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Generic remeshing of 3D triangular meshes with metric-dependent Discrete Voronoi Diagrams

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2008年第2期14卷 369-381页

作者： Valette, Sebastien Chassery, Jean-Marc Prost, Remy Univ Lyon 1 CNRS CREATIS LRMNU630 INSERMINSA LyonUMR 5220 F-69621 Villeurbanne France Domaine Univ CNRS GIPSA Lab ENSIEGUMR 5216 F-38402 St Martin Dheres France

In this paper, we propose a generic framework for 3D surface remeshing. Based on a metric-driven Discrete Voronoi Diagram construction, our output is an optimized 3D triangular mesh with a user-defined vertex budget. Our approach can deal with a wide range of applications, from high-quality mesh generation to shape approximation. By using appropriate metric constraints, the method generates isotropic or anisotropic elements. Based on point sampling, our algorithm combines the robustness and theoretical strength of Delaunay criteria with the efficiency of an entirely discrete geometry processing. Besides the general described framework, we show the experimental results using isotropic, quadric-enhanced isotropic, and anisotropic metrics, which prove the efficiency of our method on large meshes at a low computational cost.

关键词： approximation of surfaces and contours numerical analysis mathematics of computing global optimization hierarchy and geometric transformations computational geometry and object modeling computer graphics computing methodologies

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Streaming simplification of tetrahedral meshes

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2007年第1期13卷 145-155页

作者： Vo, Huy T. Callahan, Steven P. Lindstrom, Peter Pascucci, Valerio Silva, Claudio T. Sci Comp & Imaging Inst Salt Lake City UT 84112 USA Lawrence Livermore Natl Lab Ctr Appl Sci Comp Livermore CA 94551 USA Univ Utah Sch Comp Salt Lake City UT 84112 USA

Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

关键词： computational geometry and object modeling out-of-core algorithms streaming algorithms mesh simplification large meshes tetrahedral meshes

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Efficient collision detection within deforming spherical sliding contact

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2007年第3期13卷 518-529页

作者： Maciel, Anderson Boulic, Ronan Thalmann, Daniel Rensselaer Polytech Inst MANE JEC 2049 Troy NY 12180 USA Ecole Polytech Fed Lausanne IC VRLab Stn 14 CH-1015 Lausanne Switzerland

Handling the evolving permanent contact of deformable objects leads to a collision detection problem of high computing cost. Situations in which this type of contact happens are becoming more and more present with the increasing complexity of virtual human models, especially for the emerging medical applications. In this context, we propose a novel collision detection approach to deal with situations in which soft structures are in constant but dynamic contact, which is typical of 3D biological elements. Our method proceeds in two stages: First, in a preprocessing stage, a mesh is chosen under certain conditions as a reference mesh and is spherically sampled. In the collision detection stage, the resulting table is exploited for each vertex of the other mesh to obtain, in constant time, its signed distance to the fixed mesh. The two working hypotheses for this approach to succeed are typical of the deforming anatomical systems we target: First, the two meshes retain a layered configuration with respect to a central point and, second, the fixed mesh tangential deformation is bounded by the spherical sampling resolution. Within this context, the proposed approach can handle large relative displacements, reorientations, and deformations of the mobile mesh. We illustrate our method in comparison with other techniques on a biomechanical model of the human hip joint.

关键词： computer graphics computational geometry and object modeling simulation modeling and visualization kinematics and dynamics

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Learning object models from semistructured Web documents

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2006年第3期18卷 334-349页

作者： Ye, SR Chua, TS Natl Univ Singapore Dept Comp Sci Singapore 117543 Singapore

This paper presents an automated approach to learning object models by means of useful object data extracted from data-intensive semistructured web documents such as product descriptions. modeling intensive data on the Web involves the following three phrases: First, we identify the object region covering the descriptions of object data when irrelevant contents from the web documents are excluded. Second, we partition the contents of different object data appearing in the object region and construct object data using hierarchical XML outputs. Third, we induce the abstract object model from the analogous object data. This model will match the corresponding object data from a Web site more precisely and comprehensively than the existing handcrafted ontologies. The main contribution of this study is in developing a fully automated approach to extract object data and object model from semistructured web documents using kernel-based matching and View Syntax interpretation. Our system, OnModer, can automatically construct object data and induce object models from complicated web documents, such as the technical descriptions of personal computers and digital cameras downloaded from manufacturers' and vendors' sites. A comparison with the available hand-crafted ontologies and tests on an open corpus demonstrate that our framework is effective in extracting meaningful and comprehensive models.

