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21
Amira: a highly interactive system for visual data analysis
 THE VISUALIZATION HANDBOOK
, 2005
"... What characteristics should a good visualization system hold? What kinds of data should it support? What capabilities should it provide? Of course, the answers depend on the particular task and application. For some users a visualization system may be nothing more than a simple image viewer or plott ..."
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Cited by 54 (21 self)
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What characteristics should a good visualization system hold? What kinds of data should it support? What capabilities should it provide? Of course, the answers depend on the particular task and application. For some users a visualization system may be nothing more than a simple image viewer or plotting program. For others it is integrated software dedicated to their personal field of work, such as a computer algebra program or a finiteelement simulation system. While in such integrated systems visualization is usually just an addon, there are also many specialized systems whose primary focus is upon visualization itself.
Tetrahedral Mesh Generation Based on Node Insertion in . . .
, 1998
"... A method of unstructured tetrahedralmesh generation for general threedimensional domains is presented. Aconventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology. The geometry of surfaces is represented either analytically of by ..."
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Cited by 20 (13 self)
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A method of unstructured tetrahedralmesh generation for general threedimensional domains is presented. Aconventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology. The geometry of surfaces is represented either analytically of by piecewise polynomial interpolation. A preliminary surface mesh is generated by an advancing front method, with the nodes inserted by hardsphere packing in physical space in accordance with a prescribed mesh density. Interior nodes are inserted in a facecenteredcubic (FCC) crystal lattice arrangement coupled to octree spatial subdivision, with the local lattice parameter determined by a prespecified nodal density function. Prior to triangulation of the volume, the preliminary surface mesh is preprocessed by a combination of local transformations and subdivision in order to guarantee that the surface triangulation be a subcomplex of the volume Delaunay triangulation. A joint Delaunay triang...
Parallel Advancing Front Grid Generation
 in International Meshing Roundtable, Sandia National Labs
, 1999
"... . A parallel advancing front scheme has been developed. The domain to be gridded is first subdivided spatially using a relatively coarse octree. Boxes are then identified and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only co ..."
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Cited by 14 (0 self)
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. A parallel advancing front scheme has been developed. The domain to be gridded is first subdivided spatially using a relatively coarse octree. Boxes are then identified and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only considering the boxes of the active front that generate small elements. The procedure has been implemented on the SGI Origin class of machines using the shared memory paradigm. Timings for a variety of cases show speedups similar to those obtained for flow codes. The procedure has been used to generate grids in excess of a hundred million elements. Keywords. Unstructured Grid Generation, Parallel Computing, CFD. 1. INTRODUCTION The widespread availability of parallel machines with large memory, solvers that can harness the power of these machines, and the desire to model in ever increasing detail geometrical and physical features has lead to a steady increase in the number of points used in...
Tetrahedral meshes from planar cross sections
 Computer Methods in Applied Mechanics and Engineering
, 1999
"... In biomedicine, many three dimensional (3D) objects are sampled in terms of slices such as computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound imaging. It is often necessary to construct surface meshes from the cross sections for visualization, and thereafter construct tetrahe ..."
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Cited by 10 (4 self)
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In biomedicine, many three dimensional (3D) objects are sampled in terms of slices such as computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound imaging. It is often necessary to construct surface meshes from the cross sections for visualization, and thereafter construct tetrahedra for the solid bounded by the surface meshes for the purpose of nite element analysis. In paper [1], we provided a solution to the construction of a surface triangular mesh from planar crosssection contours. Here we provide an approach to tetrahedralize the solid region bounded by planar contours and the surface mesh. It is a di cult task because the solid can be of high genus (several through holes) as well as have complicated branching regions. We develop an algorithm to e ectively reduce the solid into prismatoids, and provide an approach to tetrahedralize the prismatoids. Our tetrahedralization approach is similar to the advancing front technique (AFT) for its exible control of mesh quality. The main criticism of AFT is that the remaining interior may be badly shaped or even untetrahedralizable. The emphasis of our prismatoid tetrahedralization approach is on the characterization and prevention of untetrahedralizable parts. Ruppert and Seidel [25] have shown that the problem of deciding whether a polyhedron is tetrahedralizable without adding Steiner points is NPcomplete. We characterize this problem under certain constraints, and design one rule to reduce the chance of generating untetrahedralizable shapes. The characterization also leads to the classi cation of two common untetrahedralizable categories which can be better processed if they do occur. 2 1
On an Automatically Parallel Generation Technique for Tetrahedral Meshes
, 1994
"... this paper is the extension of our parallel triangular mesh generator into the third dimension conserving both its effectiveness, adaptivity, compatibility and versatility now based on the edge related data structure for tetrahedral elements. For distinct opportunities to perform load balanced trian ..."
