Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains

Real-time transition texture synthesis for terrains.

Depicting the transitions where differing material textures meet on a terrain surface presents a particularly unique set of challenges in the field of real-time rendering. Natural landscapes are inherently irregular and composed of complex interactions between many different material types of effectively endless detail and variation. Although consumer grade graphics hardware is becoming ever increasingly powerful with each successive generation, terrain texturing remains a trade-off between realism and the computational resources available. Technological constraints aside, there is still the challenge of generating the texture resources to represent terrain surfaces which can often span many hundreds or even thousands of square kilometres. To produce such textures by hand is often impractical when operating on a restricted budget of time and funding. This thesis presents two novel algorithms for generating texture transitions in realtime using automated processes. The first algorithm, Feature-Based Probability Blending (FBPB), automates the task of generating transitions between material textures containing salient features. As such features protrude through the terrain surface FBPB ensures that the topography of these features is maintained at transitions in a realistic manner. The transitions themselves are generated using a probabilistic process that also dynamically adds wear and tear to introduce high frequency detail and irregularity at the transition contour. The second algorithm, Dynamic Patch Transitions (DPT), extends FBPB by applying the probabilistic transition approach to material textures that contain no salient features. By breaking up texture space into a series of layered patches that are either rendered or discarded on a probabilistic basis, the contour of the transition is greatly increased in resolution and irregularity. When used in conjunction with high frequency detail techniques, such as alpha masking, DPT is capable of producing endless, detailed, irregular transitions without the need for artistic input

Complexity analysis of random geometric structures made simpler

Average-case analysis of data-structures or algorithms is commonly used in compu- tational geometry when the, more classical, worst-case analysis is deemed overly pessimistic. Since these analyses are often intricate, the models of random geometric data that can be handled are often simplistic and far from "realistic inputs". We present a new simple scheme for the analy- sis of geometric structures. While this scheme only produces results up to a polylog factor, it is much simpler to apply than the classical techniques and therefore succeeds in analyzing new input distributions related to smoothed complexity analysis. Abstract: We illustrate our method on two classical structures: convex hulls and Delaunay triangulations. Specifically, we give short and elementary proofs of the classical results that n points uniformly distributed in a ball in Rd have a convex hull and a Delaunay triangulation of respective expected complexities Θ~(n^((d+1)/(d-1)) ) and Θ~(n). We then prove that if we start with n points well-spread on a sphere, e.g. an (ε,κ)-sample of that sphere, and perturb that sample by moving each point ran- domly and uniformly within distance at most δ of its initial position, then the expected complexity of the convex hull of the resulting point set is Θ~( sqrt(n)^(1−1/d) δ^(-(d-1/d)/4)). .L'analyse en moyenne de structure de données et d'algorithmes géométriques est fréquemment utilisée en géométrie algorithmique, un domaine ou' l'analyse dans le cas le pire est souvent très pessimiste. La difficulté de ce type d'analyse fait que les modèles probabilistes utilisés restent simples et relativement éloignées de données réalistes. Nous présentons une nouvelle approche pour l'analyse des structures géométriques. Nos résultats sont seulement 'a des facteurs logarithmiques près, mais notre méthode est plus simple que les classiques du domaine et nous réussissons 'a analyser de nouveau type de distribution liée à la smooth analysis. Nous illustrons notre méthode sur deux structures classiques: l'enveloppe convexe et la triangulation de Delaunay. Plus précisément, nous démontrons simplement le fait, classique, que n points uniformément distribués dans une boule de Rd ont une enveloppe convexe et une triangulation de Delaunay dont l'espérance de la taille est respectivement Θ~(n^((d+1)/(d-1)) ) et Θ~(n). Nous démontrons ensuite que si on se donne ensemble de n points bien distribu ́es sur une sphère, par exemple un (ε, κ)-échantillon de la sphère, et qu'on le perturbe ensuite en déplaçant chaque point uniformément d'une distance δ à partir de sa position initiale, alors l'espérance de la taille de l'enveloppe convexe de ces points est Θ~( sqrt(n)^(1−1/d) δ^(-(d-1/d)/4)).

Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains

Analyse de complexité d'enveloppes convexes aléatoires

In this thesis, we give some new results about the average size of convex hulls made of points chosen in a convex body. This size is known when the points are chosen uniformly (and independently) in a convex polytope or in a "smooth" enough convex body. This average size is also known if the points are independently chosen according to a centered Gaussian distribution. In the first part of this thesis, we introduce a technique that will give new results when the points are chosen arbitrarily in a convex body, and then noised by some random perturbations. This kind of analysis, called smoothed analysis, has been initially developed by Spielman and Teng in their study of the simplex algorithm. For an arbitrary set of point in a ball, we obtain a lower and a upper bound for this smoothed complexity, in the case of uniform perturbation in a ball (in arbitrary dimension) and in the case of Gaussian perturbations in dimension 2. The asymptotic behavior of the expected size of the convex hull of uniformly random points in a convex body is polynomial for a "smooth" body and polylogarithmic for a polytope. In the second part, we construct a convex body so that the expected size of the convex hull of points uniformly chosen in that body oscillates between these two behaviors when the number of points increases. In the last part, we present an algorithm to generate efficiently a random convex hull made of points chosen uniformly and independently in a disk. We also compute its average time and space complexity. This algorithm can generate a random convex hull without explicitly generating all the points. It has been implemented in C++ and integrated in the CGAL library.Dans cette thèse, nous donnons de nouveaux résultats sur la taille moyenne d’enveloppes convexes de points choisis dans un convexe. Cette taille est connue lorsque les points sont choisis uniformément (et indépendamment) dans un polytope convexe, ou un convexe suffisamment «lisse» ; ou encore lorsque les points sont choisis indépendamment selon une loi normale centrée. Dans la première partie de cette thèse, nous développons une technique nous permettant de donner de nouveaux résultats lorsque les points sont choisis arbitrairement dans un convexe, puis «bruités» par une perturbation aléatoire. Ce type d’analyse, appelée analyse lissée, a initialement été développée par Spielman et Teng dans leur étude de l’algorithme du simplexe. Pour un ensemble de points arbitraires dans une boule, nous obtenons une borne inférieure et une borne supérieure de cette complexité lissée dans le cas de perturbations uniformes dans une boule en dimension arbitraire, ainsi que dans le cas de perturbations gaussiennes en dimension 2. La taille de l'enveloppe convexe de points choisis uniformément dans un convexe, peut avoir un comportement logarithmique si ce convexe est un polytope ou polynomial s’il est lisse. Nous construisons un convexe produisant un comportement oscillant entre ces deux extrêmes. Dans la dernière partie, nous présentons un algorithme pour engendrer efficacement une enveloppe convexe aléatoire de points choisis uniformément et indépendamment dans un disque sans avoir à engendrer explicitement tous les points. Il a été implémenté en C++ et intégré dans la bibliothèque CGAL

Space-time analytics of human physiology for urban planning.

Recent advancements in mobile sensing and wearable technologies create new opportunities to improve our understanding of how people experience their environment. This understanding can inform urban design decisions. Currently, an important urban design issue is the adaptation of infrastructure to increasing cycle and e-bike use. Using data collected from 12 cyclists on a cycle highway between two municipalities in The Netherlands, we coupled location and wearable emotion data at a high spatiotemporal resolution to model and examine relationships between cyclists' emotional arousal (operationalized as skin conductance responses) and visual stimuli from the environment (operationalized as extent of visible land cover type). We specifically took a within-participants multilevel modeling approach to determine relationships between different types of viewable land cover area and emotional arousal, while controlling for speed, direction, distance to roads, and directional change. Surprisingly, our model suggests ride segments with views of larger natural, recreational, agricultural, and forested areas were more emotionally arousing for participants. Conversely, segments with views of larger developed areas were less arousing. The presented methodological framework, spatial-emotional analyses, and findings from multilevel modeling provide new opportunities for spatial, data-driven approaches to portable sensing and urban planning research. Furthermore, our findings have implications for design of infrastructure to optimize cycling experiences

