In: Computer aided geometric design, 2021, vol. 88, p. 11
Bézier curves are indispensable for geometric modelling and computer graphics. They have numerous favourable properties and provide the user with intuitive tools for editing the shape of a parametric polynomial curve. Even more control and flexibility can be achieved by associating a shape parameter with each control point and considering rational Bézier curves, which comes with the...
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In: Journal of computational and applied mathematics, 2019, vol. 349, p. 292-301
Barycentric rational Floater–Hormann interpolants compare favourably to classical polynomial interpolants in the case of equidistant nodes, because the Lebesgue constant associated with these interpolants grows logarithmically in this setting, in contrast to the exponential growth experienced by polynomials. In the Hermite setting, in which also the first derivatives of the interpolant are...
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In: Dolomites Research Notes on Approximation, 2012, vol. 5, no. 1, p. 1-6
A collection of recent papers reveals that linear barycentric rational interpolation with the weights suggested by Floater and Hormann is a good choice for approximating smooth functions, especially when the interpolation nodes are equidistant. In the latter setting, the Lebesgue constant of this rational interpolation process is known to grow only logarithmically with the number of nodes....
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In: Numerische Mathematik, 2012, vol. 121, p. 461–471
Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and important...
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In: VMV 2010 : Vision, modeling & visualization, 2010, p. 211–218
In this paper we present a new algorithm for interactively painting onto 3D meshes that exploits recent advances of GPU technology. As the user moves a brush over the 3D mesh, its paint pattern is projected onto the 3D geometry at the current viewing angle and copied to the corresponding region in the object’s texture atlas. Both operations are realized on the GPU, with the advantage that all...
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In this paper we study the ability of convergent subdivision schemes to reproduce polynomials in the sense that for initial data, which is sampled from some polynomial function, the scheme yields the same polynomial in the limit. This property is desirable because the reproduction of polynomials up to some degree d implies that a scheme has approximation order d + 1. We first show that any...
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In: Journal of approximation theory, 2011, vol. 163, no. 4, p. 413-437
In this paper, we study the ability of convergent subdivision schemes to reproduce polynomials in the sense that for initial data, which is sampled from some polynomial function, the scheme yields the same polynomial in the limit. This property is desirable because the reproduction of polynomials up to some degree d implies that a scheme has approximation order d+1. We first show that any...
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In: ACM transactions on graphics, 2010, vol. 29, no. 4, p. 120
We present a method for parameterizing subdivision surfaces in an as-rigid- as-possible fashion. While much work has concentrated on parameterizing polygon meshes, little if any work has focused on subdivision surfaces despite their popularity. We show that polygon parameterization methods produce suboptimal results when applied to subdivision surfaces and describe how these methods may be...
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In: Applied and computational harmonic analysis, 2010, vol. 29, no. 1, p. 104-110
Dual pseudo-splines are a new family of refinable functions that generalize both the even degree B-splines and the limit functions of the dual 2n-point subdivision schemes. They were introduced by Dyn et al. [10] as limits of subdivision schemes. In [10], simple algebraic considerations are needed to derive the approximation order of the members of this family. In this paper, we use Fourier...
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