Results 11  20
of
54
SOT: Compact representation for tetrahedral meshes
"... The Corner Table (CT) promoted by Rossignac et al. provides a simple and efficient representation of triangle meshes, storing 6 integer references per triangle (3 vertex references in the V table and 3 references to opposite corners in the O table that accelerate access to adjacent triangles). The C ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
(Show Context)
The Corner Table (CT) promoted by Rossignac et al. provides a simple and efficient representation of triangle meshes, storing 6 integer references per triangle (3 vertex references in the V table and 3 references to opposite corners in the O table that accelerate access to adjacent triangles). The Compact Half Face (CHF) proposed by Lage et al. extends CT to tetrahedral meshes, storing 8 references per tetrahedron (4 in the V table and 4 in the O table). We call it the Vertex Opposite Table (VOT) and propose a sorted variation, SVOT, which does not require any additional storage and yet provides, for each vertex, a reference to an incident corner from which an incident tetrahedron may be recovered and the star of the vertex may be traversed at a constant cost per visited element. We use a set of powerful wedgebased operators for querying and traversing the mesh. Finally, inspired by tetrahedral mesh encoding techniques used by Weiler et al. and by Szymczak and Rossignac, we propose our Sorted O Table (SOT) variation, which eliminates the V table completely and hence reduces storage requirements by 50 % to only 4 references and 9 bits per tetrahedron, while preserving the vertextoincidentcorner references and supporting our wedge operators with a linear average cost.
Simplex and Diamond Hierarchies: Models and Applications
, 2010
"... Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains. Several papers on this subject deal with hierarchical simplicial decompositions generated through simplex bisection. Such decompositions, originally developed for finite elements, are extensively used ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains. Several papers on this subject deal with hierarchical simplicial decompositions generated through simplex bisection. Such decompositions, originally developed for finite elements, are extensively used as the basis for multiresolution models of scalar fields, such as terrains, and static or timevarying volume data. They have also been used as an alternative to quadtrees and octrees as spatial access structures and in other applications. In this state of the art report, we distinguish between approaches that focus on a specific dimension and those that apply to all dimensions. The primary distinction among all such approaches is whether they treat the simplex or clusters of simplexes, called diamonds, as the modeling primitive. This leads to two classes of data structures and to different query approaches. We present the hierarchical models in a dimension–independent manner, and organize the description of the various applications, primarily interactive terrain rendering and isosurface extraction, according to the dimension of the domain.
Meshless Isosurface Generation from Multiblock Data
, 2004
"... We propose a meshless method for the extraction of highquality continuous isosurfaces from volumetric data represented by multiple grids, also called “multiblock” data sets. Multiblock data sets are commonplace in computational mechanics applications. Relatively little research has been performed o ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
We propose a meshless method for the extraction of highquality continuous isosurfaces from volumetric data represented by multiple grids, also called “multiblock” data sets. Multiblock data sets are commonplace in computational mechanics applications. Relatively little research has been performed on contouring multiblock data sets, particularly when the grids overlap one another. Our algorithm proceeds in two steps. In the first step, we determine a continuous interpolant using a set of locally defined radial basis functions (RBFs) in conjunction with a partition of unity method to blend smoothly between these functions. In the second step, we extract isosurface geometry by sampling points on Marching Cubes triangles and projecting these point samples onto the isosurface defined by our interpolant. A surface splatting algorithm is employed for visualizing the resulting point set representing the isosurface. Because of our method’s generality, it inherently solves the “crack problem” in isosurface generation. Results using a set of synthetic data sets and a discussion of practical considerations are presented. The importance of our method is that it can be applied to arbitrary grid data regardless of mesh layout or orientation.