关键词： Web mining machine learning intelligent web services and Semantic Web web text analysis knowledge acquisition ontology design computational geometry and object modeling DOM

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Interpolation over arbitrary topology meshes using a two-phase subdivision scheme

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2006年第3期12卷 301-310页

作者： Zheng, JM Cai, YY Nanyang Technol Univ Sch Comp Engn Singapore 639798 Singapore Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore 639798 Singapore

The construction of a smooth surface interpolating a mesh of arbitrary topological type is an important problem in many graphics applications. This paper presents a two-phase process, based on a topological modification of the control mesh and a subsequent Catmull-Clark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be interpolated. The method has the following features: 1) It is guaranteed to always work and the computation is numerically stable, 2) there is no need to solve a system of linear equations and the whole computation complexity is O(K) where K is the number of the vertices, and 3) each vertex can be associated with a scalar shape handle for local shape control. These features make interpolation using Catmull-Clark surfaces simple and, thus, make the new method itself suitable for interactive free- form shape design.

关键词： computer graphics computational geometry and object modeling curve, surface, solid, and object representations computer-aided engineering computer-aided design

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A multigrid framework for real-time simulation of deformable bodies

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COMPUTERS & GRAPHICS-UK 2006年第3期30卷 408-415页

作者： Georgii, Joachim Westermann, Ruediger Tech Univ Munich Comp Graph & Visualizat Grp D-8000 Munich Germany

In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and non-linear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus with a dynamic range of several orders of magnitude. Using the linearized strain measure, we can simulate 50 thousand tetrahedral elements with 20 fps on a single processor CPU. By using corotational linearized and non-linear Green strain, we can still simulate five thousand and two thousand elements, respectively, at the same rates. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： deformable bodies multigrid computational geometry and object modeling three-dimensional graphics and realism

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Sharpen&bend: Recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2005年第2期11卷 181-192页

作者： Attene, M Falcidieno, B Rossignac, J Spagnuolo, M CNR Ist Matemat Applicata & Tecnol Informat Sez Genova I-16149 Genoa Italy Georgia Inst Technol Coll Comp IRIS GVU TSRB Atlanta GA 30332 USA

Various acquisition, analysis, visualization, and compression approaches sample surfaces of 3D shapes in a uniform fashion without any attempt to align the samples with sharp edges or to adapt the sampling density to the surface curvature. Consequently, triangle meshes that interpolate these samples usually chamfer sharp features and exhibit a relatively large error in their vicinity. We present two new filters that improve the quality of these resampled models. EdgeSharpener restores the sharp edges by splitting the chamfer edges and forcing the new vertices to lie on intersections of planes extending the smooth surfaces incident upon these chamfers. Bender refines the resulting triangle mesh using an interpolating subdivision scheme that preserves the sharpness of the recovered sharp edges while bending their polyline approximations into smooth curves. A combined Sharpen&Bend postprocessing significantly reduces the error produced by feature-insensitive sampling processes. For example, we have observed that the mean-squared distortion introduced by the SwingWrapper remeshing-based compressor can often be reduced by 80 percent executing EdgeSharpener alone after decompression. For models with curved regions, this error may be further reduced by an additional 60 percent if we follow the EdgeSharpening phase by Bender.

关键词： computer graphics computational geometry and object modeling boundary representations geometric algorithms languages and systems

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Boolean operations with implicit and parametric representation of primitives using R-functions

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2005年第5期11卷 529-539页

作者： Fougerolle, YD Gribok, A Foufou, S Truchetet, F Abidi, MA Univ Tennessee Knoxville TN 37996 USA Univ Bourgogne CNRS UMR 5158 UFR Sci & Tech F-21078 Dijon France IUT Le Creusot Lab Le2i CNRS UMR 5158 F-71200 Le Creusot France

We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a Constructive Solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.

关键词： computational geometry and object modeling constructive solid geometry object representation volume visualization R-functions superquadrics supershapes Dupin cyclides

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Optimal global conformal surface parameterization 04

Optimal global conformal surface parameterization

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IEEE Visualization 2004 Conference

作者： Jin, M Wang, YL Yau, ST Gu, XF SUNY Stony Brook Dept Comp Sci Stony Brook NY 11794 USA

ISBN: (纸本)0780387880

All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion and electro-magnetic fields on the surface. A good parameterization is crucial for simulation and visualization. This paper provides an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology type;of differential forms. The implementation is based on a finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserves angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.

关键词： computational geometry and object modeling curve, surface, solid, and object representations surface parameterization

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Optimal discrete Morse functions for 2-manifolds

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computational geometry-THEORY AND APPLICATIONS 2003年第3期26卷 221-233页

作者： Lewiner, T Lopes, H Tavares, G Pontificia Univ Catolica Rio de Janeiro Dept Matemat Lab MatMidia BR-22453900 Rio De Janeiro Brazil

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. The main objective of this paper is to introduce a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality. (C) 2003 Elsevier B.V. All rights reserved.

关键词： Morse theory Forman theory computational topology computational geometry and object modeling

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