Abstract: Digital elevation models can represent many types of geographic data. One of the common digital elevation models is the triangulated irregular network (also called TIN, or polyhedral terrain, or triangulated terrain). We discuss ways to represent a TIN in a data structure, and give some of the basic algorithms that work on TINs. These include retrieving contour lines, computing perspective views, and constructing TINS from other digital elevation data. We also give a recent method to compress and decompress a TIN for storage and transmission purposes.

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TL;DR: The requirements, methodologies, models, and algorithms for the GPSLoc framework, a framework for the proposed quality of service ~QoS! assurance for GPS, are discussed and the experimentation with one of the GPS QoS parameters ~visibility!.

Abstract: While currently numerous existing engineering applications benefit from the global positioning system~GPS!, it is anticipated that operation of many new, emerging applications ~e.g., applications related to ubiquitous mobile computing! will rely on the information provided by this technology. Depending on the application requirement, GPS data may be collected and post-processed or collected and processed in real time. In either case, there are questions about availability, quality, and reliability of GPS data in engineering applications. To date, despite available techniques for realizing, and to some extent improving, a certain level of GPS accuracy, there is no integrated, coherent approach or technique that would provide users with solutions that combine GPS availability, quality, and reliability. To that end, we propose quality of service ~QoS! assurance for GPS. With GPS QoS, users and applications would be provided with the means for predicting GPS solutions in advance meeting the requirements in a timely and cost-effective manner. We have developed a framework for the proposed GPS QoS called GPSLoc. In this paper, we discuss the requirements, methodologies, models, and algorithms for the GPSLoc framework and the experimentation with one of the GPS QoS parameters ~visibility!.

12 citations

Cites background or methods from "Algorithms for Triangulated Terrain..."

...A satellite is visible to the receiver if the line segment that joins them does not intercept any terrain features, such as mountains, or 3D objects, such as buildings ~Kreveld 1997!....

[...]

...This method seamlessly joins both triangle sets, from TIN and objects, and maintains the Delaunay triangulation property ~Kreveld 1997! in TIN....

Abstract: Submitted in fullfilment of the requirements of the Degree of Master of the Built Environment (Survey), Durban University of Technology, Durban, South Africa, 2015.

Abstract: The change from paper maps to GIS, in various kinds of ge- ographical data analysis and applications, has made it easy to use the same spatial data for dierent

TL;DR: This paper proposes an efficient MapReduce algorithm for constructing a geometric spanner in a constant number of rounds, using linear amount of communication.

Abstract: A geometric spanner on a point set is a sparse graph that approximates the Euclidean distances between all pairs of points in the point set. Here, we intend to construct a geometric spanner for a massive point set, using a distributed algorithm on parallel machines. In particular, we use the MapReduce model of computation to construct spanners in several rounds with inter-communications in between. An algorithm in this model is called efficient if it uses a sublinear number of machines and runs in a polylogarithmic number of rounds. In this paper, we propose an efficient MapReduce algorithm for constructing a geometric spanner in a constant number of rounds, using linear amount of communication. The stretch factors of our spanner is \(1+\epsilon \), for any \(\epsilon >0\).

4 citations

Cites background from "Algorithms for Triangulated Terrain..."

...Most efficient spanner construction algorithms are geometric and they find practical applications in areas such as terrain construction [12,21], metric space searching [19], broadcasting in communication networks [11] and solving approximately geometric problems like traveling salesman problem [20]....

TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.

Abstract: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry...The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two."

6,443 citations

"Algorithms for Triangulated Terrain..." refers methods in this paper

...More information on the Delaunay triangulation is in the book of Okabe, Boots, and Sugihara [19] and in textbooks on computational geometry [6, 20, 21]....

Abstract: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Abstract: Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.

TL;DR: The current issues will remain at 32 pages until a more adequate supply of paper is assured, due to a shortage of paper for Bacto-Agar research.

Abstract: The current issues will remain at 32 pages until we are assured of a more adequate supply ofpaper. Bacto-Agar is a purified Agar prepared from domestic material. In the manufacture of Bacto-Agar extraneous matter, pigmented portions, and salts are reduced to a minimum, so that the finished product in the form of fine granules will dissolve rapidly, giving clear solutions. Bacto-Asparagine Bacto-Asparagine is a purified amino acid widely used in synthetic culture media and in the preparation of tuberculin.

3,793 citations

"Algorithms for Triangulated Terrain..." refers methods in this paper

...(Traditionally, four scales of measurement were used: nominal, ordinal, interval, and ratio [27]....

Abstract: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry...The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two."