Computational Geometry

(Geometriske Algoritmer)

“the pizza meeting”

Kim Skak Larsen

IMADAUniversity of Southern Denmark

kslarsen@imada.sdu.dk

May 15, 2018

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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 GeometryAlgorithms and Applications, 3. eds.de Berg, Cheong, van Kreveld, OvermarsSpringer, 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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