Real-time rendering of triangulated surfaces has attracted growing interest in the last few years. However, interactive visualization of very large scale grid digital elevation models is still difficult. The graphics load must be controlled by adaptive surface triangulation and by taking advantage of different levels of detail. Furthermore, management of the visible scene requires efficient access to the terrain database. We describe an all-in-one visualization system which integrates adaptive triangulation, dynamic scene management and spatial data handling. The triangulation model is based on the restricted quadtree triangulation. Furthermore, we present new algorithms of restricted quadtree triangulation. These include among others exact error approximation, progressive meshing, performance enhancements and spatial access.

Large scale terrain visualization using the restricted quadtree triangulation

In this paper we survey some of the major data structures for encoding Level Of Detail (LOD) models. We classify LOD data structures according to the dimensionality of the basic structural element they represent into point-, triangle-, and tetrahedron-based data structures. Within each class we will review single-level data structures, general data structures for LOD models based on irregular meshes as well as more specialised data structures that assume a certain (semi-) regularity of the data.

A Survey on Data Structures for Level-of-Detail Models

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 time-varying 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

Simplex and Diamond Hierarchies: Models and Applications.

Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. We introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates

Interactive Point-Based Rendering of Higher-Order Tetrahedral Data

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 regular 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 time-varying volume data. They have also been used as an alternative to quadtrees and octrees as spatial access structures. The primary distinction among all such approaches is whether they treat the simplex or clusters of simplices, 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.

/pdf/simplex-and-diamond-hierarchies-models-and-applications-37cxm76x1j.pdf

Simplex and Diamond Hierarchies: Models and Applications

Techniques are presented for moving between adjacent tetrahedra in a tetrahedral mesh. The tetrahedra result from a recursive decomposition of a cube into six initial congruent tetrahedra. A new technique is presented for labeling the triangular faces. The labeling enables the implementation of a binary-like decomposition of each tetrahedron which is represented using a pointerless representation. Outlines of algorithms are given for traversing adjacent triangular faces of equal size in constant time.

/pdf/constant-time-neighbor-finding-in-hierarchical-tetrahedral-13vrivscpp.pdf

Constant-time neighbor finding in hierarchical tetrahedral meshes

We consider a recursive decomposition of a four-dimensional hypercube into a hierarchy of nested 4-dimensional simplexes, that we call pentatopes. The paper presents an algorithm for finding the neighbors of a pentatope along its five tetrahedral faces in constant time. To this aim, we develop a labeling technique for nested pentatopes that enables their identification by using location codes. The constant-time behavior is achieved through bit manipulation operations, thus avoiding traversing the simplicial hierarchy via pointer following. We discuss an application of this representation to multi-resolution representations of four-dimensional scalar fields. Extracting adaptive continuous approximations of the scalar field from such a model requires generating conforming meshes, i.e., meshes in which the pentatopes match along their tetrahedral faces. Our neighbor finding algorithm enables computing face-adjacent pentatopes efficiently.

/pdf/constant-time-navigation-in-four-dimensional-nested-2ywibejc8g.pdf

Constant-time navigation in four-dimensional nested simplicial meshes

We consider a multi-resolution representation based on a decomposition of the field domain into nested tetrahedral cells generated by recursive tetrahedron bisection, that we call a Hierarchy of Tetrahedra (HT) We describe our implementation of an HT, and discuss how to extract conforming meshes from an HT so as to avoid discontinuities in the approximation of the associated scalar field. We describe algorithms for selective refinement, which either extract a variable-resolution mesh from scratch through a depth-first, or through a priority-based traversal technique, or which locally refine and coarsen a previously-extracted adaptive mesh through an incremental approach. We show experimental results in connection with a set of basic queries for performing analysis and visualization of a volume data set at different levels of detail.

Selective Refinement on Nested Tetrahedral Meshes

The paper deals with the problem of analyzing and visualizing large-size volume data sets. To this aim, we consider multiresolution representations based on a decomposition of the field domain into tetrahedral cells. We compare two types of multiresolution representations that differ on the rule applied to refine an initial coarse mesh: one is based on tetrahedron bisection, and one based on vertex split. The two representations can be viewed as instances of a common multiresolution model, that we call a multiresolution mesh. Encoding data structures for the two representations are briefly described. An experimental comparison on structured volume data sets is presented.

Multiresolution Tetrahedral Meshes: An Analysis and a Comparison (figures 4, 6, and 9)

We deal with the problem of analyzing and visualizing large-size volume data sets. To this aim, we consider multiresolution representations based on a decomposition of the field domain into tetrahedral cells. We compare two types of multiresolution representations that differ on the rule applied to refine an initial coarse mesh: one is based on tetrahedron bisection, and one based on vertex split. The two representations can be viewed as instances of a common multiresolution model, that we call a multiresolution mesh. Encoding data structures for the two representations are briefly described. An experimental comparison on structured volume data sets is presented.

/pdf/multiresolution-tetrahedral-meshes-an-analysis-and-a-i5ohwdksr9.pdf

Multiresolution tetrahedral meshes: an analysis and a comparison

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