Searching edges in the overlap of two plane graphs

Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains one of which is convex in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n) time and O(n+m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n axis-aligned rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure

Spectral Variability among Rocks in Visible and Near Infrared Multispectral Pancam Data Collected at Gusev Crater: Examinations using Spectral Mixture Analysis and Related Techniques

Visible and Near Infrared (VNIR) multispectral observations of rocks made by the Mars Exploration Rover Spirit s Panoramic camera (Pancam) have been analysed using a spectral mixture analysis (SMA) methodology. Scenes have been examined from the Gusev crater plains into the Columbia Hills. Most scenes on the plains and in the Columbia Hills could be modeled as three endmember mixtures of a bright material, rock, and shade. Scenes of rocks disturbed by the rover s Rock Abrasion Tool (RAT) required additional endmembers. In the Columbia Hills there were a number of scenes in which additional rock endmembers were required. The SMA methodology identified relatively dust-free areas on undisturbed rock surfaces, as well as spectrally unique areas on RAT abraded rocks. Spectral parameters from these areas were examined and six spectral classes were identified. These classes are named after a type rock or area and are: Adirondack, Lower West Spur, Clovis, Wishstone, Peace, and Watchtower. These classes are discriminable based, primarily, on near-infrared (NIR) spectral parameters. Clovis and Watchtower class rocks appear more oxidized than Wishstone class rocks and Adirondack basalts based on their having higher 535 nm band depths. Comparison of the spectral parameters of these Gusev crater rocks to parameters of glass-dominated basaltic tuffs indicates correspondence between measurements of Clovis and Watchtower classes, but divergence for the Wishstone class rocks which appear to have a higher fraction of crystalline ferrous iron bearing phases. Despite a high sulfur content, the rock Peace has NIR properties resembling plains basalts

The protection project of Hanyuan Hall and Linde Hall of the Daming Palace

AbstractThis paper expounds the consideration to the design of protection and exhibition of Hanyuan Hall and Linde Hall of the Daming Palace. Based on in-depth study on their existing conditions after archeological excavation, and in combination with comprehensive considerations in terms of the protection of the main body of sites, the restoration research of existing bases and superstructures, the requirement of site open exhibition, etc., it proposes the design to restore the rammed earth bases by surrounding them with bricks and stones or rammed earth. Besides the protection and exhibition of the site of Hanyuan Hall bases, it also integrates the features of landform there to design the protection and exhibition of brick and tile kiln of Tang Dynasty within the relic area. Under the condition at that time, a semi-underground small exhibition center is designed by taking advantage of the height difference of base side slopes, satisfying the requirement of exhibition, and meanwhile preserving the overall landscape of the site. The integration of the design of protection project with archeology as well as the science and technology of heritage preservation is a brand-new probe into site protection design

Terrain visibility optimization problems

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 2001.Thesis (Master's) -- Bilkent University, 2001.Includes bibliographical references leaves 92-96The Art Gallery Problem is the problem of determining the number of observers necessary to cover an art gallery such that every point is seen by at least one observer. This problem is well known and has a linear time solution for the 2 dimensional case, but little is known about 3-D case. In this thesis, the dominance relationship between vertex guards and point guards is searched and found that a convex polyhedron can be constructed such that it can be covered by some number of point guards which is one third of the number of the vertex guards needed. A new algorithm which tests the visibility of two vertices is constructed for the discrete case. How to compute the visible region of a vertex is shown for the continuous case. Finally, several potential applications of geometric terrain visibility in geographic information systems and coverage problems related with visibility are presented.Düger, İbrahimM.S

Chasing Puppies: Mobile Beacon Routing on Closed Curves

We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others' work on beacon-based routing. Consider a human and a puppy on a simple closed curve in the plane. The human can walk along the curve at bounded speed and change direction as desired. The puppy runs with unbounded speed along the curve as long as the Euclidean straight-line distance to the human is decreasing, so that it is always at a point on the curve where the distance is locally minimal. Assuming that the curve is smooth (with some mild genericity constraints) or a simple polygon, we prove that the human can always catch the puppy in finite time.Comment: Full version of a SOCG 2021 paper, 28 pages, 27 figure

