Emanuele Danovaro

Morphology-driven simplification and multiresolution modeling of terrains

We propose a technique for simplification and multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform morphological properties (such as valleys, basins, etc.) separated by a network of critical lines and points. We describe an algorithm to compute the above decomposition and the critical net, and a TIN simplification algorithm that preserves them. On this basis, we build a multiresolution terrain model, which provides a representation of critical features at any level of detail.

Multiresolution tetrahedral meshes: an analysis and a comparison

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.

Computer Graphics in Italy: Level-of-detail for data analysis and exploration: A historical overview and some new perspectives

Level-of-detail (LOD) techniques have been studied for many years in computer graphics. Research in this area has reached maturity and several effective tools in LOD modeling are now available. However, most models and tools proposed in the literature are oriented to rendering. This is just one among many tasks that LOD should support in the context of applications involving geometric meshes of large size. Our approach to the research on LOD has always been to develop models and data structures that can support a range of spatial queries, rather than being optimized for rendering. Here, we present a historical overview, by highlighting the impact of this approach in the design of LOD models and data structures, and we briefly describe our current research, outlining new challenges in which LOD finds important applications.

A multi-resolution representation for terrain morphology

Mesh-based terrain representations provide accurate descriptions of a terrain, but fail in capturing its morphological structure. The morphology of a terrain is defined by its critical points and by the critical lines joining them, which form a so-called surface network. Because of the large size of current terrain data sets, a multi-resolution representation of the terrain morphology is crucial. Here, we address the problem of representing the morphology of a terrain at different resolutions. The basis of the multi-resolution terrain model, that we call a Multi-resolution Surface Network (MSN), is a generalization operator on a surface network, which produces a simplified representation incrementally. An MSN is combined with a multi-resolution mesh-based terrain model, which encompasses the terrain morphology at different resolutions. We show how variable-resolution representations can be extracted from an MSN, and we present also an implementation of an MSN in a compact encoding data structure.

A Discrete Approach to Compute Terrain Morphology

We consider the problem of extracting morphology of a terrain represented as a Triangulated Irregular Network (TIN). We propose a new algorithm and compare it with representative algorithms of the main approaches existing in the literature to this problem. The new algorithm has the advantage of being simple, using only comparisons (and no floating-point computations), and of being suitable for an extension to higher dimensions. Our experiments consider both real data and artificial test data. We evaluate the difference in the results produced on the same terrain data, as well as the impact of resolution level on such a difference, by considering representations of the same terrain at different resolutions.

Multi-resolution out-of-core modeling of terrain and teological data

Multi-resolution is a useful tool for managing the complexity of huge terrain and geological data sets. Since encoding large data sets may easily exceed main memory capabilities, data structures and algorithms capable of efficiently working in external memory are needed. In our work, we aim at developing an out-of-core multi-resolution model dimension-independent, that can be used for both terrains, represented by Triangulated Irregular Networks(TINs), and 3D data, such as geological data, represented by tetrahedral meshes. We have based our approach on a general multi-resolution model, that we have proposed in our previous work, which supports the extraction of variable-resolution representations. As first step, we have developed, in a prototype simulation system, a large number of clustering techniques for the modifications in a multi-resolution model. Here, we describe such techniques, and analyze and evaluate them experimentally. The result of this investigation has led us to select a specific clustering approach as the basis for an efficient out-of-core data structure.

The half-edge tree: a compact data structure for level-of-detail tetrahedral meshes

We propose a new data structure for the compact encoding of a level-of detail (LOD) model of a three-dimensional scalar field based on unstructured tetrahedral meshes. Such data structure, called a half-edge tree (HET), is built through the iterative application of a half-edge collapse, i.e. by contracting an edge to one of its endpoints. We also show that selective refined meshes extracted from an HET contain on average about 34% and up to 75% less tetrahedra than those extracted from an LOD model built through a general edge collapse.

DATA STRUCTURES FOR 3D MULTI-TESSELLATIONS: AN OVERVIEW

Multiresolution models support the interactive visualization of large volumetric data through selective refinement, an operation which permits to focus resolution only on the most relevant portions of the domain, or in the proximity of interesting field values. A 3D Multi-Tessellation (MT) is a multiresolution model, consisting of a coarse tetrahedral mesh at low resolution, and of a set of updates refining such a mesh, arranged as a partial order. In this paper, we describe and compare different data structures which permit to encode a 3D MT and to support selective refinement.

Compressing Multiresolution Triangle Meshes

In this paper, we consider triangle-based two-dimensional multiresolution complexes, called Multi-Triangulations (MTs), constructed based on a vertex-removal simplification strategy, which is the most common strategy used to build simplified representations of surfaces, e.g., terrains. We describe and compare compact encoding structures for such MTs. We show that these structures provide good compression ratios not only with respect to an economical data structure for general MTs, but also with respect to encoding the original mesh (i.e., the mesh at the full resolution). We also analyze the basic atomic operations needed for performing selective refinement on an MT, and we show that such operations are efficiently supported by the data structures described.

Multiresolution morse triangulations

We address the problem of representing the geometry and the morphology of a triangulated surface endowed with a scalar field in a combined geometric and topological multiresolution model. The model, called a Multiresolution Morse Triangulation (MMT), is composed of a multiresolution triangle mesh, and of a multiresolution Morse complex describing the morphology of the field. The MMT is built through a combined morphological and geometrical generalization, and supports queries to extract consistent geometrical and morphological representations of the field at both uniform and variable resolutions.