33 research outputs found

    Separating bichromatic point sets in the plane by restricted orientation convex hulls

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    The version of record is available online at: http://dx.doi.org/10.1007/s10898-022-01238-9We explore the separability of point sets in the plane by a restricted-orientation convex hull, which is an orientation-dependent, possibly disconnected, and non-convex enclosing shape that generalizes the convex hull. Let R and B be two disjoint sets of red and blue points in the plane, and O be a set of k=2 lines passing through the origin. We study the problem of computing the set of orientations of the lines of O for which the O-convex hull of R contains no points of B. For k=2 orthogonal lines we have the rectilinear convex hull. In optimal O(nlogn) time and O(n) space, n=|R|+|B|, we compute the set of rotation angles such that, after simultaneously rotating the lines of O around the origin in the same direction, the rectilinear convex hull of R contains no points of B. We generalize this result to the case where O is formed by k=2 lines with arbitrary orientations. In the counter-clockwise circular order of the lines of O, let ai be the angle required to clockwise rotate the ith line so it coincides with its successor. We solve the problem in this case in O(1/T·NlogN) time and O(1/T·N) space, where T=min{a1,…,ak} and N=max{k,|R|+|B|}. We finally consider the case in which O is formed by k=2 lines, one of the lines is fixed, and the second line rotates by an angle that goes from 0 to p. We show that this last case can also be solved in optimal O(nlogn) time and O(n) space, where n=|R|+|B|.Carlos Alegría: Research supported by MIUR Proj. “AHeAD” no 20174LF3T8. David Orden: Research supported by Project PID2019-104129GB-I00 / AEI / 10.13039/501100011033 of the Spanish Ministry of Science and Innovation. Carlos Seara: Research supported by Project PID2019-104129GB-I00 / AEI / 10.13039/501100011033 of the Spanish Ministry of Science and Innovation. Jorge Urrutia: Research supported in part by SEP-CONACYThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie Grant Agreement No 734922.Peer ReviewedPostprint (published version

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    The Dispersive Art Gallery Problem

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    We introduce a new variant of the art gallery problem that comes from safety issues. In this variant we are not interested in guard sets of smallest cardinality, but in guard sets with largest possible distances between these guards. To the best of our knowledge, this variant has not been considered before. We call it the Dispersive Art Gallery Problem. In particular, in the dispersive art gallery problem we are given a polygon ? and a real number ?, and want to decide whether ? has a guard set such that every pair of guards in this set is at least a distance of ? apart. In this paper, we study the vertex guard variant of this problem for the class of polyominoes. We consider rectangular visibility and distances as geodesics in the L?-metric. Our results are as follows. We give a (simple) thin polyomino such that every guard set has minimum pairwise distances of at most 3. On the positive side, we describe an algorithm that computes guard sets for simple polyominoes that match this upper bound, i.e., the algorithm constructs worst-case optimal solutions. We also study the computational complexity of computing guard sets that maximize the smallest distance between all pairs of guards within the guard sets. We prove that deciding whether there exists a guard set realizing a minimum pairwise distance for all pairs of guards of at least 5 in a given polyomino is NP-complete. We were also able to find an optimal dynamic programming approach that computes a guard set that maximizes the minimum pairwise distance between guards in tree-shaped polyominoes, i.e., computes optimal solutions; due to space constraints, details can be found in the full version of our paper [Christian Rieck and Christian Scheffer, 2022]. Because the shapes constructed in the NP-hardness reduction are thin as well (but have holes), this result completes the case for thin polyominoes

    Factors Affecting Bird-Window Collisions in a Small Urban Area: Stillwater, Oklahoma

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    This dissertation consists of four concurrent studies of bird-building collisions, which primarily occur at glass surfaces (e.g., windows) and are a major source of direct anthropogenic mortality for birds globally. Although research, public, and policy interest concerning bird-window collisions are increasing, this issue has primarily been studied in larger metropolitan areas, particularly in the eastern third of North America. It is unknown if bird-window collisions in smaller urban areas in other regions (e.g., the U.S. Great Plains) are influenced similarly by the same factors. Chapter 1 examined some biases that cause researchers to underestimate the number of fatal bird-window collisions. Because of high carcass persistence and observer detection rates, we estimated that across seasons we detected about 88% of fatal collision victims. Also, we provided formal definitions to distinguish scavenging and removal events to promote consistent terminology use. Chapter 2 investigated the temporal patterns of fatal and non-fatal window collisions. We found that more collisions occurred at night or early morning than late morning or afternoon. In addition, weekly and monthly variation indicated more collisions during migratory periods, especially spring, and greater mortality of non-migrating individuals than expected. Chapter 3 assessed the fine-scale spatial patterns of window collision mortality. The inter-seasonal and inter-species variation that we found across building facades suggested that targeted mitigation efforts may be applied at small spatial scales but need to identify conservation goals for maximum effect. Chapter 4 considered the effects of artificial lighting at night on building collision frequency. We did not find a strong spatial relationship between the lightscape (variation in nocturnal light intensity) and the collision mortality intensity, but there were several factors that may have confounded our results. Overall, our findings both corroborated and disputed results from previous studies, indicating that although the general phenomenon of bird-window collisions is similar across various contexts, the details of urban development, geographic region, and building facade structure may strongly influence local outcomes. These findings should help inform conservation efforts to reduce bird-window mortality and suggest that further research should be conducted in under-studied localities

    Design and Experimental Evaluation of a Hybrid Wheeled-Leg Exploration Rover in the Context of Multi-Robot Systems

