Hierarchical topology-preserving simplification of terrains (original) (raw)
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Computational methods for simplification and generalisation of Digital Terrain Modelling
Istituto per la Matematica Applicata -Consiglio Nazionale delle Ricerche Storage, manipulation and rendering of huge data sets are frequently required in spatial data handling and need memory and processing resources beyond the available ones, especially in real-time or interactive environments. Thus it is necessary to define data models which use the minimum amount of data for retrieving the maximum of information possible, and modelling issues have to be considered in addition to traditional hardware or software optimisation problems.
Terrain complexity and reduction of topographic data
Journal of Geographical Systems, 1999
Digital terrain data are useful for a variety of applications in mapping and spatial analysis. Most available terrain data are organized in a raster format, among them being the most extensively-used Digital Elevation Models (DEM) of the U.S. Geological Survey. A common problem with DEM for spatial analysis at the landscape scale is that the raster encoding of topography is subject to data redundancy and, as such, data volumes may become prohibitively large. To improve e½ciency in both data storage and information processing, the redundancy of the terrain data must be minimized by eliminating unnecessary elements. To what extent a set of terrain data can be reduced for improving storage and processing e½ciency depends on the complexity of the terrain. In general, data elements for simpler, smoother surfaces can be substantially reduced without losing critical topographic information. For complex terrains, more data elements should be retained if the topography is to be adequately represented. In this paper, we present a measure of terrain complexity based on the behavior of selected data elements in representing the characteristics of a surface. The index of terrain complexity is derived from an estimated parameter which denotes the relationship between terrain representation (percentage surface representation) and relative data volume (percentage DEM elements). The index can be used to assess the required volume of topographic data and determine the appropriate level of data reduction. Two quadrangles of distinct topographic characteristics were examined to illustrate the e½cacy of the developed methodology.
Topological Landscapes: A Terrain Metaphor for Scientific Data
IEEE Transactions on Visualization and Computer Graphics, 2000
Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex information easily accessible by using commonly known concepts. In this paper we propose a new metaphor, called "Topological Landscapes," which facilitates understanding the topological structure of scalar functions. The basic idea is to construct a terrain with the same topology as a given dataset and to display the terrain as an easily understood representation of the actual input data. In this projection from an n-dimensional scalar function to a two-dimensional (2D) model we preserve function values of critical points, the persistence (function span) of topological features, and one possible additional metric property (in our examples volume). By displaying this topologically equivalent landscape together with the original data we harness the natural human proficiency in understanding terrain topography and make complex topological information easily accessible.
Visualizing Multifolded and Multifaulted Terrain Geometry Using Computer Graphics
Geoinformatics
The POLYPLI software makes it possible to visualize the geometry of stratified terrain which have been deformed by numerous fold and fault events in a quick and efficient way. Strata deformation is carried out by simple geometric transformations which affect the various material points. These transformations simulate the displacements which are registered in similar folding. Faults are simulated in a similar way.Stratigraphy , fold profiles wavelength amplitudes and orientations of the various fold phases and of the various faults are interactively defined by the user.POLYPLI can represent unconformities and deformations which simultaneously affect a previously deformed basement and its sedimentary cover. POLYPLI provides a new type of help for structural analysis : its provides a good approximation to the topology of intricate deformations such as those which are commonly observed in basement located metasedimentary terrains. Run under UNIX operating system, POLY-PLI is very interactive and easy to use because of a multiwindow presentation which can input most data with the mouse.
Representation and Visualization of Terrain Surfaces at Variable Resolution
The Visual Computer, 1997
We present a new approach for managing the representation of discrete topographic surfaces at variable resolution, which is based on a unified model encoding a history of either refinement or simplification of a triangulation decomposing a plane domain. An efficient data structure is proposed, which is obtained by interpreting the model containing all triangles of the history as a cell complex embedded in three-dimensional space. A major feature of the model is the ability to provide efficiently a representation of the surface at resolution variable over the domain, according to an application-dependent threshold function. Experimental results on real world data are presented, and applications to flight simulation are discussed.
