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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In: Computer graphics forum, 2010, vol. 29, no. 2, p. 309-318
Interpolating vertex positions among triangle meshes with identical vertex-edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mesh, model desired interpolations of the affine transformations, and then optimize vertex...
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