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Cited by 9 (0 self)
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this paper is the extension of our parallel triangular mesh generator into the third dimension conserving both its effectiveness, adaptivity, compatibility and versatility now based on the edge related data structure for tetrahedral elements. For distinct opportunities to perform load balanced triangular mesh generation the efficiency of our 3Dmesh generator is essentially determined by we refer back to [4, 18]. Provided that this adequate handling with the program is guaranteed our parallel mesh generator will be much more efficient than every conventional one, whereas often the latter tools are capable of sequential mesh generating in 3Dregions of near arbitrary shape, cf. e.g. [13, 14]. But the introduced mesh generation strategy can be generalized by the description of more variable curvilinear boundaryfaces to become more robust in this sense. In section 2 we describe the specific mesh generation method for producing regularly connected tetrahedral layers based on its 2Dreference triangulations. In addition to we explain the structure of the inputdata file the geometry of the class of meshable 3Ddomains is reflected by, where the specification of the corresponding boundary conditions is incorporated into. In section 3 the background for the parallelization of the mesh generation is given, where the other program's capabilities e.g. such as parallel grid smoothing and (inner) nodal renumbering are overviewed. Section 4 gives the outputdata structure of the tetrahedral mesh. Here we are able to complete the edgerelated data structure of triangular meshes introduced in [4] appropriately. Finally in section 5 several numerical examples are involved in order to demonstrate both user's operating with the program and its efficiency. 2 The specific 3Dmesh generati...
Reliable isotropic tetrahedral mesh generation based on an advancing front method
 In Proceedings 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories
, 2004
"... In this paper, we propose a robust isotropic tetrahedral mesh generation method. An advancing front method is employed to control local mesh density and to easily preserve the original connectivity of boundary surfaces. Tetrahedra are created by each layer. Instead of preparing a background mesh for ..."
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Cited by 7 (2 self)
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In this paper, we propose a robust isotropic tetrahedral mesh generation method. An advancing front method is employed to control local mesh density and to easily preserve the original connectivity of boundary surfaces. Tetrahedra are created by each layer. Instead of preparing a background mesh for mesh spacing control, this information is estimated at the beginning of each layer at each node from the area of connecting triangles on the front and a userspecified stretching factor. An alternating digital tree (ADT) is prepared to correct the mesh spacing information and to perform geometric search efficiently. At the end of the mesh generation process, anglebased smoothing and Delaunay refinement are employed to enhance the resulting mesh quality. Surface meshes are prepared beforehand using a direct advancing front method for discrete surfaces extracted from computed tomography (CT) or magnetic resonance imaging (MRI) data. The algorithm is demonstrated with several biomedical models.
Towards an Adaptive Advancing Front Method
 6 th International Meshing Roundtable
, 1997
"... . This paper presents the main features of an advancing front method designed to mesh arbitrary 3D geometries with tetrahedral elements. A control space is used to govern the element sizes, which proves to be useful in an adaption scheme. Several improvements to the scheme of the standard advancing ..."
