Computational Geometry

Author: Ketan Mulmuley
Publisher: Prentice Hall
ISBN: STANFORD:36105003459646
Release Date: 1994
Genre: Computers

This introduction to computational geometry is designed for beginners. It emphasizes simple randomized methods, developing basic principles with the help of planar applications, beginning with deterministic algorithms and shifting to randomized algorithms as the problems become more complex. It also explores higher dimensional advanced applications and provides exercises.

Computational Geometry in C

Author: Joseph O'Rourke
Publisher: Cambridge University Press
ISBN: 0521649765
Release Date: 1998-10-13
Genre: Computers

This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The code in this new edition is significantly improved from the first edition, and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.

Handbook of Computational Geometry

Author: J.R. Sack
Publisher: Elsevier
ISBN: 0080529682
Release Date: 1999-12-13
Genre: Mathematics

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Computational Geometry

Author: de Berg (M.T.)
Publisher: Springer Science & Business Media
ISBN: 3540656200
Release Date: 2000
Genre: Computers

Algorithms are the focus of this introduction to computational geometry, which presents techniques applied to robotics, graphics, CAD/CAM, and geographic information systems.

Computer Graphics and Geometric Modelling

Author: Max K. Agoston
Publisher: Springer Science & Business Media
ISBN: 9781846281082
Release Date: 2005-12-06
Genre: Computers

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Implementation and Algorithms, covers the computer graphics part of the field of geometric modelling and includes all the standard computer graphics topics. The first part deals with basic concepts and algorithms and the main steps involved in displaying photorealistic images on a computer. The second part covers curves and surfaces and a number of more advanced geometric modelling topics including intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, blending etc. The third part touches on some aspects of computational geometry and a few special topics such as interval analysis and finite element methods. The volume includes two companion programs.

New Trends in Discrete and Computational Geometry

Author: Janos Pach
Publisher: Springer Science & Business Media
ISBN: 9783642580437
Release Date: 2012-12-06
Genre: Mathematics

Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are well-known experts in these fields. They give concise and self-contained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilon-nets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results.

Algorithmen Eine Einf hrung

Author: Thomas H. Cormen
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110522013
Release Date: 2013-01-01
Genre: Computers

Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.

Topics in Combinatorial and Computational Geometry

Author: Edgar Arturo Ramos
Publisher:
ISBN: UIUC:30112121897646
Release Date: 1995
Genre: Combinatorial analysis

This thesis consists of two parts dealing with combinatorial and computational problems in geometry, respectively. In the first part three independent problems are considered: (1) We determine an upper bound $lfloor 11n/6rfloor$ + 1 for the number of extreme triples of n points in the plane, almost matching a known lower bound $lfloor 11n/6rfloor$; (2) we determine some bounds for the smallest dimension $d = Delta(j, k)$ such that for any j mass distributions in $IRsp{d}$, there are k hyperplanes so that each orthant contains a fraction 1/2$sp{k}$ of each of the masses; it is easily shown that $j(2sp{k}-1)/k le Delta(j, k)le j2sp{k-1}$; we believe the lower bound is tight, but can only prove it in a few cases (as a tool we prove a Borsuk-Ulam theorem on a product of balls, which is of independent interest); (3) for a collection B of pseudo-disks in the plane, we show the existence of a two-dimensional abstract simplicial complex, $chi subseteq 2sp{B}$, which has some nice topological properties, such that the inclusion-exclusion relation $mu(cup B) = Sigma sb{sigmain 2sp{B} - {phi}}( -1)sp{rm card sigma -1}mu(capsigma)$ holds when $chi$ is substituted for 2$sp{B}$. In the second part, using geometric sampling techniques, we give algorithms for three similar problems: (4) Computing the intersection of halfspaces in $IRsp3$; (5) computing the intersection of balls of equal radius in $IRsp3$; and (6) computing the Voronoi diagram of line segments in $IRsp2$; in each case we obtain a deterministic parallel algorithm for the EREW PRAM model that runs in time $O({rm log}sp2 n)$ and uses work $O(n {rm log} n)$ for a problem of size n (for ball intersection this is also the first optimal deterministic and sequential algorithm, using the Dobkin-Kirkpatrick decomposition, we can only achieve time $O(n {rm log}sp2 n$)). Using the parallel algorithm for ball intersection, one obtains (7) a sequential deterministic algorithm for computing the diameter of a point set in $IRsp3$ that runs in time $O(n {rm log}sp3 n)$. Using also geometric sampling techniques, (8) we describe an algorithm for computing the arrangement of n segments in the plane in time $O(logsp2 n)$ and using work $O(n log n + k)$ where k is the number of pairwise intersections, also in the EREW PRAM model (sequentially this results in an algorithm that outputs all the intersections in optimal time using O(n) space); and (9) assuming that certain sampling result can be derandomized in polynomial time, we describe a sequential algorithm for computing one face in an arrangement of segments that runs in time $O(nalphasp2(n) log n)$ where $alpha(n)$ is a very slowly growing function.

Parallel and Distributed Computing Handbook

Author: Albert Y. Zomaya
Publisher: McGraw Hill Professional
ISBN: 0070730202
Release Date: 1996
Genre: Computers

With over 1,000 pages and a wealth of illustrations and data tables, this handbook offers readers the first information source with the scope to encompass the parallel and distributed computing revolution. Written by an international team of experts, the book summarizes the current state of the art, interprets the most promising trends, and spotlights commercial applications.

Automata Languages and Programming

Author: Michele Bugliesi
Publisher: Springer
ISBN: 9783540359050
Release Date: 2006-06-29
Genre: Computers

The two-volume set LNCS 4051 and LNCS 4052 constitutes the refereed proceedings of the 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006, held in Venice, Italy, July 2006. In all, these volumes present more 100 papers and lectures. Volume I (4051) presents 61 revised full papers together with 1 invited lecture, focusing on algorithms, automata, complexity and games, on topics including graph theory, quantum computing, and more.