Maintaining Contour Trees of Dynamic Terrains

We consider maintaining the contour tree $\mathbb{T}$ of a piecewise-linear triangulation $\mathbb{M}$ that is the graph of a time varying height function $h: \mathbb{R}^2 \rightarrow \mathbb{R}$. We carefully describe the combinatorial change in $\mathbb{T}$ that happen as $h$ varies over time and how these changes relate to topological changes in $\mathbb{M}$. We present a kinetic data structure that maintains the contour tree of $h$ over time. Our data structure maintains certificates that fail only when $h(v)=h(u)$ for two adjacent vertices $v$ and $u$ in $\mathbb{M}$, or when two saddle vertices lie on the same contour of $\mathbb{M}$. A certificate failure is handled in $O(\log(n))$ time. We also show how our data structure can be extended to handle a set of general update operations on $\mathbb{M}$ and how it can be applied to maintain topological persistence pairs of time varying functions

Maintaining Contour Trees of Dynamic Terrains

We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present a kinetic data structure (KDS) for maintaining T efficiently. It maintains certificates that fail, i.e., an event occurs, only when the heights of two adjacent vertices become equal or two saddle vertices appear on the same contour. Assuming that the heights of two vertices of Sigma become equal only O(1) times and these instances can be computed in O(1) time, the KDS processes O(kappa + n) events, where n is the number of vertices in Sigma and kappa is the number of events at which the combinatorial structure of T changes, and processes each event in O(log n) time. The KDS can be extended to maintain an augmented contour tree and a join/split tree

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

Maintaining Reeb Graphs of Triangulated 2-Manifolds

Let M be a triangulated, orientable 2-manifold of genus g without boundary, and let h be a height function over M that is linear within each triangle. We present a kinetic data structure (KDS) for maintaining the Reeb graph R of h as the heights of M\u27s vertices vary continuously with time. Assuming the heights of two vertices of M become equal only O(1) times, the KDS processes O((k + g) n polylog n) events; n is the number of vertices in M, and k is the number of external events which change the combinatorial structure of R. Each event is processed in O(log^2 n) time, and the total size of our KDS is O(gn). The KDS can be extended to maintain an augmented Reeb graph as well

Real-time Photorealistic Visualisation of Large-scaleMultiresolution Terrain Models

Height field terrain rendering is an important aspect of GIS, outdoor virtual reality applicationssuch as flight simulation, 3-D games, etc. A polygonal model of very large terrain data requiresa large number of triangles. So, even most high-performance graphics workstations have greatdifficulty to display even moderately sized height fields at interactive frame rates. To bringphotorealism in visualisation, it is required to drape corresponding high-resolution satellite oraerial phototexture over 3-D digital terrain and also to place multiple collections of point-location-based static objects such as buildings, trees, etc and to overlay polyline vector objects suchas roads on top of the terrain surface. It further complicates the requirement of interactive framerates while navigation over the terrain. This paper describes a novel approach for objects andterrain visualisation by combination of two algorithms, one for terrain data and the other forobjects. The terrain rendering is accomplished by an efficient dynamic multiresolution view-dependent level-of-detail mesh simplification algorithm. It is augmented with out-of-corevisualisation of large-height geometry and phototexture terrain data populated with 3-D/2-Dstatic objects as well as vector overlays without extensive memory load. The proposedmethodology provides interactive frame rates on a general-purpose desktop PC with OpenGL-enabled graphics hardware. The software TREND has been successfully tested on different real-world height maps and satellite phototextures of sizes up to 16K*16K coupled with thousandsof static objects and polyline vector overlays

Realistic reconstruction and rendering of detailed 3D scenarios from multiple data sources