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Cited by 6 (0 self)
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. This paper presents the main features of an advancing front method designed to mesh arbitrary 3D geometries with tetrahedral elements. A control space is used to govern the element sizes, which proves to be useful in an adaption scheme. Several improvements to the scheme of the standard advancing front method are detailed. Numerical examples are provided to illustrate the proposed approach and possible extensions are indicated. Keywords. Unstructured mesh, advancing front method, mesh adaption. Introduction Problem statement. In the context of finite element methods, the accuracy of the numerical results depends on the quality of surface and volume meshes. For a given computational domain, the numerical solution is more accurate as the mesh quality is controlled. Different meshing techniques can be used to achieve finite element meshes. Irrespective of the choice of the method, difficulties are encountered to achieve a fully automatic mesh generation. With an advancing front method, ...
Piecewise Linear Hypersurfaces using the Marching Cubes Algorithm
, 1999
"... Surface visualization is very important within scientic visualization. The surfaces depict a value of equal density (an isosurface) or display the surrounds of specied objects within the data. Likewise, in two dimensions contour plots may be used to display the information. Thus similarly, in four d ..."
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Cited by 6 (0 self)
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Surface visualization is very important within scientic visualization. The surfaces depict a value of equal density (an isosurface) or display the surrounds of specied objects within the data. Likewise, in two dimensions contour plots may be used to display the information. Thus similarly, in four dimensions hypersurfaces may be formed around hyperobjects. These surfaces (or contours) are often formed from a set of connected triangles (or lines). These piecewise segments represent the simplest nondegenerate object of that dimension and are named simplices. In four dimensions a simplex is represented by a tetrahedron, which is also known as a 3simplex. Thus, a continuous n dimensional surface may be represented by a lattice of connected n1 dimensional simplices. This lattice of connected simplices may be calculated over a set of adjacent n dimensional cubes, via for example the Marching Cubes Algorithm. We propose that the methods of this localcell tiling method may be usefullyap...
Surface and 3D Triangular Meshes from Planar Cross Sections
 Sections, 5th International Meshing Roundtable, Sandia National Laboratories
, 1996
"... . This paper presents two unstructured mesh generation algorithms with a discussion of their implementation. One algorithm is for the generation of a surface triangular mesh from a parallel stack of planar crosssections (polygons). The other algorithm is for the construction of a 3D triangular (tet ..."
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Cited by 3 (1 self)
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. This paper presents two unstructured mesh generation algorithms with a discussion of their implementation. One algorithm is for the generation of a surface triangular mesh from a parallel stack of planar crosssections (polygons). The other algorithm is for the construction of a 3D triangular (tetrahedral) mesh of the solid region (polyhedron) bounded by the surface mesh and the planar crosssections. Construction of a surface triangular mesh from planar contours is difficult because of "correspondence", "tiling" and "branching" problems. We provide a simultaneous solution to all three of these problems. This is accomplished by imposing a set of three constraints on the constructed surface mesh and then by deriving precise correspondence and tiling rules from these constraints. The constraints ensure that the regions tiled by these rules obey physical constructs and have a natural appearance. Regions which cannot be tiled by these rules without breaking one or more constraints are ti...
L.: Mesh Generation on HighCurvature Surfaces Based on a Background Quadtree Structure
 Proc. 11th International Meshing Roundtable, Sandia National Laboratories
"... This paper extends a previously proposed algorithm for generating unstructured meshes in threedimensional and in twodimensional domains to generate surface meshes. A surface mesh is generated in parametric space and mapped to Cartesian space. Finite elements may be stretched on parametric space, bu ..."
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Cited by 1 (0 self)
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This paper extends a previously proposed algorithm for generating unstructured meshes in threedimensional and in twodimensional domains to generate surface meshes. A surface mesh is generated in parametric space and mapped to Cartesian space. Finite elements may be stretched on parametric space, but they present a goodquality shape on the 3D surface. The algorithm uses a metric map defined by Tristano et al. to obtain correct distances and stretches. A background quadtree structure is used to store local surface metrics and to develop local guidelines for node location in an advancingfront meshing strategy.