computational geometry geometriske algoritmer
play

Computational Geometry (Geometriske Algoritmer) the pizza meeting - PowerPoint PPT Presentation

Nov 02, 2022 •28 likes •278 views

Computational Geometry (Geometriske Algoritmer) the pizza meeting Kim Skak Larsen IMADA University of Southern Denmark kslarsen@imada.sdu.dk May 15, 2018 Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 1 / 25

  1. Computational Geometry (Geometriske Algoritmer) “the pizza meeting” Kim Skak Larsen IMADA University of Southern Denmark kslarsen@imada.sdu.dk May 15, 2018 Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 1 / 25

  2. Overview Why an Independent Subject? 1 Example Topics 2 Applications 3 Formal Details 4 Disclaimer 5 Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 2 / 25

  3. One-Dimensional Data Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 3 / 25

  4. One-Dimensional Data Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 4 / 25

  5. Two-Dimensional Data Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 5 / 25

  6. Two-Dimensional Data Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 6 / 25

  7. Two-Dimensional Data Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 7 / 25

  8. Two-Dimensional Data Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 8 / 25

  9. Convex Hull Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 9 / 25

  10. Convex Hull Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 10 / 25

  11. Dynamic Convex Hull Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 11 / 25

  12. Dynamic Convex Hull Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 12 / 25

  13. Dynamic Convex Hull Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 13 / 25

  14. Triangulations Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 14 / 25

  15. Nice Triangulations Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 15 / 25

  16. Range Searching Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 16 / 25

  17. Range Searching Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 17 / 25

  18. Range Searching Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 18 / 25

  19. Range Searching Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 19 / 25

  20. Example Applications Geometric algorithms are important parts of: Computer Graphics Geographic Information Systems (GIS) Robot Motion Planning Design: CAD, VLSI, . . . Image Analysis Computer Games Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 20 / 25

  21. Course Content Algorithms and Data Structures for Geometric Objects Triangulations and Voronoi Diagrams Interval and Point Searches Convex Hulls Range Searching Motion Planning etc. Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 21 / 25

  22. Course Content Introduction to (continuation of) important general techniques: Line Sweeping Fractional Cascading Randomization Amortization Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 22 / 25

  23. Prerequisites Analysis of Algorithms and Data Structures (DM507 + DM553, or equivalent) Search Trees Divide and Conquer Asymptotic Notation Time and Space Analysis Correctness Analysis Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 23 / 25

  24. Format 10 ECTS over one semester Obligatory assignment in parts (some individual) Oral exam 2h lectures, 2h discussion section per week Good book: Computational Geometry Algorithms and Applications, 3. eds. de Berg, Cheong, van Kreveld, Overmars Springer, 2008. Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 24 / 25

  25. Disclaimer Chalk & blackboard lectures. . . Core algorithmic problems (not graphics and games) Focus on efficient algorithms – O ( n log n ) This is not math! But there will be proofs in every lecture (of correctness and complexity) Course language is English, if necessary Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 25 / 25

Recommend

Computational Geometry Algorithm Library Efi Fogel Tel Aviv University Computational Geometry

Computational Geometry Algorithm Library Efi Fogel Tel Aviv University Computational Geometry

Computational Geometry Algorithm Library Efi Fogel Tel Aviv University Computational Geometry Apr. 7 th , 2014 Cgal : Mission Make the large body of geometric algorithms developed in the field of computational geometry available for

542 views • 21 slides
Computational Geometry (Master Course) Computational Geometry Course Outline Mohammad Farshi

Computational Geometry (Master Course) Computational Geometry Course Outline Mohammad Farshi

Yazd Univ. Computational Geometry (Master Course) Computational Geometry Course Outline Mohammad Farshi Textbook Grading Prerequisties Department of Computer Science, Introduction What is CG? Yazd University Research on CG Journals

367 views • 20 slides
Computational Geometry Exercise session #1 Yaron Ostrovsky-Berman, Computational Geometry, Spring

Computational Geometry Exercise session #1 Yaron Ostrovsky-Berman, Computational Geometry, Spring

Computational Geometry Exercise session #1 Yaron Ostrovsky-Berman, Computational Geometry, Spring 2005 1 Administrivia Exercise sessions (Shprinzak 202): Wednesday, 11:00 11:45. Course web page: www.cs.huji.ac.il/~compgeom

770 views • 9 slides
Challenges in Computational Algebraic David A. Cox Geometry Challenge 1: Other Computational

Challenges in Computational Algebraic David A. Cox Geometry Challenge 1: Other Computational

