'Sweep line' diaporamas de présentation

Lecture 7: Voronoi Diagrams

Lecture 7: Voronoi Diagrams. Presented by Allen Miu 6.838 Computational Geometry September 27, 2001. p i : site points. q : free point. e : Voronoi edge. v : Voronoi vertex. v. q. e. p i. Post Office: What is the area of service?. Definition of Voronoi Diagram.

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Voronoi Diagram

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Voronoi Diagrams

Voronoi Diagrams. e : Voronoi edge. v : Voronoi vertex. v. e. p i. Post Office: What is the area of service?. p i : site points. Definition of Voronoi Diagram. Let P be a set of n distinct points (sites) in the plane.

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COMPUTATIONAL GEOMETRY -- VORONOI DIAGRAM

COMPUTATIONAL GEOMETRY -- VORONOI DIAGRAM. Sophie Che. THE LARGEST EMPTY CIRCLE PROBLEM. An application of Voronoi Diagram. S : site points. v : Voronoi vertex. v. Largest Empty Circle. e : Voronoi edge. e. Definitions & Basic Properties. Of Voronoi Diagram. p i. Definition.

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15-211 Fundamental Data Structures and Algorithms

15-211 Fundamental Data Structures and Algorithms. Klaus Sutner April 22, 2004. Computational Geometry. Announcements. HW7 the clock is ticking ... Quiz 3: Today, after class Final Exam on Tuesday May 4, 5:30 pm review session April 29. The Basics. Computational Geometry.

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SICS Seminar, May 29 2001

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Coloured Petri Nets Modelling and Validation of Concurrent Systems

1 {1}. 2 {2}. 3 {3,5}. 4 {4,6}. 9 {9,11}. 7 {7}. 8 {8,10}. Chapter 8: Advanced State Space Methods. Coloured Petri Nets Modelling and Validation of Concurrent Systems. Kurt Jensen & Lars Michael Kristensen {kjensen,lmkristensen} @cs.au.dk. State space methods.

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The Lower Envelope: The Pointwise Minimum of a Set of Functions

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The Lower Envelope The Pointwise Minimum of a Set of Functions

The Lower Envelope The Pointwise Minimum of a Set of Functions. Definition of the Lower Envelope (untere Kontur) of a set of functions: Given n real-valued functions, all defined on a common interval I , then the minimum is : f(x) = min 1 ?i?n f i (x)

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CS 6463: AT Computational Geometry Fall 2010

CS 6463: AT Computational Geometry Fall 2010. Triangulations and Guarding Art Galleries Carola Wenk. Guarding an Art Gallery. Region enclosed by simple polygonal chain that does not self-intersect.

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CMPS 3120: Computational Geometry

CMPS 3120: Computational Geometry. Triangulations and Guarding Art Galleries Carola Wenk. Guarding an Art Gallery. Region enclosed by simple polygonal chain that does not self-intersect.

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Two Segments Intersect?

x < x ? x > x ? y < y ? y > y. if and only if. 4 1 3 2 4 1 3 2. ( x , y ). 4 4. ( x , y ). 2 2. M. ( x , y ). 3 3. L. ( x , y ). 1 1. Two Segments Intersect?.

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CS 6463: AT Computational Geometry Fall 2006

CS 6463: AT Computational Geometry Fall 2006. Plane Sweep Algorithms and Segment Intersection Carola Wenk. Closest Pair. Problem: Given P ? R 2 , | P |= n , find the distance of the closest pair in P. Plane Sweep: An Algorithm Design Technique.

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Computational Geometry

Computational Geometry. Piyush Kumar (Lecture 3: Convexity and Convex hulls). Welcome to CIS5930. p. q. p. convex. non-convex. q. Convexity. A set S is convex if for any pair of points p,q ? S we have pq ? S. Convex Hulls : Equivalent definitions.

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Computational Geometry

Computational Geometry. Piyush Kumar (Lecture 3: Convexity and Convex hulls). Welcome to CIS5930. p. q. p. convex. non-convex. q. Convexity. A set S is convex if for any pair of points p,q ? S we have pq ? S. Convex Hulls : Equivalent definitions.

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Last Time: Convex Hulls

Last Time: Convex Hulls. Today: Plane Sweep Algorithms, Segment Intersection, + (Element Uniqueness, and a good use for complicated data structures from CSE241). Some slides in this lecture come from Carola Wenk, Univ. Texas, San Antonio. From UNC.

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Line Segment Intersection

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Line Segment Intersection

Line Segment Intersection. M otivation: Computing the overlay of several maps The Sweep -Line-P aradigm: A visibility problem L ine S egment Intersection The D oubly Connected E dge L ist Computing boolean operations on p olygon s. Maps. river. road. overlaid maps.

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