Open AccessProceedings Article
Exact and Approximate Quadratures for Curvature Tensor Estimation
Torsten Langer,Alexander Belyaev,Hans-Peter Seidel +2 more
- pp 421-428
TLDR
In this paper, exact quadrature formulae for mean curvature, Gaussian curvature and the Taubin integral representation of the curvature tensor are derived for a smooth surface approximated by a dense triangle mesh.Abstract:
Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. In this paper, we derive exact quadrature formulae for mean curvature, Gaussian curvature, and the Taubin integral representation of the curvature tensor. The exact quadratures are then used to obtain reliable estimates of the curvature tensor of a smooth surface approximated by a dense triangle mesh. The proposed method is fast and easy to implement. It is highly competitive with conventional curvature tensor estimation approaches. Additionally, we show that the curvature tensor approximated as proposed by us converges towards the true curvature tensor as the edge lengths tend to zero.read more
Citations
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Geometric Modeling Based on Polygonal Meshes
Leif Kobbelt,Stephan Bischoff,Mario Botsch,Kolja Kähler,Christian Rössl,Robert Schneider,Jens Vorsatz +6 more
TL;DR: This course discusses the whole geometry processing pipeline based on triangle meshes, and introduces general concepts of surface representations and point out the advantageous properties of triangle meshes in order to present efficient data structures for their implementation.
Proceedings ArticleDOI
Geometric modeling based on triangle meshes
TL;DR: This course is designed to cover the entire geometry processing pipeline based on triangle meshes, with a focus on multiresolution and freeform modeling, 3D model optimization, as well as the efficient handling of polygonal mesh data.
Proceedings ArticleDOI
Consistent computation of first- and second-order differential quantities for surface meshes
Xiangmin Jiao,Hongyuan Zha +1 more
TL;DR: This paper investigates a general, flexible numerical framework to estimate the derivatives of the height function based on local polynomial fittings formulated as weighted least squares approximations, and proposes an iterative fitting scheme to improve accuracy.
Journal ArticleDOI
Exact and interpolatory quadratures for curvature tensor estimation
TL;DR: The idea is to compute the curvature integrals by a weighted sum by making use of the periodic structure of the normal curvatures to make the quadratures exact.
References
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Implicit fairing of irregular meshes using diffusion and curvature flow
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