Isosurface extraction and spatial filtering using persistent octree
 In IEEE Transactions on Visualization and Computer Graphics
, 2006
"... Abstract — We propose a novel Persistent OcTree (POT) indexing structure for accelerating isosurface extraction and spatial filtering from volumetric data. This data structure efficiently handles a wide range of visualization problems such as the generation of viewdependent isosurfaces, ray tracing, ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Abstract — We propose a novel Persistent OcTree (POT) indexing structure for accelerating isosurface extraction and spatial filtering from volumetric data. This data structure efficiently handles a wide range of visualization problems such as the generation of viewdependent isosurfaces, ray tracing, and isocontour slicing for high dimensional data. POT can be viewed as a hybrid data structure between the interval tree and the BranchOnNeed Octree (BONO) in the sense that it achieves the asymptotic bound of the interval tree for identifying the active cells corresponding to an isosurface and is more efficient than BONO for handling spatial queries. We encode a compact octree for each isovalue. Each such octree contains only the corresponding active cells, in such a way that the combined structure has linear space. The inherent hierarchical structure associated with the active cells enables very fast filtering of the active cells based on spatial constraints. We demonstrate the effectiveness of our approach by performing viewdependent isosurfacing on a wide variety of volumetric data sets and 4D isocontour slicing on the timevarying RichtmyerMeshkov instability dataset. Index Terms—scientific visualization, isosurface extraction, indexing. 1
Constanttime navigation in fourdimensional nested simplicial meshes
 In Proceedings Shape Modeling International 2004
, 2004
"... Constanttime navigation in fourdimensional nested simplicial meshes ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
Constanttime navigation in fourdimensional nested simplicial meshes
Supercubes: A highlevel primitive for diamond hierarchies
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2009
"... Volumetric datasets are often modeled using a multiresolution approach based on a nested decomposition of the domain into a polyhedral mesh. Nested tetrahedral meshes generated through the longest edge bisection rule are commonly used to decompose regular volumetric datasets since they produce highl ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Volumetric datasets are often modeled using a multiresolution approach based on a nested decomposition of the domain into a polyhedral mesh. Nested tetrahedral meshes generated through the longest edge bisection rule are commonly used to decompose regular volumetric datasets since they produce highly adaptive crackfree representations. Efficient representations for such models have been achieved by clustering the set of tetrahedra sharing a common longest edge into a structure called a diamond. The alignment and orientation of the longest edge can be used to implicitly determine the geometry of a diamond and its relations to the other diamonds within the hierarchy. We introduce the supercube as a highlevel primitive within such meshes that encompasses all unique types of diamonds. A supercube is a coherent set of edges corresponding to three consecutive levels of subdivision. Diamonds are uniquely characterized by the longest edge of the tetrahedra forming them and are clustered in supercubes through the association of the longest edge of a diamond with a unique edge in a supercube. Supercubes are thus a compact and highly efficient means of associating information with a subset of the vertices, edges and tetrahedra of the meshes generated through longest edge bisection. We demonstrate the effectiveness of the supercube representation when encoding multiresolution diamond hierarchies built on a subset of the points of a regular grid. We also show how supercubes can be used to efficiently extract meshes from diamond hierarchies and to reduce the storage requirements of such variableresolution meshes.
3D ROAM for scalable volume visualization
 In 2004 IEEE Symposium on Volume Visualization and Graphics (VV’04
, 2004
"... (d) 0.15 fps – 3065000 tetrahedra ..."
(Show Context)
Efficient isosurface extraction for large scale timevarying data using the persistent hyperoctree (phot
, 2006
"... We introduce the Persistent HyperOcTree (PHOT) to handle the 4D isocontouring problem for large scale timevarying data sets. This novel data structure is provably space efficient and optimal in retrieving active cells. More importantly, the set of active cells for any possible isovalue are already ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
We introduce the Persistent HyperOcTree (PHOT) to handle the 4D isocontouring problem for large scale timevarying data sets. This novel data structure is provably space efficient and optimal in retrieving active cells. More importantly, the set of active cells for any possible isovalue are already organized in a Compact Hyperoctree, which enables very efficient slicing of the isocontour along spatial and temporal dimensions. Experimental results based on the very large RichtmyerMeshkov instability data set demonstrate the effectiveness of our approach. This technique can also be used for other isosurfacing schemes such as viewdependent isosurfacing and raytracing, which will benefit from the inherent hierarchical structure associated with the active cells. 1
Discrete distortion for 3D data analysis
 Visualization in Medicine and Life Sciences (VMLS), Mathematics and Visualization
, 2011
"... Summary. We investigate a morphological approach to the analysis and understanding of threedimensional scalar fields, and we consider applications to 3D medical and molecular images as examples. We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedr ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
Summary. We investigate a morphological approach to the analysis and understanding of threedimensional scalar fields, and we consider applications to 3D medical and molecular images as examples. We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedral mesh. In particular, our meshes correspond to approximations at uniform or variable resolution extracted from a multiresolution model of the 3D scalar field, that we call a hierarchy of diamonds. We analyze the images based on the concept of discrete distortion, that we have introduced in [26], and on segmentations based on Morse theory. Discrete distortion is defined by considering the graph of the discrete 3D field, which is a tetrahedral hypersurface in R 4, and measuring the distortion of the transformation which maps the tetrahedral mesh discretizing the scalar field domain into the mesh representing its graph in R 4. We describe a segmentation algorithm to produce Morse decompositions of a 3D scalar field which uses a watershed approach and we apply it to 3D images by using as scalar field both intensity and discrete distortion. We present experimental results by considering the influence of resolution on distortion computation. In particular, we show that the salient features of the distortion field appear prominently in lower resolution approximations to the dataset. 1
Modeling and Visualization Approaches for TimeVarying Volumetric Data
"... Abstract. Timevarying volumetric data arise in a variety of application domains, and thus several techniques for dealing with such data have been proposed in the literature. A timevarying dataset is typically modeled either as a collection of discrete snapshots of volumetric data, or as a fourdim ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Timevarying volumetric data arise in a variety of application domains, and thus several techniques for dealing with such data have been proposed in the literature. A timevarying dataset is typically modeled either as a collection of discrete snapshots of volumetric data, or as a fourdimensional dataset. This choice influences the operations that can be efficiently performed on such data. Here, we classify the various approaches to modeling timevarying scalar fields, and briefly describe them. Since most models of timevarying data have been abstracted from wellknown approaches to volumetric data, we review models of volumetric data as well as schemes to accelerate isosurface extraction and discuss how these approaches have been applied to timevarying datasets. Finally, we discuss multiresolution approaches which allow interactive processing and visualization of large time varying datasets. 1