Development and Field Testing of the FootFall Planning System for the ATHLETE Robots

The FootFall Planning System is a ground-based planning and decision support system designed to facilitate the control of walking activities for the ATHLETE (All-Terrain Hex-Limbed Extra-Terrestrial Explorer) family of robots. ATHLETE was developed at NASA's Jet Propulsion Laboratory (JPL) and is a large six-legged robot designed to serve multiple roles during manned and unmanned missions to the Moon; its roles include transportation, construction and exploration. Over the four years from 2006 through 2010 the FootFall Planning System was developed and adapted to two generations of the ATHLETE robots and tested at two analog field sites (the Human Robotic Systems Project's Integrated Field Test at Moses Lake, Washington, June 2008, and the Desert Research and Technology Studies (D-RATS), held at Black Point Lava Flow in Arizona, September 2010). Having 42 degrees of kinematic freedom, standing to a maximum height of just over 4 meters, and having a payload capacity of 450 kg in Earth gravity, the current version of the ATHLETE robot is a uniquely complex system. A central challenge to this work was the compliance of the high-DOF (Degree Of Freedom) robot, especially the compliance of the wheels, which affected many aspects of statically-stable walking. This paper will review the history of the development of the FootFall system, sharing design decisions, field test experiences, and the lessons learned concerning compliance and self-awareness

The interpretation and characterisation of lineaments identified from Landsat TM imagery of SW England

Two Landsat TM scenes of SW England and a sub-scene of North Cornwall have been analysed visually in order to examine the effect of resolution on lineament interpretation. Images were viewed at several different scales as a result of varying image resolution whilst maintaining a fixed screen pixel size. Lineament analysis at each scale utilised GIS techniques and involved several stages: initial lineament identification and digitisation; removal of lineaments related to anthropogenic features to produce cleansed lineament maps; compilation of lineament attributes using ARC/INFO; cluster analysis for identification of lineament directional families; and line sampling of lineament maps in order to determine spacing. SW England lies within the temperate zone of Europe and the extensive agricultural cover and infrastructure conceal the underlying geology. The consequences of this for lineament analysis were examined using sub-images of North Cornwall. Here anthropogenic features are visible at all resolutions between 30m and 120m pixel sizes but lie outside the observation threshold at 150m. Having confidence that lineaments at this resolution are of non-anthropogenic origin optimises lineament identification since the image may be viewed in greater detail. On this basis, lineament analysis of SW England was performed using image resolutions of 150m. Valuable geological information below the observation threshold in 150m resolution images is likely, however, to be contained in the lineament maps produced from higher resolution images. For images analysed at higher resolutions, therefore, knowledge-based rules were established in order to cleanse the lineament populations. Compiled lineament maps were 'ground truthed' (primarily involving comparison with published geological maps but included phases of field mapping) in order to characterise their geological affinities. The major lineament trends were correlated to lithotectonic boundaries, and cross-cutting fractures sets. Major lineament trends produced distinct frequency/orientation maxima. Multiple minor geological structures, however, produced semi-overlapping groups. A clustering technique was devised to resolve overlapping groups into lineament directional families. The newly defined lineament directional families were further analysed in two ways: (i) Analysis of the spatial density of the length and frequency of lineaments indicates that individual and multiple lineament directional families vary spatially and are compartmentalised into local tectonic domains, often bounded by major lineaments. Hence, such density maps provide useful additional information about the structural framework of SW England. (ii) Lineament spacing and length of the lineament directional families were analysed for the effect of scale and geological causes on their frequency/size distributions. Spacing of fracture lineaments were found to be power-law, whereas lengths showed power-law and non-power-law distributions. Furthermore the type of frequency/size distribution for a lineament directional family can change with increasing resolution