Simple I/O-efficient flow accumulation on grid terrains

The flow accumulation problem for grid terrains takes as input a matrix of flow directions, that specifies for each cell of the grid to which of its eight neighbours any incoming water would flow. The problem is to compute, for each cell c, from how many cells of the terrain water would reach c. We show that this problem can be solved in O(scan(N)) I/Os for a terrain of N cells. Taking constant factors in the I/O-efficiency into account, our algorithm may be an order of magnitude faster than the previously known algorithm that is based on time-forward processing and needs O(sort(N)) I/Os.Comment: This paper is an exact copy of the paper that appeared in the abstract collection of the Workshop on Massive Data Algorithms, Aarhus, 200

A hybrid representation for modeling, interactive editing, and real-time visualization of terrains with volumetric features

Cataloged from PDF version of article.Terrain rendering is a crucial part of many real-time applications. The easiest way to process and visualize terrain data in real time is to constrain the terrain model in several ways. This decreases the amount of data to be processed and the amount of processing power needed, but at the cost of expressivity and the ability to create complex terrains. The most popular terrain representation is a regular 2D grid, where the vertices are displaced in a third dimension by a displacement map, called a heightmap. This is the simplest way to represent terrain, and although it allows fast processing, it cannot model terrains with volumetric features. Volumetric approaches sample the 3D space by subdividing it into a 3D grid and represent the terrain as occupied voxels. They can represent volumetric features but they require computationally intensive algorithms for rendering, and their memory requirements are high. We propose a novel representation that combines the voxel and heightmap approaches, and is expressive enough to allow creating terrains with caves, overhangs, cliffs, and arches, and efficient enough to allow terrain editing, deformations, and rendering in real time

Implicit flow routing on terrains with applications to surface networks and drainage structures

Flow-related structures on terrains are defined in terms of paths of steepest descent (or ascent). A steepest descent path on a polyhedral terrain T with n vertices can have T(n^2) complexity. The watershed of a point p --- the set of points on T whose paths of steepest descent reach p --- can have complexity T(n^3). We present a technique for tracing a collection of n paths of steepest descent on T implicitly in O(n logn) time. We then derive O(n log n) time algorithms for: (i) computing for each local minimum p of T the triangles contained in the watershed of p and (ii) computing the surface network graph of T. We also present an O(n^2) time algorithm that computes the watershed area for each local minimum of T

Interactive Procedural Modelling of Coherent Waterfall Scenes

International audienceCombining procedural generation and user control is a fundamental challenge for the interactive design of natural scenery. This is particularly true for modelling complex waterfall scenes where, in addition to taking charge of geometric details, an ideal tool should also provide a user with the freedom to shape the running streams and falls, while automatically maintaining physical plausibility in terms of flow network, embedding into the terrain, and visual aspects of the waterfalls. We present the first solution for the interactive procedural design of coherent waterfall scenes. Our system combines vectorial editing, where the user assembles elements to create a waterfall network over an existing terrain, with a procedural model that parametrizes these elements from hydraulic exchanges; enforces consistency between the terrain and the flow; and generates detailed geometry, animated textures and shaders for the waterfalls and their surroundings. The tool is interactive, yielding visual feedback after each edit

Flow Computations on Imprecise Terrains

We study the computation of the flow of water on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x,y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time

Query-by-Pointing: Algorithms and Pointing Error Compensation

People typically communicate by pointing, talking, sketching, writing, and typing. Pointing can be used to visualize or exchange information about an object when there is no other mutually understood way of communication. Despite its proven expressiveness, however, it has not yet become a frequently used modality to interact with computer systems. With the rapid move towards the adoption of mobile technologies, geographic information systems (GISs) have a particular need for advanced forms of interaction that enable users to query the geographic world directly. To enable pointing-based query system on a handheld device, a number of fundamental technical challenges have to be overcome. For such a system to materialize we need models stored in the device\u27s knowledge base that can be used as surrogate of real world objects. These computations, however, assume that (1) the pointing direction matches with the line-of-sight and (2) the observations about location and direction are precise enough so that a computational model will determine the same object as what the user points at. Both assumptions are not true. This thesis, therefore, develops an efficient error compensation model to reduce the discrepancy between the line-of-sight of the eye and the pointer direction. The model is based on a coordinate system centered at the neck and distances measured from neck to eye, neck to shoulder, shoulder to handheld pointer, and the pointing direction. An experiment was conducted using a gyro-enhanced sensor and three subjects who pointed at marked targets in a given room. It showed that the error compensation algorithm significantly reduces errors in pointing with arms outstretched

Modeling Shallow Water Flows on General Terrains

A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of gravity forces is not exact in the general case of a tilted curved bottom. We claim that an integration path that better adapts to the shallow water hypotheses follows the "cross-flow" surface, i.e., a surface that is normal to the velocity field at any point of the domain. Because of the implicitness of this definition, we approximate this "cross-flow" path by performing depth integration along a local direction normal to the bottom surface, and propose a rigorous derivation of this approximation and its numerical solution as an essential step for the future development of the full "cross-flow" integration procedure. We start by defining a local coordinate system, anchored on the bottom surface to derive a covariant form of the Navier-Stokes equations. Depth integration along the local normals yields a covariant version of the shallow water equations, which is characterized by flux functions and source terms that vary in space because of the surface metric coefficients and related derivatives. The proposed model is discretized with a first order FORCE-type Godunov Finite Volume scheme that allows implementation of spatially variable fluxes. We investigate the validity of our SW model and the effects of the bottom geometry by means of three synthetic test cases that exhibit non negligible slopes and surface curvatures. The results show the importance of taking into consideration bottom geometry even for relatively mild and slowly varying curvatures

Digital surface modelling and 3D information extraction from spaceborne very high resolution stereo pairs

This report discusses the potentials of VHR stereo imagery for automatic digital surface modelling (DSM) and 3D information extraction on large metropolitan cities. Stereo images acquired by GeoEye-1 on Dakar and Guatemala City and by WorldView-2 on Panama City, Constitucion (Chile), Kabul, Teheran, Kathmandu and San Salvador were processed following a rigorous photogrammetric approach. The work focusing on evaluating the quality of the DSMs in relation to the image and terrain characteristics and, among the possible DSM’s application, present a solution for buildings height estimation. The size of the datasets, the variety of case studies and the complexity of the scenarios allow to critically analyzing the potentials of VHR stereo imagery for 3D landscape modeling for natural hazards assessment.JRC.G.2-Global security and crisis managemen