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Time Critical Isosurface Refinement and Smoothing
, 2000
"... Multiresolution datastructures and algorithms are key in Visualization to achieve realtime interaction with large datasets. Research has been primarily focused on the offline construction of such representations mostly using decimation schemes. Drawbacks of this class of approaches include: (i) ..."
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Cited by 10 (4 self)
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Multiresolution datastructures and algorithms are key in Visualization to achieve realtime interaction with large datasets. Research has been primarily focused on the offline construction of such representations mostly using decimation schemes. Drawbacks of this class of approaches include: (i) the inability to maintain interactivity when the displayed surface changes frequently, (ii) inability to control the global geometry of the embedding (no selfintersections) of any approximated level of detail of the output surface. In this paper we introduce a technique for online construction and smoothing of progressive isosurfaces (see Figure 1). Our hybrid approach combines the flexibility of a progressive multiresolution representation with the advantages of a recursive subdivision scheme. Our main contributions are: (i) a progressive algorithm that builds a multiresolution surface by successive refinements so that a coarse representation of the output is generated as soon as a coarse representation of the input is provided, (ii) application of the same scheme to smooth the surface by means of a 3D recursive subdivision rule, (iii) a multiresolution representation where any adaptively selected level of detail surface is guaranteed to be free of selfintersections.
Mesh Refinement Based on the 8Tetrahedra LongestEdge Partition
 Partition,” Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories
, 2003
"... The 8tetrahedra longestedge (8TLE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longestedge. The associated local refinement algorithm can be described in terms of the polyhedron skeleton concept using either a set of preco ..."
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Cited by 3 (0 self)
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The 8tetrahedra longestedge (8TLE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longestedge. The associated local refinement algorithm can be described in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint tetrahedron bisection procedure. An e#ective 3D derefinement algorithm can be also simply stated. In this paper we discuss the 8tetrahedra partition, the refinement algorithm and its properties, including a nondegeneracy fractal property. Empirical experiments show that the 3D partition has analogous behavior to the 2D case in the sense that after the first refinement level, a clear monotonic improvement behavior holds. For some tetrahedra a limited decreasing of the tetrahedron quality can be observed in the first partition due to the introduction of a new face which reflects a local feature size related with the tetrahedron thickness.
Nonequivalent partitions of dtriangles with Steiner points
, 2004
"... In this paper we present lower and upper bounds for the number of equivalence classes of dtriangles with additional or Steiner points. We also study the number of possible partitions that may appear by bisecting a tetrahedron with Steiner points at the midpoints of its edges. This problem arises, f ..."
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In this paper we present lower and upper bounds for the number of equivalence classes of dtriangles with additional or Steiner points. We also study the number of possible partitions that may appear by bisecting a tetrahedron with Steiner points at the midpoints of its edges. This problem arises, for example, when refining a 3D triangulation by bisecting the tetrahedra. To begin with, we look at the analogous 2D case, and then the 1irregular tetrahedra (tetrahedra with at most one Steiner point on each edge) are classified into equivalence classes, and each element of the class is subdivided into several nonequivalent bisectionbased partitions which are also studied. Finally, as an example of the application of refinement and coarsening of 3D bisectionbased algorithms, a simulation evolution problem is shown.
Tetrahedral Mesh Refinement in Distributed Environments
, 2006
"... The Adaptive Mesh Refinement is one of the main techniques used for the solution of Partial Differential Equations. Since 3dimensional structures are more complex, there are few refinement methods especially for parallel environments. On the other hand, many algorithms have been proposed for 2dime ..."
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The Adaptive Mesh Refinement is one of the main techniques used for the solution of Partial Differential Equations. Since 3dimensional structures are more complex, there are few refinement methods especially for parallel environments. On the other hand, many algorithms have been proposed for 2dimensional structures. We analyzed the Rivara’s longestedge bisection algorithm, studied parallelization techniques for the problem, and presented a parallel methodology for the refinement of nonuniform tetrahedral meshes. The main goal of this research is to propose a practical refinement framework for reallife applications. We describe a usable data structure for distributed environments and present a utility capable of distributing the mesh data among processors to solve large mesh structures.
EUROGRAPHICS ITALIAN CHAPTER PSP: Progressive Subdivision Paradigm for Large Scale
"... The increasing rate of growth in size of currently available datasets is a well known issue. The possibility of developing fast and easy to implement frameworks able to visualize at least part of a terasized volume is a challenging task. Subdivision methods in recent years have been one of the most ..."
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The increasing rate of growth in size of currently available datasets is a well known issue. The possibility of developing fast and easy to implement frameworks able to visualize at least part of a terasized volume is a challenging task. Subdivision methods in recent years have been one of the most successful techniques applied to the multiresolution representation and visualization of surface meshes. Extensions of these techniques to the volumetric case presents positive effects and major challenges mainly concerning the generalization of the combinatorial structure of the refinement procedure and the analysis of the smoothness of the limit mesh. In this paper we address mainly the first part of the problem, presenting a framework that exploits a subdivision scheme suitable for extension to 3D and higher dimensional meshes. 1.