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

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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

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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

SLIDE 2

Overview

1

Why an Independent Subject?

2

Example Topics

3

Applications

4

Formal Details

5

Disclaimer

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One-Dimensional Data

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One-Dimensional Data

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Two-Dimensional Data

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Two-Dimensional Data

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Two-Dimensional Data

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Two-Dimensional Data

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Convex Hull

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Convex Hull

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Dynamic Convex Hull

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Dynamic Convex Hull

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Dynamic Convex Hull

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Triangulations

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Nice Triangulations

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Range Searching

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Range Searching

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Range Searching

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Range Searching

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Example Applications

Geometric algorithms are important parts of: Computer Graphics Geographic Information Systems (GIS) Robot Motion Planning Design: CAD, VLSI, . . . Image Analysis Computer Games

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Course Content

Algorithms and Data Structures for Geometric Objects Triangulations and Voronoi Diagrams Interval and Point Searches Convex Hulls Range Searching Motion Planning etc.

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Course Content

Introduction to (continuation of) important general techniques: Line Sweeping Fractional Cascading Randomization Amortization

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Prerequisites

Analysis of Algorithms and Data Structures

(DM507 + DM553, or equivalent) Search Trees Divide and Conquer Asymptotic Notation Time and Space Analysis Correctness Analysis

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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.

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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

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