Detection of Salient Curvature Features on Polygonal Surfaces

Watanabe, Kenji; Belyaev, Alexander

doi:10.1111/1467-8659.00531

Cited by 121 publications

(59 citation statements)

References 16 publications

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“…For example, several definitions of normals, principal directions and curvatures over a mesh can be found in [Tau95,CW00]. Ridges of polyhedral surfaces as well as cuspidal edges of the focal sets are computed in [WB01]. Geodesics and discrete versions of the Gauss-Bonnet theorem are considered in [PS98].…”

Section: Estimating Differential Quantitiesmentioning

confidence: 99%

Estimating differential quantities using polynomial fitting of osculating jets

Cazals

Pouget

2005

Computer Aided Geometric Design

321

282

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This paper addresses the point-wise estimation of differential properties of a smooth manifold S -a curve in the plane or a surface in 3D-assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation or approximation. A jet is a truncated Taylor expansion, and the incentive for using jets is that they encode all local geometric quantities -such as normal, curvatures, extrema of curvature.On the way to using jets, the question of estimating differential properties is recasted into the more general framework of multivariate interpolation / approximation, a well-studied problem in numerical analysis. On a theoretical perspective, we prove several convergence results when the samples get denser. For curves and surfaces, these results involve asymptotic estimates with convergence rates depending upon the degree of the jet used. For the particular case of curves, an error bound is also derived. To the best of our knowledge, these results are among the first ones providing accurate estimates for differential quantities of order three and more. On the algorithmic side, we solve the interpolation/approximation problem using Vandermonde systems. Experimental results for surfaces of R 3 are reported. These experiments illustrate the asymptotic convergence results, but also the robustness of the methods on general Computer Graphics models.

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Section: Estimating Differential Quantitiesmentioning

confidence: 99%

Estimating differential quantities using polynomial fitting of osculating jets

Cazals

Pouget

2005

Computer Aided Geometric Design

321

282

View full text Add to dashboard Cite

show abstract

“…Difficulties arise due to the feature-insensitive sampling and the noise of the given data. Various approaches have been proposed to address this problem, mostly for surfaces which are described by triangular meshes [2,11,36].…”

Section: Related Workmentioning

confidence: 99%

Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

Song

Jüttler

2009

Computers & Graphics

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We propose a new method for describing sharp features (i.e., edges and vertices) of implicitly defined surfaces. We consider an initial implicitly defined surface, which is represented as the zero set of a C 1 smooth scalar field with non-vanishing gradients. In order to represent sharp edges and vertices, this surface is augmented by adding new types of implicit representations, called edge descriptors and vertex descriptors. They are defined with the help of the distance field of edge curves. In our implementation, we use circular splines to describe these edge curves, since they support a fast and non-iterative closest point computation.After adding the edge and vertex descriptors to the initial scalar field, the zero set of the augmented function contains the sharp features. We apply the new representation to surface modelling by implicitly defined surfaces with sharp features and to object reconstruction. In the latter case we describe an algorithm for detecting the sharp curves and vertices of a shape which is given by an unorganized point cloud, which are then approximated by circular splines, in order to define the edge and vertex descriptors.

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“…A simple method for estimating the principal curvatures of a surface that is approximated by a triangular mesh was proposed in [18].…”

Section: The Watanabe and Belyaev Approachmentioning

confidence: 99%

“…We also considered two modifications to the algorithm of Watanabe and Belyaev [18]. In the two following modificated algorithms, the first step was the same.…”

Section: Modificationsmentioning

confidence: 99%