منابع مشابه
Approximation by Conic Splines
We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε +O(1), if the spline consists of parabolic arcs, and c2ε + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We also show that...
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We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...
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Bootstrapping is a computer-intensive statistical method which treats the data set as a population and draws samples from it with replacement. This resampling method has wide application areas especially in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a spe...
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Given a segment of a conic section in the form of a rational Bézier curve, a quadratic spline approximation is constructed and an explicit error bound is derived. The convergence order of the error bound is shown to be O(h) which is optimal, and the spline curve is both C and G. The approximation method is very efficient as it is based on local Hermite interpolation and subdivision. The approxi...
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We develop a Hermite interpolation scheme and prove error bounds forC bivariate piecewise polynomial spaces of Argyris type vanishing on the boundary of curved domains enclosed by piecewise conics.
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2013
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2011.06.027