Results 261 to 270 of about 36,511 (307)
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The Hilbert transform of cubic splines
Communications in Nonlinear Science and Numerical Simulation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mina B Abd-El-Malek, Samer S Hanna
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Representations for parametric cubic splines
Computer Aided Geometric Design, 1989Geometrically continuous cubic splines [see \textit{B. A. Barsky}, Ph. D. Dissertation, Univ. of Utah (1981); \textit{W. Boehm}, Comput. Aided Geom. Des. 2, 313-323 (1985; Zbl 0645.53002); the author, ibid. 3, 155-162 (1986; Zbl 0592.41011), \textit{G. M. Nielson}, Proc. Conf., Univ. Utah Salt Like City, Utah 1974, 209-235 (1974; M.R.
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On the condition of cubic B-splines
Journal of Approximation Theory, 2023B-Splines are the most attractive form of bases of polynomial splines spaces. Their advantages, among many others, are their compact support and positivity inside the support. They also form stable bases, and in this connection, their condition numbers are very important. In this paper, bounds on these condition numbers are provided.
Tom Lyche, Knut Mørken, Ulrich Reif
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A cubic spline approximation of an offset curve of a planar cubic spline
International Journal of Computer Mathematics, 2001We derive an easier way to calculate an algorithm for a cubic spline approximation of an offset curve of a given planar cubic spline and a sufficient condition on an offset length for its existence.
K. Suenaga, M. Sakai
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Monotonic cubic spline interpolation
Proceedings Computer Graphics International CGI-99, 1999This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have C/sup 2/ continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable
George Wolberg, Itzik Alfy
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IBM Journal of Research and Development, 1978
Control curves used in industry are usually planar cubic splines, continuous and single-valued for a specific independent variable. If large slopes are specified at certain points, the spline coefficients, which are computed in order to preserve second derivative continuity of the spline, invariably lead to wildly oscillatory curves. Normally the large
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Control curves used in industry are usually planar cubic splines, continuous and single-valued for a specific independent variable. If large slopes are specified at certain points, the spline coefficients, which are computed in order to preserve second derivative continuity of the spline, invariably lead to wildly oscillatory curves. Normally the large
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Optimal parameterization for cubic splines
Computer-Aided Design, 1991The author proposes an algorithm which produces a unique \(C^ 2\)-spline with nearly optimal arc-length parametrization. In order to determine the spline in question a minimization problem with interpolatory constraints has to be solved. Shape preserving interpolation is also discussed.
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Smoothing With Periodic Cubic Splines
Bell System Technical Journal, 1983In this paper we present a mathematical algorithm for constructing a smoothing cubic spline with periodic end conditions and a predetermined ‘closeness of fit’ to a given set of points in the plane. In addition to providing a mathematical tool for smoothing raw data in which the underlying function is known to be periodic, this algorithm has special ...
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IMA Journal of Numerical Analysis, 1984
A cubic X-spline with knots \(\{x_ i\}^ N_{i=0}\) and parameter vector \(\{c_ i\}\) is a function \(s\in C^ 1[a,b]\) if \[ (i)\quad s(x)\text{ is a cubic on each } [x_{i-1},x_ i], \] \[ (ii)\quad s'(a)=[s(x_ 1)-s(x_ 0)]/h_ 1\text{ and } s'(b)=[s(x_ N)-s(x_{N- 1})]/h_ n, \] and \[ (iii)\quad s^{(2)}(x_ i+)-s^{(2)}(x_ i- )=(c_ ih_{i+1}/3)[s^{(3)}(x_ i ...
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A cubic X-spline with knots \(\{x_ i\}^ N_{i=0}\) and parameter vector \(\{c_ i\}\) is a function \(s\in C^ 1[a,b]\) if \[ (i)\quad s(x)\text{ is a cubic on each } [x_{i-1},x_ i], \] \[ (ii)\quad s'(a)=[s(x_ 1)-s(x_ 0)]/h_ 1\text{ and } s'(b)=[s(x_ N)-s(x_{N- 1})]/h_ n, \] and \[ (iii)\quad s^{(2)}(x_ i+)-s^{(2)}(x_ i- )=(c_ ih_{i+1}/3)[s^{(3)}(x_ i ...
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Discrete weighted cubic splines
Numerical Algorithms, 2014The paper presents methods for spline interpolation preserving the shape of the data (monotonicity and convexity) by using discrete weighted cubic splines.
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