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About Surface Remeshing
"... In this paper, we present a general scheme suitable to optimize an arbitrary given surface triangulation representing a piecewise linear approximation of an underlying surface geometry. The proposed approach is based on two steps related to i) the extraction of a geometric mesh (based on a simplific ..."
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Cited by 53 (11 self)
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In this paper, we present a general scheme suitable to optimize an arbitrary given surface triangulation representing a piecewise linear approximation of an underlying surface geometry. The proposed approach is based on two steps related to i) the extraction of a geometric mesh (based on a simplification procedure), ii) the optimization of this mesh with respect to the model geometry as well as to the element shape quality (for finite element computations). This last stage involves the creation of a geometric (G¹ continuous) support that de nes an adequate approximation of the underlying surface and the definition of a geometric (curvaturebased) metric. Details about the construction of the metric and the de nition of a proper simplification "enveloppe" are provided. Examples of surface mesh simplification are given to illustrate the various stages of the proposed approach.
Anisotropic centroidal Voronoi tessellations and their applications
 SIAM J. SCI. COMPUT
, 2005
"... In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Llo ..."
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Cited by 47 (7 self)
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In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay triangulation under the given Riemannian metric. The ACVT is applied to optimization of two dimensional anisotropic Delaunay triangulation, to the generation of surface CVT and high quality triangular mesh on general surfaces. Various numerical examples demonstrate the effectiveness of the proposed method.
Identification and Preservation of Surface Features
 Proceedings of 13th International Meshing Roundtable
, 2004
"... A surface is often approximated by a network of triangular facets. In the absence of a precise mathematical description of the underlying surface all information about surface properties such as smoothness and curvature must be inferred from the triangulation itself. Enrichment and coarsening of the ..."
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Cited by 11 (0 self)
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A surface is often approximated by a network of triangular facets. In the absence of a precise mathematical description of the underlying surface all information about surface properties such as smoothness and curvature must be inferred from the triangulation itself. Enrichment and coarsening of the surface geometry, for example, can only be carried out if singular features, where C continity is lost, are properly accounted for. In the absence of a well defined surface geometry it is necessary to extract these features and establish suitable data structures so that the features persist after enrichment and/or coarsening of the triangulation. This paper describes a feature extraction scheme that is based on estimates of the local normals and principal curvatures at each mesh point. The feature extraction scheme has been combined with an algorithm that adapts a tetrahedral mesh by the selective enrichment and coarsening of both the volume and surface triangulation.
Isolating Geometry in Mesh Programming
 Proc. of the 8th Int'l Meshing Roundtable
, 1999
"... . We discuss enhancing the generality of 2D unstructured mesh programming by isolating some geometric dependencies so that they can be easily changed. The specific task discussed is quality mesh generation for a 2D manifold by local refinement with Delaunay insertion. The geometric dependenc ..."
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Cited by 2 (0 self)
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. We discuss enhancing the generality of 2D unstructured mesh programming by isolating some geometric dependencies so that they can be easily changed. The specific task discussed is quality mesh generation for a 2D manifold by local refinement with Delaunay insertion. The geometric dependencies that we wish to isolate are its embedded global coordinate system, including its dimension (planar or surface meshing), and its metric, (curvilinear coordinate systems, anisotropic meshing). We discuss object oriented techniques and a coordinate system local to the mesh triangles to enhance isolating these geometric features. keywords. manifold meshing, object oriented, Delaunay insertion 1 Introduction Unstructured mesh generation algorithms such as refinement based on Delaunay insertion, or advancing front techniques can usually be expressed mathematically as meshing abstract 2D manifolds. These manifolds are basically characterized by the usual incidence relations of meshes...
Toolkit for registration and evaluation for 3d laser scanner acquisition
 Plzen: University of West Behemia
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Shape Interrogation
"... Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where ”class A” surfaces are required and no surface imperfections are allowed, shape interrogation has become recently an important tool ..."
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Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where ”class A” surfaces are required and no surface imperfections are allowed, shape interrogation has become recently an important tool for various other types of surface representations such as triangulated or polygonal surfaces, subdivision surface, and algebraic surfaces. In this paper we present the stateoftheart of shape interrogation methods including methods for detecting surface imperfections, surface analysis tools and methods for visualizing intrinsic surface properties. Furthermore we focus on stable numerical and symbolic solving of algebraic systems of equations, a problem that arises in most shape interrogation methods.
Open Access
"... An ordered topological representation of 3D triangular mesh facial surface: concept and applications ..."
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An ordered topological representation of 3D triangular mesh facial surface: concept and applications
SMOOTHING OF COMPLEX SURFACE TRIANGULATIONS WITH EFFICIENT LOCAL NODE MOVEMENTS
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"... This paper studies triangulations obtained from Poisson disc sampling. The Poisson disc sampling strategy with radius parameter α canbeusedtoobtainasetofpoints in the interior or on the boundary of a given solid object in the plane. Using this sampling, one can construct a triangulation from its αc ..."
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This paper studies triangulations obtained from Poisson disc sampling. The Poisson disc sampling strategy with radius parameter α canbeusedtoobtainasetofpoints in the interior or on the boundary of a given solid object in the plane. Using this sampling, one can construct a triangulation from its αcomplex. In this work we give two contributions: the quality of this triangulation in terms of triangles ’ aspect ratio and a sampling condition with topological guarantee. If we choose the same parameter α for the Poisson disc sampling and for the solid αcomplex, we prove that all the triangles in the complex have aspect ratio less or equal than 4 √ 3, which is only three times the aspect ratio of an equilateral triangle. Moreover, we prove that this bound is tight. We also establish a condition on radius parameter α that allows to recover, with topological guarantees, the original solid object from the αcomplex representation.