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Computational Geometry
(Geometriske Algoritmer)
“the pizza meeting”
Kim Skak Larsen
IMADAUniversity of Southern Denmark
May 15, 2018
Kim Skak Larsen (CS, IMADA) Elective Courses Presentation May 15, 2018 1 / 25
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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