Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner

Three-Dimensional Modelling of the Terra Nova Bay Sea Floor (Ross Sea - Antarctica)

The importance of gathering data on the Antarctic coastline and its adjacent waters has been widely recognised by the Antarctic Treaty Consultative Meeting (ATCM), the Council of Managers of National Antarctic Programs (COMNAP) and the Scientific Committee on Antarctic Research (SCAR). In particular, both for navigational safety and environmental monitoring, it is very desirable to increase hydrographic activity in those areas which have the most significant importance from a scientific or navigational point of view - such as in the continental shelf and continental slope areas of the western part of the Ross Sea. Quite apart from the safety of navigation requirements, knowledge of the seabed topography is necessary to study and understand the various phenomena taking place in the marine environment. For example, the movement of water masses and their mixing processes depend on the shape of the seabed and adjacent coastline. The sea area surrounding Antarctica is one of the least explored parts of the world’s oceans and the available bathymetric data is only sufficient to allow a very general analysis to be made. With the probable growth of tourism and fishing around Antarctica and with the increasing need to understand the effects on the world’s climate of Antarctic water patterns, it is necessary to consider powerful new techniques - such as threedimensional modelling of the sea floors - in order to build up more quickly an effective and reliable bathymetric data base of Antarctic waters

Techniques for augmenting the visualisation of dynamic raster surfaces

Despite their aesthetic appeal and condensed nature, dynamic raster surface representations such as a temporal series of a landform and an attribute series of a socio-economic attribute of an area, are often criticised for the lack of an effective information delivery and interactivity.In this work, we readdress some of the earlier raised reasons for these limitations -information-laden quality of surface datasets, lack of spatial and temporal continuity in the original data, and a limited scope for a real-time interactivity. We demonstrate with examples that the use of four techniques namely the re-expression of the surfaces as a framework of morphometric features, spatial generalisation, morphing, graphic lag and brushing can augment the visualisation of dynamic raster surfaces in temporal and attribute series

Survey of semi-regular multiresolution models for interactive terrain rendering

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multiresolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster-based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accurac

Surface networks

© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou

Lossless data compression of grid-based digital elevation models: a PNG image format evaluation

At present, computers, lasers, radars, planes and satellite technologies make possible very fast and accurate topographic data acquisition for the production of maps. However, the problem of managing and manipulating this data efficiently remains. One particular type of map is the elevation map. When stored on a computer, it is often referred to as a Digital Elevation Model (DEM). A DEM is usually a square matrix of elevations. It is like an image, except that it contains a single channel of information (that is, elevation) and can be compressed in a lossy or lossless manner by way of existing image compression protocols. Compression has the effect of reducing memory requirements and speed of transmission over digital links, while maintaining the integrity of data as required. In this context, this paper investigates the effects of the PNG (Portable Network Graphics) lossless image compression protocol on floating-point elevation values for 16-bit DEMs of dissimilar terrain characteristics. The PNG is a robust, universally supported, extensible, lossless, general-purpose and patent-free image format. Tests demonstrate that the compression ratios and run decompression times achieved with the PNG lossless compression protocol can be comparable to, or better than, proprietary lossless JPEG variants, other image formats and available lossless compression algorithms

Variable-resolution Compression of Vector Data

The compression of spatial data is a promising solution to reduce the space of data storage and to decrease the transmission time of spatial data over the Internet. This paper proposes a new method for variable-resolution compression of vector data. Three key steps are encompassed in the proposed method, namely, the simplification of vector data via the elimination of vertices, the compression of removed vertices, and the decoding of the compressed vector data. The proposed compression method was implemented and applied to compress vector data to investigate its performance in terms of the compression ratio, distortions of geometric shapes. The results show that the proposed method provides a feasible and efficient solution for the compression of vector data, is able to achieve good compression ratios and maintains the main shape characteristics of the spatial objects within the compressed vector dat

Topographic map visualization from adaptively compressed textures

Raster-based topographic maps are commonly used in geoinformation systems to overlay geographic entities on top of digital terrain models. Using compressed texture formats for encoding topographic maps allows reducing latency times while visualizing large geographic datasets. Topographic maps encompass high-frequency content with large uniform regions, making current compressed texture formats inappropriate for encoding them. In this paper we present a method for locally-adaptive compression of topographic maps. Key elements include a Hilbert scan to maximize spatial coherence, efficient encoding of homogeneous image regions through arbitrarily-sized texel runs, a cumulative run-length encoding supporting fast random-access, and a compression algorithm supporting lossless and lossy compression. Our scheme can be easily implemented on current programmable graphics hardware allowing real-time GPU decompression and rendering of bilinear-filtered topographic maps.Postprint (published version

Wavelet-based multiresolution data representations for scalable distributed GIS services

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2002.Includes bibliographical references (p. 155-160).Demand for providing scalable distributed GIS services has been growing greatly as the Internet continues to boom. However, currently available data representations for these services are limited by a deficiency of scalability in data formats. In this research, four types of multiresolution data representations based on wavelet theories have been put forward. The designed Wavelet Image (WImg) data format helps us to achieve dynamic zooming and panning of compressed image maps in a prototype GIS viewer. The Wavelet Digital Elevation Model (WDEM) format is developed to deal with cell-based surface data. A WDEM is better than a raster pyramid in that a WDEM provides a non-redundant multiresolution representation. The Wavelet Arc (WArc) format is developed for decomposing curves into a multiresolution format through the lifting scheme. The Wavelet Triangulated Irregular Network (WTIN) format is developed to process general terrain surfaces based on the second generation wavelet theory. By designing a strategy to resample a terrain surface at subdivision points through the modified Butterfly scheme, we achieve the result: only one wavelet coefficient needs to be stored for each point in the final representation. In contrast to this result, three wavelet coefficients need to be stored for each point in a general 3D object wavelet-based representation. Our scheme is an interpolation scheme and has much better performance than the Hat wavelet filter on a surface. Boundary filters are designed to make the representation consistent with the rectangular boundary constraint.(cont.) We use a multi-linked list and a quadtree array as the data structures for computing. A method to convert a high resolution DEM to a WTIN is also provided. These four wavelet-based representations provide consistent and efficient multiresolution formats for online GIS. This makes scalable distributed GIS services more efficient and implementable.by Jingsong Wu.Ph.D