Course Information: In many areas of computer science such as robotics, computer graphics, virtual reality, and geographic information systems, it is necessary to store, analyze, and create or manipulate spatial data. This course deals with the algorithmic aspects of these tasks: we study techniques and concepts needed for the design and analysis of geometric algorithms and data structures. Each technique and concept will be illustrated on the basis of a problem arising in one of the application areas mentioned above.
Goals:
At the end of this course participants should be able
- to decide which algorithm or data structure to use in order to solve a given basic geometric problem,
- to analyze new problems and come up with their own efficient solutions using concepts and techniques from the course.
Prerequisites:
In order to successfully take this course, you should already have a basic knowledge of algorithms and mathematics. Here's a short list of what you are supposed to know:
- O-notation, Ω-notation, Θ-notation; how to analyze algorithms
- Basic calculus: manipulating summations, solving recurrences, working with logarithms, etc.
- Basic probability theory: events, probability distributions, random variables, expected values etc.
- Basic data structures: linked lists, binary search trees, etc.
- Graph terminology
- Programming skills for practical assignments
Most of the material in this course is based on the following book:
M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars. Computational Geometry: Algorithms and Applications (3rd edition). Springer-Verlag, 2008.
It is not mandatory to buy this book. However if participants want to know more than is offered in this course or want to have another look at the material discussed in the lectures, we recommend buying this book.
The video lectures contain a few very minor mistakes. A list of these mistakes can be found under resources. If you think you found an error, report a problem by clicking the square flag at the bottom of the lecture or quiz where you found the error.
Geometric Algorithms
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EIT Digital
Программа курса: что вы изучите
Неделя
1Plane Sweep Algorithms
In this module we will discuss an algorithm for line segment intersection that does not only depend on the input size, i.e. the number of line segments, but also on the output size, i.e. the number of intersections. This algorithm uses the Plane Sweep technique, which is applicable to many algorithmic problems in the Euclidean plane.
4 видео ((всего 25 мин.)), 6 тестов
4 видео
Introduction5мин
Plane Sweep: Concept6мин
Data Structures for Plane Sweep Algorithms8мин
Line Sweep: Missing Parts4мин
4 практического упражнения
Plane Sweep: Concept15мин
Data Structures for Plane Sweep Algorithms20мин
Line Sweep: missing parts20мин
Line Sweep Algorithms15мин
Неделя
2Voronoi diagrams and Delaunay triangulations
In this module we will introduce the notions of Voronoi diagrams and Delaunay triangulations and its properties. Furthermore we will an algorithm for constructing Delaunay triangulations using the technique of randomized incremental construction. We will see how to analyze these types of algorithms.
8 видео ((всего 45 мин.)), 6 тестов
8 видео
Voronoi Diagrams4мин
Voronoi Diagrams: Structure4мин
Complexity of Voronoi Diagrams4мин
Delaunay Triangulations5мин
Angle-Optimal Triangulations6мин
Legal Triangulations5мин
Randomized Incremental Construction4мин
Randomized Incremental Construction: Analysis10мин
4 практического упражнения
Voronoi15мин
Triangulations15мин
Randomized incremental construction20мин
Voronoi Diagrams and Delaunay triangulations15мин
Неделя
3Orthogonal range searching
In this module we will introduce the problem of range searching. We will first look at the one dimensional case and later on generalize to higher dimensions. We will see two data structures that allow for range searching, namely KD Trees and Range Trees. We will compare them by looking at construction time, space usage and query time.
6 видео ((всего 43 мин.)), 3 тестов
6 видео
1D Range Searching6мин
KD Trees5мин
Queries in KD-Trees7мин
Range Trees7мин
Range Trees: Extensions10мин
3 практического упражнения
KD-trees20мин
Range Trees20мин
KD and range trees30мин
Преподаватель
Kevin Buchin
DrEindhoven University of Technology, Mathematics and Computer Science
О EIT Digital
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Часто задаваемые вопросы
When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
What is the refund policy?
Is financial aid available?
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