Visualization of Large Terrains Made Easy
Visualization, 2001. VIS'01. Proceedings, 2001
We present an elegant and simple to implement framework for performing out-of-core visualization and view-dependent refinement of large terrain surfaces. Contrary to the recent trend of increasingly elaborate algorithms for large-scale terrain visualization, our algorithms and data structures have been designed with the primary goal of simplicity and efficiency of implementation. Our approach to managing large terrain data also departs from more conventional strategies based on data tiling. Rather than emphasizing how to segment and efficiently bring data in and out of memory, we focus on the manner in which the data is laid out to achieve good memory coherency for data accesses made in a top-down (coarse-to-fine) refinement of the terrain. We present and compare the results of using several different data indexing schemes, and propose a simple to compute index that yields substantial improvements in locality and speed over more commonly used data layouts. Our second contribution is a new and simple, yet easy to generalize method for view-dependent refinement. Similar to several published methods in this area, we use longest edge bisection in a top-down traversal of the mesh hierarchy to produce a continuous surface with subdivision connectivity. In tandem with the refinement, we perform view frustum culling and triangle stripping. These three components are done together in a single pass over the mesh. We show how this framework supports virtually any error metric, while still being highly memory and compute efficient.
This chapter reviews recent development in terrain generalisation. The focus is put on cartographic generalisation where the terrain representation is adapted with consideration to the aesthetics and legibility of the map for a specific purpose. Generalisation methods apply to traditional terrain representations (spot heights, contours, hypsometric colours, shaded relief) but also to grid and triangulated surface generalisation. First, issues related to relief representation on maps at different scales are discussed. As generalisation requires knowledge about the terrain morphology, several approaches focusing on the classification of terrain features according to morphometric or topological criteria were developed. Cartographic generalisation methods are reviewed with consideration to conflicts between terrain representations and other object type data on the map. In the second part, three case studies illustrating previous developments are presented. First, a generalisation method for hypsometric map production is described where important valleys and mountain ridges are accentuated to improve the representation. Second, a method selecting features represented by isobaths and answering specific constraints of nautical charts is presented. The third case study is a generalisation method which takes into account other objects of the map such as buildings and rivers.
VARIANT---processing and visualizing terrains at variable resolution
Proceedings of the fifth ACM international workshop on Advances in geographic information systems - GIS '97, 1997
We describe VARIANT (VAriable Resolution Interactive ANalysis of Terrains), a prototype system for processing and visualizing terrains at variable resolution, which is based on a multiresolution terrain model, called a Multi-Triangulation (MT).
Presented at the 19th ICA Meeting …, 1999
It is believed that Web-based visualisation of spatial information could be greatly enhanced through the use of dynamic or 'onthe-fly' map generalisation. This involves dynamically deriving scale-and theme-dependent displays from a single detailed dataset, thus eliminating the need to maintain duplicate datasets at different resolutions. Dynamic generalisation also prevents the generation of cartographically-poor maps that result from the display of spatial information at a considerably different resolution from that at which it was captured. The implementation involves combining automated generalisation and symbolisation techniques together in a simple rule-base to produce a virtual map of central Edinburgh in which both the level of detail and the symbology is dynamically tailored to a user-specified scale and map theme (tourist or topographic maps). The paper explores the inherent differences between the generalisation of a virtual map and that of a paper map, and also considers issues such as those arising from the relationship between map scale, map theme and utility. The research demonstrates that it is possible to achieve effective results using a limited number of simple mechanisms, and argues that the true potential of dynamic generalisation lies in two main areas -firstly, in an ability to narrowly-define the map theme, thus enhancing map clarity and more closely matching user requirements; and secondly, in using control over the map scale as a gateway to other types of map use and other themes.