Use of 3D models as a didactic resource in archaeology. A case study analysis

The generation of 3D models through Terrestrial Laser Scanning has proved to be valuable tools for the study, documentation and recreation of archaeological remains. In this context, it is described how to generate a physical model to provide not only to researchers, but also as teaching material for teachers for university students, facilitating their access and study. As a practical case, this article describes the acquisition, processing and management of archaeological data in the archaeological site of Cástulo, Jaén, in South Spain. We expound how to get the 3D-printed model of the Muslim tower, showing how it is possible to generate a scale and very reliable reproduction of the structure, being also an useful and tangible material in the teaching of cultural heritage

An Optimal Algorithm to Compute the Inverse Beacon Attraction Region

The beacon model is a recent paradigm for guiding the trajectory of messages or small robotic agents in complex environments. A beacon is a fixed point with an attraction pull that can move points within a given polygon. Points move greedily towards a beacon: if unobstructed, they move along a straight line to the beacon, and otherwise they slide on the edges of the polygon. The Euclidean distance from a moving point to a beacon is monotonically decreasing. A given beacon attracts a point if the point eventually reaches the beacon. The problem of attracting all points within a polygon with a set of beacons can be viewed as a variation of the art gallery problem. Unlike most variations, the beacon attraction has the intriguing property of being asymmetric, leading to separate definitions of attraction region and inverse attraction region. The attraction region of a beacon is the set of points that it attracts. It is connected and can be computed in linear time for simple polygons. By contrast, it is known that the inverse attraction region of a point - the set of beacon positions that attract it - could have Omega(n) disjoint connected components. In this paper, we prove that, in spite of this, the total complexity of the inverse attraction region of a point in a simple polygon is linear, and present a O(n log n) time algorithm to construct it. This improves upon the best previous algorithm which required O(n^3) time and O(n^2) space. Furthermore we prove a matching Omega(n log n) lower bound for this task in the algebraic computation tree model of computation, even if the polygon is monotone

Evaluating the Effectiveness of Tree Locations and Arrangements for Improving Urban Thermal Environment

abstract: Trees serve as a natural umbrella to mitigate insolation absorbed by features of the urban environment, especially building structures and pavements. For a desert community, trees are a particularly valuable asset because they contribute to energy conservation efforts, improve home values, allow for cost savings, and promote enhanced health and well-being. The main obstacle in creating a sustainable urban community in a desert city with trees is the scarceness and cost of irrigation water. Thus, strategically located and arranged desert trees with the fewest tree numbers possible potentially translate into significant energy, water and long-term cost savings as well as conservation, economic, and health benefits. The objective of this dissertation is to achieve this research goal with integrated methods from both theoretical and empirical perspectives. This dissertation includes three main parts. The first part proposes a spatial optimization method to optimize the tree locations with the objective to maximize shade coverage on building facades and open structures and minimize shade coverage on building rooftops in a 3-dimensional environment. Second, an outdoor urban physical scale model with field measurement is presented to understand the cooling and locational benefits of tree shade. The third part implements a microclimate numerical simulation model to analyze how the specific tree locations and arrangements influence outdoor microclimates and improve human thermal comfort. These three parts of the dissertation attempt to fill the research gap of how to strategically locate trees at the building to neighborhood scale, and quantifying the impact of such arrangements. Results highlight the significance of arranging residential shade trees across different geographical scales. In both the building and neighborhood scales, research results recommend that trees should be arranged in the central part of the building south front yard. More cooling benefits are provided to the building structures and outdoor microclimates with a cluster tree arrangement without canopy overlap; however, if residents are interested in creating a better outdoor thermal environment, open space between trees is needed to enhance the wind environment for better human thermal comfort. Considering the rapid urbanization process, limited water resources supply, and the severe heat stress in the urban areas, judicious design and planning of trees is of increasing importance for improving the life quality and sustaining the urban environment.Dissertation/ThesisDoctoral Dissertation Geography 201