During the last years, we have witnessed significant improvements in digital terrain modeling, mainly through photogrammetric techniques based on satellite and aerial photography, as well as laser scanning. These techniques allow the creation of Digital Elevation Models (DEM) and Digital Surface Models (DSM) that can be streamed over the network and explored through virtual globe applications like Google Earth or NASA WorldWind. The resolution of these 3D scenes has improved noticeably in the last years, reaching in some urban areas resolutions up to 1m or less for DEM and buildings, and less than 10 cm per pixel in the associated aerial imagery. However, in rural, forest or mountainous areas, the typical resolution for elevation datasets ranges between 5 and 30 meters, and typical resolution of corresponding aerial photographs ranges between 25 cm to 1 m. This current level of detail is only sufficient for aerial points of view, but as the viewpoint approaches the surface the terrain loses its realistic appearance. One approach to augment the detail on top of currently available datasets is adding synthetic details in a plausible manner, i.e. including elements that match the features perceived in the aerial view. By combining the real dataset with the instancing of models on the terrain and other procedural detail techniques, the effective resolution can potentially become arbitrary. There are several applications that do not need an exact reproduction of the real elements but would greatly benefit from plausibly enhanced terrain models: videogames and entertainment applications, visual impact assessment (e.g. how a new ski resort would look), virtual tourism, simulations, etc. In this thesis we propose new methods and tools to help the reconstruction and synthesis of high-resolution terrain scenes from currently available data sources, in order to achieve realistically looking ground-level views. In particular, we decided to focus on rural scenarios, mountains and forest areas. Our main goal is the combination of plausible synthetic elements and procedural detail with publicly available real data to create detailed 3D scenes from existing locations. Our research has focused on the following contributions: - An efficient pipeline for aerial imagery segmentation - Plausible terrain enhancement from high-resolution examples - Super-resolution of DEM by transferring details from the aerial photograph - Synthesis of arbitrary tree picture variations from a reduced set of photographs - Reconstruction of 3D tree models from a single image - A compact and efficient tree representation for real-time rendering of forest landscapesDurant els darrers anys, hem presenciat avenços significatius en el modelat digital de terrenys, principalment gràcies a tècniques fotogramètriques, basades en fotografia aèria o satèl·lit, i a escàners làser. Aquestes tècniques permeten crear Models Digitals d'Elevacions (DEM) i Models Digitals de Superfícies (DSM) que es poden retransmetre per la xarxa i ser explorats mitjançant aplicacions de globus virtuals com ara Google Earth o NASA WorldWind. La resolució d'aquestes escenes 3D ha millorat considerablement durant els darrers anys, arribant a algunes àrees urbanes a resolucions d'un metre o menys per al DEM i edificis, i fins a menys de 10 cm per píxel a les fotografies aèries associades. No obstant, en entorns rurals, boscos i zones muntanyoses, la resolució típica per a dades d'elevació es troba entre 5 i 30 metres, i per a les corresponents fotografies aèries varia entre 25 cm i 1m. Aquest nivell de detall només és suficient per a punts de vista aeris, però a mesura que ens apropem a la superfície el terreny perd tot el realisme. Una manera d'augmentar el detall dels conjunts de dades actuals és afegint a l'escena detalls sintètics de manera plausible, és a dir, incloure elements que encaixin amb les característiques que es perceben a la vista aèria. Així, combinant les dades reals amb instàncies de models sobre el terreny i altres tècniques de detall procedural, la resolució efectiva del model pot arribar a ser arbitrària. Hi ha diverses aplicacions per a les quals no cal una reproducció exacta dels elements reals, però que es beneficiarien de models de terreny augmentats de manera plausible: videojocs i aplicacions d'entreteniment, avaluació de l'impacte visual (per exemple, com es veuria una nova estació d'esquí), turisme virtual, simulacions, etc. En aquesta tesi, proposem nous mètodes i eines per ajudar a la reconstrucció i síntesi de terrenys en alta resolució partint de conjunts de dades disponibles públicament, per tal d'aconseguir vistes a nivell de terra realistes. En particular, hem decidit centrar-nos en escenes rurals, muntanyes i àrees boscoses. El nostre principal objectiu és la combinació d'elements sintètics plausibles i detall procedural amb dades reals disponibles públicament per tal de generar escenes 3D d'ubicacions existents. La nostra recerca s'ha centrat en les següents contribucions: - Un pipeline eficient per a segmentació d'imatges aèries - Millora plausible de models de terreny a partir d'exemples d’alta resolució - Super-resolució de models d'elevacions transferint-hi detalls de la fotografia aèria - Síntesis d'un nombre arbitrari de variacions d’imatges d’arbres a partir d'un conjunt reduït de fotografies - Reconstrucció de models 3D d'arbres a partir d'una única fotografia - Una representació compacta i eficient d'arbres per a navegació en temps real d'escenesPostprint (published version

I/O-Efficient Algorithms for Contour Line Extraction and Planar Graph Blocking

For a polyhedral terrain C, the contour at z-coordinate h, denoted Ch, is defined to be the intersection of the plane z = h with C. In this paper, we study the contour-line extraction problem, where we want to preprocess C into a data structure so that given a query z-coordinate h, we can report Ch quickly. This is a central problem that arises in geographic information systems (GIS), where terrains are often stored as Triangular Irregular Networks (TINS). We present an I/O-optimal algorithm for this problem which stores a terrain C with N vertices using O(N/B) blocks, where B is the size of a disk block, so that for any query h, the contour ch can be computed using o(log, N + I&l/B) I/O operations, where l&l denotes the size of Ch. We also present en improved algorithm for a more general problem of blocking bounded-degree planar graphs such as TINS (i.e., storing them on disk so that any graph traversal algorithm can traverse the graph in an I/O-efficient manner), and apply it to two problms that arise in GIS

A framework for local terrain deformation based on diffusion theory

Terrains have a key role in making outdoor virtual scenes believable and immersive as they form the support for every other natural element in the scene. Although important, terrains are often given limited interactivity in real-time applications. However, in nature, terrains are dynamic and interact with the rest of the environment changing shape on different levels, from tracks left by a person running on a gravel soil (micro-scale), to avalanches on the side of a mountain (macro-scale). The challenge in representing dynamic terrains correctly is that the soil that forms them is vastly heterogeneous and behaves differently depending on its composition. This heterogeneity introduces difficulties at different levels in dynamic terrains simulations, from modelling the large amount of different elements that compose the oil to simulating their dynamic behaviour. This work presents a novel framework to simulate multi-material dynamic terrains by taking into account the soil composition and its heterogeneity. In the proposed framework soil information is obtained from a material description map applied to the terrain mesh. This information is used to compute deformations in the area of interaction using a novel mathematical model based on diffusion theory. The deformations are applied to the terrain mesh in different ways depending on the distance of the area of interaction from the camera and the soil material. Deformations away from the camera are simulated by dynamically displacing normals. While deformations in a neighbourhood of the camera are represented by displacing the terrain mesh, which is locally tessellated to better fit the displacement. For gravel based soils the terrain details are added near the camera by reconstructing the meshes of the small rocks from the texture image, thus simulating both micro and macro-structure of the terrain. The outcome of the framework is a realistic interactive dynamic terrain animation in real-time