Challenges in Computational Algebraic Geometry Challenges in Computational Algebraic David A. Cox Geometry Challenge 1: Other Computational Algebraic Geometry Workshop Disciplines Article in Nature The Mathematics Methods Challenge 2:

343 views • 33 slides
CS133 Computational Geometry Computational Geometry Primitives 1 Point Representation A point

CS133 Computational Geometry Computational Geometry Primitives 1 Point Representation A point

CS133 Computational Geometry Computational Geometry Primitives 1 Point Representation A point in the 2D Cartesian space is represented as a vector from the origin to the point = , p p y O x 2 Line Segment Representation

727 views • 16 slides
Pseudotriangulations in Computational Geometry G unter Rote Freie Universit at Berlin,

Pseudotriangulations in Computational Geometry G unter Rote Freie Universit at Berlin,

1 Pseudotriangulations in Computational Geometry G unter Rote Freie Universit at Berlin, Institut f ur Informatik Fall School on Computational Geometry Graduate Program Combinatorics, Geometry, and Computing October 24,

1.65k views • 151 slides
Plane Sweep Algorithms II Carola Wenk 1/22/15 1 CMPS 3130/6130 Computational Geometry

Plane Sweep Algorithms II Carola Wenk 1/22/15 1 CMPS 3130/6130 Computational Geometry

CMPS 3130/6130 Computational Geometry Spring 2015 Plane Sweep Algorithms II Carola Wenk 1/22/15 1 CMPS 3130/6130 Computational Geometry Geometric Intersections Important and basic problem in Computational Geometry Solid modeling:

425 views • 14 slides
CS133 Computational Geometry Computational Geometry on Big Data 1 Big Geometric Data Geotagged

CS133 Computational Geometry Computational Geometry on Big Data 1 Big Geometric Data Geotagged

CS133 Computational Geometry Computational Geometry on Big Data 1 Big Geometric Data Geotagged Satellite Imagery Check ins Tweets Billions of check ins More than 17 PB Billions of tweets Millions more every day 2 MapReduce Map Reduce

558 views • 20 slides
Computational Geometry Lecture 13: More on Voronoi diagrams Computational Geometry Lecture 13:

Computational Geometry Lecture 13: More on Voronoi diagrams Computational Geometry Lecture 13:

Voronoi diagrams of line segments Farthest-point Voronoi diagrams More on Voronoi diagrams Computational Geometry Lecture 13: More on Voronoi diagrams Computational Geometry Lecture 13: More on Voronoi diagrams Motion planning for a disc

1.69k views • 92 slides
Computational Geometry Lecture 6: Smallest enclosing circles and more Computational Geometry

Computational Geometry Lecture 6: Smallest enclosing circles and more Computational Geometry

Introduction Smallest enclosing circle algorithm Randomized incremental construction Smallest enclosing circles and more Computational Geometry Lecture 6: Smallest enclosing circles and more Computational Geometry Lecture 6: Smallest

706 views • 53 slides
Voronoi Diagrams Carola Wenk Based on: Computational Geometry: Algorithms and Applications

Voronoi Diagrams Carola Wenk Based on: Computational Geometry: Algorithms and Applications

CMPS 3130/6130 Computational Geometry Spring 2015 Voronoi Diagrams Carola Wenk Based on: Computational Geometry: Algorithms and Applications 2/19/15 1 CMPS 3130/6130 Computational Geometry Voronoi Diagram (Dirichlet Tesselation) Given: A

477 views • 19 slides
Computational Geometry Exercise session #4: Polygon decompositions Art Gallery Theorem

Computational Geometry Exercise session #4: Polygon decompositions Art Gallery Theorem

Computational Geometry Exercise session #4: Polygon decompositions Art Gallery Theorem Trapezoidal decomposition Convex decomposition Solution to homework 1 1 Yaron Ostrovsky-Berman, Computational Geometry, Spring 2005 The

544 views • 11 slides
PRESENTATION OF THE COURSE Vera Sacrist an Rodrigo Silveira Computational Geometry Facultat

PRESENTATION OF THE COURSE Vera Sacrist an Rodrigo Silveira Computational Geometry Facultat

PRESENTATION OF THE COURSE Vera Sacrist an Rodrigo Silveira Computational Geometry Facultat dInform` atica de Barcelona Universitat Polit` ecnica de Catalunya PRESENTATION OF THE COURSE The kernel of Computational Geometry is the

895 views • 65 slides
Introduction to several models from stochastic geometry Pierre Calka Computational Geometry Week

Introduction to several models from stochastic geometry Pierre Calka Computational Geometry Week

