary conditions for the arc length \(s(t) = \int^ t_ 0 \sqrt{x'{}^ 2(\tau) + y'{}^ 2(\tau)} d\tau\) of a polynomial parametric curve to be an algebraic function of the parameter are ...
Takis Sakkalis, Rida T. Farouki
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On the Parametrization of an Algebraic Curve

Mathematical Notes, 2019
Given an algebraic plane curve, the existence of a global uniformization is guaranteed by the Uniformization Theorem, but there is no an algorithm for its calculation. Currently, it is very well known how to parametrize the curve if its genus is equal to \(0\) or \(1\) or if its group of birational authomorphisms is sufficiently large. The main goal of
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Parametric and nonparametric curve fitting

Automatica, 2006
This article summarizes the convergence issues for the classical curve fitting problem. The properties of the input signal that ensure convergence of the estimate are investigated. In the parametric case, the standard least squares method is used and the sufficient conditions under which the estimated parameters converge to their true values almost ...
K. HSU, NOVARA, Carlo, T. VINCENT, MILANESE, Mario, K. POOLLA   +4 more
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Prescribing the length of parametric curves

Computer Aided Geometric Design, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John A. Roulier, Bruce R. Piper
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On rational parametric curve approximation

Computer Aided Geometric Design, 1993
A new method is proposed for the rational approximation of functions. The autors describe extensions to the basic method which permit the generation of approximations satisfying point constraints and derivative constraints of arbitrary order at the endpoints of the interval of interest.
Michael J. Pratt, Ray J. Goult, L. Ye
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Blending two parametric curves

Computer-Aided Design, 2009
Segments of two given curves can be blended to produce a segment of a new curve. Blending can provide a smooth transition from one curve to another and can give various degrees of smoothness at the endpoints of the blend, where the smoothness is measured analogously to parametric continuity C^(^n^) and geometric continuity G^(^n^). Blending can provide
Dereck S. Meek, Desmond J. Walton
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Parametrization of curves in characteristic \(p\)

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 2004
Let \(K\) be an algebraically closed field of characteristic \(p\), complete for an ultrametric absolute value. It is shown that many algebraic curves over \(K\) admit no parametrization by unbounded meromorphic functions inside an open disc. For example, theorem 3.1 shows that there are no such functions \(f,g\) satifying \(f^m + g^n = 1\) provided ...
A., Boutabaa, A., Escassut
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Finding parametric curves in an image

1992
We present a reliable and efficient method for extracting simple geometric structures, i.e., straight lines, parabolas, and ellipses, from edge images. The reliability of the recovery procedure which builds the parametric models is ensured by an iterative procedure through simultaneous data classification and parameter estimation.
Ales Leonardis, Ruzena Bajcsy
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Modular Parametrizations of Elliptic Curves

Canadian Mathematical Bulletin, 1985
AbstractMany — conjecturally all — elliptic curves E/ have a "modular parametrization," i.e. for some N there is a map φ from the modular curve X0(N) to E such that the pull-back of a holomorphic differential on E is a modular form (newform) f of weight 2 and level N.
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Parametric cubics as algebraic curves

Computer Aided Geometric Design, 1988
Planar parametric cubics are used to model curves, both by themselves, and as segments of splines. This paper provides first a background in the algebraic curve theory of cubics; specifically, double points, inflection points, tangent lines, standard curves, and slope parametrizations are discussed.
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