Enrico Puppo

Speeding up isosurface extraction using interval trees

The interval tree is an optimally efficient search structure proposed by Edelsbrunner (1980) to retrieve intervals on the real line that contain a given query value. We propose the application of such a data structure to the fast location of cells intersected by an isosurface in a volume dataset. The resulting search method can be applied to both structured and unstructured volume datasets, and it can be applied incrementally to exploit coherence between isosurfaces. We also address issues of storage requirements, and operations other than the location of cells, whose impact is relevant in the whole isosurface extraction task. In the case of unstructured grids, the overhead, due to the search structure, is compatible with the storage cost of the dataset, and local coherence in the computation of isosurface patches is exploited through a hash table. In the case of a structured dataset, a new conceptual organization is adopted, called the chess-board approach, which exploits the regular structure of the dataset to reduce memory usage and to exploit local coherence. In both cases, efficiency in the computation of surface normals on the isosurface is obtained by a precomputation of the gradients at the vertices of the mesh. Experiments on different kinds of input show that the practical performance of the method reflects its theoretical optimality.

Hierarchical triangulation for multiresolution surface description

A new hierarchical triangle-based model for representing surfaces over sampled data is proposed, which is based on the subdivision of the surface domain into nested triangulations, called a hierarchical triangulation (HT). The model allows compression of spatial data and representation of a surface at successively finer degrees of resolution. An HT is a collection of triangulations organized in a tree, where each node, except for the root, is a triangulation refining a face belonging to its parent in the hierarchy. We present a topological model for representing an HT, and algorithms for its construction and for the extraction of a triangulation at a given degree of resolution. The surface model, called a hierarchical triangulated surface (HTS) is obtained by associating data values with the vertices of triangles, and by defining suitable functions that describe the surface over each triangular patch. We consider an application of a piecewise-linear version of the HTS to interpolate topographical data, and we describe a specialized version of the construction algorithm that builds an HTS for a terrain starting from a high-resolution rectangular grid of sampled data. Finally, we present an algorithm for extracting representations of terrain at variable resolution over the domain.

Representation and visualization of terrain surfaces at variable resolution

1 Istituto Elaborazione dell’Informazione — Consiglio Nazionale delle Ricerche, Via S. Maria, 46—56126 Pisa, Italy e-mail: cignoni@iei.pi.cnr.it 2 Istituto per la Matematica Applicata — Consiglio Nazionale delle Ricerche, Via dei Marini, 6 (Torre di Francia) — 16149 Genova, Italy e-mail: puppo@ima.ge.cnr.it 3CNUCE — Consiglio Nazionale delle Ricerche, Via S. Maria 36—56126 Pisa, Italy e-mail: r.scopigno@cnuce.cnr.it

Quad-Mesh Generation and Processing: A Survey

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi‐regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing.

Efficient implementation of multi-triangulations

Multi-triangulation (MT) is a general framework for managing the level-of-detail in large triangle meshes, which we have introduced in our previous work. In this paper, we describe an efficient implementation of an MT based on vertex decimation. We present general techniques for querying an MT, which are independent of a specific application, and which can be applied for solving problems, such as selective refinement, windowing, point location, and other spatial interference queries. We describe alternative data structures for encoding an MT, which achieve different trade-offs between space and performance. Experimental results are discussed.

Multiresolution representation and visualization of volume data

A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built off-line through data simplification techniques, and stored in a compact data structure that supports fast on-line access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task and to the performance of a specific hardware platform. Representations at different resolutions can be used together to further enhance interaction and performance through progressive and multiresolution rendering.

Building and traversing a surface at variable resolution

The authors consider the multi-triangulation, a general model for representing surfaces at variable resolution based on triangle meshes. They analyse characteristics of the model that make it effective for supporting basic operations such as extraction of a surface approximation, and point location. An interruptible algorithm for extracting a representation at a resolution variable over the surface is presented. Different heuristics for building the model are considered and compared. Results on both the construction and the extraction algorithm are presented.

Multiresolution models for topographic surface description

Multiresolution terrain models describe a topographic surface at various levels of resolution. Besides providing a data compression mechanism for dense topographic data, such models enable us to analyze and visualize surfaces at a variable resolution. This paper provides a critical survey of multiresolution terrain models. Formal definitions of hierarchical and pyramidal models are presented. Multiresolution models proposed in the literature (namely, surface quadtree, restricted quadtree, quaternary triangulation, ternary triangulation, adaptive hierarchical triangulation, hierarchical Delaunay triangulation, and Delaunay pyramid) are described and discussed within such frameworks. Construction algorithms for all such models are given, together with an analysis of their time and space complexities.

Multiresolution modeling and visualization of volume data based on simplicial complexes

A scattered volumetric dataset is regarded as a sampled version of a scalar field defined over a three-dimensional domain, whose graph is a hypersurface embedded in a fourdimensional space. We propose a multiresolution model for the representation and visualization of such dataset, based on a decomposition of the three-dimensional domain into tetrahedra. Multiresolution is achieved through a sequence of tetrahedralizations that approximate the scalar field at increasing precision. The construction of the model is based on an adaptive incremental approach driven by the local coherence of the scalar field. The proposed model allows an efficient extraction of compact isosurfaces with adaptive resolution levels as well as the development of progressive and multiresolution rendering approaches. Experimental evaluations of the proposed approach on different scattered datasets are reported.

Line-of-sight communication on terrain models

Abstract Line-of-sight communication on topographic surfaces has relevance for several applications of Geographical Information Systems. In this paper, we study the problem of linking a set of transceiver stations in a visibility-connected communication network, by placing a minimum number of relays on the terrain surface. The problem is studied in the framework of a discrete visibility model, where the mutual visibility of a finite set of sites on the terrain is represented through a graph, called the visibility graph. While in the special case of only two transceivers an optimal solution can be found in polynomial time, by computing a minimum path on the visibility graph, the general problem is equivalent to a Steiner problem on the visibility graph, and, thus, it is untractable in practice. In the latter case, we propose a practical approximate solution based on a Steiner heuristic. For both the special and the general case, we propose both a static and a dynamic algorithm that allow computation of a s...