Delaunay-Triangulierungen in zwei und drei Dimensionen

Name: Delaunay-Triangulierungen in zwei und drei Dimensionen
Brand: Atlantic Books
SKU: 9783838666464
Price: 7366.0 INR
Availability: InStock

by Jörg Krämer

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ISBN13: 9783838666464
Binding: Paperback
Subject: N/A
Publisher: Diplom.de
Publisher Imprint: Diplom.de
Publication Date: April 8, 2003
Pages: 104
Original Price: GBP 66.5
Language: German
Edition: N/A
Item Weight: 146 grams
BISAC Subject(s): General

About The Book

Inhaltsangabe: Einleitung: Das Voronoi-Diagramm und sein Dual, die Delaunay-Triangulierung, haben in vielen Gebieten der Naturwissenschaft und der Technik Anwendung gefunden, wie z.B. in der Kristallographie, in der Geographie und in der Metallurgie. Nachdem am Anfang dieses Jahrhunderts der russische Mathematiker Georges Voronoi Veröffentlichungen über die nach ihm benannte Struktur schrieb, verwendete in den 30er Jahren der Kristallograph Delaunay diese Struktur für die Simulation von Kristallwachstum sowie zur Beschreibung und Untersuchung von Kristallstrukturen. Weitere geographische Anwendungen finden sich in der Kartographie und in der Stadtplanung. Heute sind das Voronoi-Diagramm und die Delaunay-Triangulierung grundlegende Strukturen in der algorithmischen Geometrie (Computational Geometry). Eine naheliegende geometrische Anwendung des Voronoi-Diagramms besteht im Post-Office-Problem d.h. im Beantworten von Anfragen der Form, welcher Punkt einer Punktmenge in der Ebene oder im Raum zu einem vorgegebenen Punkt der nächste ist. Bei vielen Anfragen lohnt es sich, das Voronoi-Diagramm für die Bestimmung der nächsten 'Postämter' zu benutzen. Die geometrische Struktur des Voronoi-Diagramms kann schnell konstruiert werden (O(n log n) Zeit und enthält alle wichtigen Informationen über Nachbarschaften (O(n) Speicherplatzbedarf), aus denen sich in linearer Zeit wichtige Probleme der algorithmischen Geometrie berechnen lassen. Zu diesen zählen u.a. der euklidische minimale Spannbaum (EMST), der grö te leere Kreis und die zwei nächsten Nachbarpunkte. Eine Näherungslösung für ein NP-vollständiges, graphentheoretisches Problem, das Problems des Handlungsreisenden, kann mit Hilfe der zweidimensionalen Delaunay-Triangulierung bzw. des EMST gewonnen werden. Das Problem des Handlungsreisenden besteht aus dem Bestimmen einer optimalen Rundtour durch n vorgegebene Punkte (Städte), ohne einen Punkt zweimal zu besuchen. In der Computer-Graphik eignet sich die Delaunay-Triangul

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