Introduction to several models from stochastic geometry Pierre Calka Computational Geometry Week 2015 Eindhoven , 25 June 2015 default Plan From game to theory: Buffon, integral geometry, random tessellations From game to theory: 150 years of

1.34k views • 61 slides
Announcements Computational Geometry for Thursday, March 2 the Tablet PC ABET Program

Announcements Computational Geometry for Thursday, March 2 the Tablet PC ABET Program

Announcements Computational Geometry for Thursday, March 2 the Tablet PC ABET Program review Give important feedback on the CSE 481b program Free Donuts! Lecture 17 Overview Tablet Geometry Computational Basic

229 views • 6 slides
Computational Geometry Lecture 1: Introduction and convex hulls 1 Computational Geometry

Computational Geometry Lecture 1: Introduction and convex hulls 1 Computational Geometry

Computational Geometry Lecture 1: Introduction and convex hulls 1 Computational Geometry Lecture 1: Introduction and Convex Hulls Geometry: points, lines, ... Plane (two-dimensional), R 2 Space (three-dimensional), R 3 Space

1.14k views • 55 slides
Delaunay Triangulations Carola Wenk Based on: Computational Geometry: Algorithms and

Delaunay Triangulations Carola Wenk Based on: Computational Geometry: Algorithms and

CMPS 6640/4040 Computational Geometry Spring 2016 p r Delaunay Triangulations Carola Wenk Based on: Computational Geometry: Algorithms and Applications 2/18/16 CMPS 6640/4040 Computational Geometry 1 Applications of DT All nearest

334 views • 6 slides
Computational Geometry Lecture 6: Smallest enclosing circles and more Computational Geometry

Computational Geometry Lecture 6: Smallest enclosing circles and more Computational Geometry

Smallest enclosing circles and more Computational Geometry Lecture 6: Smallest enclosing circles and more Computational Geometry Lecture 6: Smallest enclosing circles and more Facility location Given a set of houses and farms in an isolated

882 views • 61 slides
Planar Subdivisions and Point Location Carola Wenk Based on: Computational Geometry: Algorithms

Planar Subdivisions and Point Location Carola Wenk Based on: Computational Geometry: Algorithms

CMPS 3130/6130 Computational Geometry Spring 2015 p Planar Subdivisions and Point Location Carola Wenk Based on: Computational Geometry: Algorithms and Applications and David Mounts lecture notes 2/5/15 CMPS 3130/6130 Computational

679 views • 30 slides
The Algebraic Revolution in Combinatorial and Computational Geometry: State of the Art Micha

The Algebraic Revolution in Combinatorial and Computational Geometry: State of the Art Micha

The Algebraic Revolution in Combinatorial and Computational Geometry: State of the Art Micha Sharir Tel Aviv University 1 Historical Review: To get us to the present Combinatorial Geometry owes its roots to (many, but especially to) Paul

868 views • 69 slides
Computational geometry Inge Li Grtz CLRS Chapter 33.0, 33.1, 33.3. Convex Hull Convex

Computational geometry Inge Li Grtz CLRS Chapter 33.0, 33.1, 33.3. Convex Hull Convex

Computational Geometry Geometric problems (this course Euclidean plane). Does a set of line segments intersect, dividing plane into regions, find closest point, motion planning (robotics), overlaying of maps, lightening of

438 views • 5 slides
Computational Geometry Lecture 2b: Subdivision representation and map overlay 1 Computational

Computational Geometry Lecture 2b: Subdivision representation and map overlay 1 Computational

Motivation Doubly-connected edge list Map overlay Subdivision representation and map overlay Computational Geometry Lecture 2b: Subdivision representation and map overlay 1 Computational Geometry Lecture 2b: Subdivision representation and

926 views • 51 slides
Computational Geometry Lecture 2b: Subdivision representation and map overlay Computational

Computational Geometry Lecture 2b: Subdivision representation and map overlay Computational

Motivation Doubly-connected edge list Map overlay Subdivision representation and map overlay Computational Geometry Lecture 2b: Subdivision representation and map overlay Computational Geometry Lecture 2b: Subdivision representation and map

641 views • 42 slides
INF4130 Algoritmer: Design og effektivitet 30th August 2018 Petter Kristiansen Praktisk

INF4130 Algoritmer: Design og effektivitet 30th August 2018 Petter Kristiansen Praktisk

INF4130 Algoritmer: Design og effektivitet 30th August 2018 Petter Kristiansen Praktisk info Gruppeundervisning Gruppe 1: tirsdag 12:15-14:00 Gruppe 2: torsdag 12:15-14:00, siste gang 4/10 Obliger (ca datoer, ikke fastlagt)

395 views • 21 slides

More recommend