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    With this dissertation, the electromechanic design, implementation, locomotion control, and experimental evaluation of a novel type of hybrid wheeled-leg exploration rover are presented. The actively articulated suspension system of the rover is the basis for advanced locomotive capabilities of a mobile exploration robot. The developed locomotion control system abstracts the complex kinematics of the suspension system and provides platform control inputs usable by autonomous behaviors or human remote control. Design and control of the suspension system as well as experimentation with the resulting rover are in the focus of this thesis. The rover is part of a heterogeneous modular multi-robot exploration system with an aspired sample return mission to the lunar south pole or currently hard-to-access regions on Mars. The multi-robot system pursues a modular and reconfigurable design methodology. It combines heterogeneous robots with different locomotion capabilities for enhanced overall performance. Consequently, the design of the multi-robot system is presented as the frame of the rover developments. The requirements for the rover design originating from the deployment in a modular multi-robot system are accentuated and summarized in this thesis

    Genauigkeitsbewertung einer kostengĂĽnstigen terrestrischen und UAV-basierten Photogrammetrie fĂĽr Geomatikanwendungen im Kontext von architektonischem und kulturellem Erbe

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    In the last decades, the field of Geomatics applied to architectural and cultural heritage has benefited from some major advances. Upon their introduction, laser scanners have revolutionized the surveying world, gradually establishing as a basic tool, at first for terrestrial and later for airborne surveys. At about the same time, photogrammetry also experienced its own evolution, culminating with Structure from Motion (SfM) and MVS (Multi-View Stereo) algorithms. These algorithms generate dense 3D colour point clouds that however may not always be considered reliable. In fact, matching algorithms can be very sensitive to data collection, lighting and texture, and accuracy control is difficult. The high automation levels attainable also require caution because, while allowing for quicker modelling, control and perception of the steps to follow become looser. In terrestrial surveys, accessibility can still present challenging issues, where both Terrestrial Laser Scanning (TLS) and terrestrial photogrammetry are not viable options. Many situations do not allow acquisition of both images and TLS data, necessary to generate 3D models. A solution of this problem is a new technique for the acquisition of photogrammetric data, based on the use of Unmanned Aerial Vehicles (UAVs). Within the broader field of study of Terrestrial and UAV-based photogrammetry in architectural and cultural heritage contexts, this thesis focuses on four aspects in order to provide an operating methodology for surveys: 1-Influence of number and position of Ground Control Points (GCPs) and tie points in SfM and MVS techniques; 2-Best methods for survey assessment; 3-TLS/SfM-MVS integration; 4-Original applications in architecture surveys. Besides, introduction of UAV-based applications has been investigated in some cases. The thesis provides guidelines for low-cost terrestrial and UAV-based photogrammetry aimed at any figure involved in surveying in architectural and cultural heritage contexts. These guidelines include methodologies for accuracy checks and data integration as well as a workflow enabling survey optimization and devising original applications. Besides, integration of the research aspects has allowed to provide accuracy checks of the acquired data and integration of data from different sources, as well as accuracy controls of both each single-technique model and models obtained through technique integration.In den letzten Jahrzehnten sind im Bereich der Geomatik bei architektonischem und kulturellem Erbe große Fortschritte zu verzeichnen. Nach Einführung des Laserscanners, hat dieser die Welt revolutioniert und sich als Instrument etabliert, zunächst für Untersuchungen am Boden und später auch aus der Luft. Im gleichen Zeitraum erfuhr die Photogrammetrie ebenfalls eine Evolution durch die Algorithmen des Structure from Motion (SfM) und Multi-View Stereo Verfahrens (MVS). Diese Algorithmen erzeugen dichte 3D-Punktwolken, die allerdings nicht immer als zuverlässig gelten. Tatsächlich können Matching-Algorithmen sensibel auf Datenerfassung, Lichtverhältnisse und Oberflächenstruktur reagieren, was die Genauigkeitskontrolle erschwert. Die höchstmöglichen Automatisierungsstufen fordern ebenfalls Vorsicht, denn bei schnellerem Modelling werden Kontrolle und Erfassung auch ungenauer. Bei terrestrischen Vermessungen kann die Zugänglichkeit eine Herausforderung darstellen, wo sowohl Laserscanning (TLS) als auch Photogrammetrie nicht praktikabel sind. Viele Situationen lassen keine gleichzeitige Erfassung von Bildern und TLS-Daten zu, die für die Erzeugung von 3D-Modellen erforderlich ist. Eine Lösung bietet eine neue Technik zur Erfassung von photogrammetrischen Daten, die auf der Verwendung von unbemannten Luftfahrzeugen (UAVs) basiert. Auf dem Forschungsgebiet der terrestrischen und UAV-basierten Photogrammetrie im Kontext von architektonischem und kulturellem Erbe fokussiert diese Arbeit vier Aspekte für eine optimale Untersuchungsmethodik: 1. Einfluss der Anzahl und Positionen der Bodenkontrollpunkte (GCPs) und Passpunkte im SfM und MVS; 2. die besten Untersuchungsmethoden; 3. Integration von TLS/SfM und MVS; 4. Originalanwendungen bei Architekturerhebungen. Zudem wurde auch die Einführung von UAV-basierten Anwendungen untersucht. Diese Dissertation bietet Richtlinien für eine kostengünstige terrestrische und UAV-basierte Photogrammetrie, die sich auf jede Untersuchung im Bereich architektonischen und kulturellen Erbes bezieht. Dazu gehören Methoden zur Genauigkeitsprüfung und Datenintegration sowie ein Workflow, der eine Erhebungsoptimierung und die Anpassung von Originalanwendungen ermöglicht. Darüber hinaus ermöglicht die Integration der Forschungsaspekte die Genauigkeitsprüfung der erfassten Daten und die Einbeziehung von Daten verschiedener Quellen, und damit auch die Genauigkeitskontrolle des Einzeltechnikmodells und von Modellen der Technikintegration
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