Paola Magillo

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.

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.

Algorithms for Visibility Computation on Terrains: A Survey:

Several environment applications require the computation of visibility information on a terrain. Examples are optimal placement of observation points, line-of-sight communication, and computation of hidden as well as scenic paths. Visibility computations on a terrain may involve either one or many viewpoints, and range from visibility queries (for example, testing whether a given query point is visible), to the computation of structures that encode the visible portions of the surface. In this paper, the authors consider a number of visibility problems on terrains and present an overview of algorithms to tackle such problems on triangulated irregular networks and regular square grids.

Visibility algorithms on triangulated digital terrain models

Abstract In this paper, we address the problem of computing visibility information on triangulated digital terrain models. We present first a general introduction to digital terrain models. Visibility problems on terrains are classified, according to the kind of visibility information they compute, into point visibility, line visibility and region visibility. A survey of the state-of-the-art of the algorithms for computing the different kinds of visibility information is presented, according to the previous classification. A new algorithm for computing the horizon on a digital terrain model is also described.

Multiresolution Mesh Representation: Models and Data Structures

Multiresolution meshes are a common basis for building representations of a geometric shape at different levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to the density (size and number) of its cells. A multiresolution mesh provides several alternative mesh-based approximations of a spatial object (e.g., a surface describing the boundary of a solid object, or the graph of a scalar field).

VARIANT: A System for Terrain Modeling at Variable Resolution

We describe VARIANT (VAriable Resolution Interactive ANalysis of Terrain), an extensible system for processing and visualizing terrains represented through Triangulated Irregular Networks (TINs), featuring the accuracy of the representation, possibly variable over the terrain domain, as a further parameter in computation.VARIANT is based on a multiresolution terrain model, which we developed in our earlier research. Its architecture is made of a kernel, which provides primitive operations for building and querying the multiresolution model; and of application programs, which access a terrain model based on the primitives in the kernel.VARIANT directly supports basic queries (e.g., windowing, buffering, computation of elevation at a given point, or along a given line) as well as high-level operations (e.g., fly-over visualization, contour map extraction, viewshed analysis). However, the true power of VARIANT lies in the possibility of extending it with new applications that can exploit its multiresolution features in a transparent way.

Selective refinement queries for volume visualization of unstructured tetrahedral meshes

We address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes. Multiresolution models, also called Level-Of-Detail (LOD) models, allow encoding the whole data set at a virtually continuous range of different resolutions. We have identified a set of queries for extracting meshes at variable resolution from a multiresolution model, based on field values, domain location, or opacity of the transfer function. Such queries allow trading off between resolution and speed in visualization. We define a new compact data structure for encoding a multiresolution tetrahedral mesh built through edge collapses to support selective refinement efficiently and show that such a structure has a storage cost from 3 to 5.5 times lower than standard data structures used for tetrahedral meshes. The data structures and variable resolution queries have been implemented together with state-of-the art visualization techniques in a system for the interactive visualization of three-dimensional scalar fields defined on tetrahedral meshes. Experimental results show that selective refinement queries can support interactive visualization of large data sets.

Dynamic view-dependent multiresolution on a client–server architecture

Abstract We consider the problem of transmitting huge triangle meshes in the context of a Web-like client–server architecture. Approximations of the original mesh are transmitted by applying selective refinement. A multiresolution geometric model is maintained by the server. A client may query the server for a mesh at an arbitrary, continuously variable, level of detail. The client makes repeated queries over time with different query parameters. The server answers to queries by traversing the multiresolution model and transmitting updates to the client, which uses them to progressively modify a current mesh. We study this problem in the context of a vertex-based multiresolution model, which is a special instance of the Multi-Triangulation (a model that was developed in an earlier work), based on vertex insertion and removal. We define a compact data structure for such a model that exploits the specific update rule. We propose a dynamic algorithm for selective refinement and we discuss in detail its implementation as a client–server application. In order to reduce memory requirements and channel traffic, we develop a compressed representation which allows us to express mesh updates with a code of small size. We also address client caching to further limit bandwidth occupancy. Experimental results show that the Multi-Triangulation can be a key Web technology for triangle mesh manipulation.

A Formal Approach to Multiresolution Hypersurface Modeling

Multiresolution geometrie models support the representation and processing of geometric entities at different levels of detail, and are useful in several application fields, such as geographic information systems, CAD systems and scientific visualization. The aim of this paper is to provide a framework for multiresolution geometric modeling, independent both of the dimension of spatial objects under consideration, and of the specific application. This paper introduces a formal model, called the Multiresolution Simplicial Model (MSM), capable of capturing the characteristics of most multiresolution models proposed in the literature. The paper provides an analysis of the relationships between the intrinsic structures of different multiresolution models, as well as a definition of relevant application-independent operations on them. Major data structures used to encode multiresolution models are reviewed, as well as algorithms which implement the operations on each data structure.

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.