Geometric Algorithms

EIT Digital

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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.

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Fechas límite flexibles

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Nivel intermedio

Aprox. 18 horas para completar

Inglés (English)

Subtítulos: Inglés (English)

Certificado para compartir

Obtén un certificado al finalizar

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.

Nivel intermedio

Aprox. 18 horas para completar

Inglés (English)

Subtítulos: Inglés (English)

Instructor

Kevin Buchin

Eindhoven University of Technology, Mathematics and Computer Science

2,996 alumnos

1 curso

ofrecido por

EIT Digital

EIT Digital is a pan-European organization whose mission is to foster digital technology innovation and entrepreneurial talent for economic growth and quality of life. By linking education, research and business, EIT Digital empowers digital top talents for the future.

EIT Digital provides online and blended Innovation and Entrepreneurship education to raise quality, increase diversity and availability of the top-level content provided by 20 leading technical universities around Europe. The universities deliver a unique blend of the best of technical excellence and entrepreneurial skills and mindset to digital engineers and entrepreneurs at all stages of their careers. The academic partners support Coursera’s bold vision to enable anyone, anywhere, to transform their lives by accessing the world’s best learning experience. This means that EIT Digital gradually shares parts of its entrepreneurial and academic education programmes to demonstrate its excellence and make it accessible to a much wider audience. EIT Digital’s online education portfolio can be used as part of blended education settings, in both Master and Doctorate programmes, and for professionals as a way to update their knowledge. EIT Digital offers an online programme in 'Internet of Things through Embedded Systems'. Achieving all certificates of the online courses and the specialization provides an opportunity to enroll in the on campus program and get a double degree. Please visit https://www.eitdigital.eu/eit-digital-academy/

Programa - Qué aprenderás en este curso

Semana

Semana 1

7 horas para completar

Plane 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.

7 horas para completar

4 videos (Total 25 minutos)

4 videos

Introduction5m

Plane Sweep: Concept6m

Data Structures for Plane Sweep Algorithms8m

Line Sweep: Missing Parts4m

4 ejercicios de práctica

Plane Sweep: Concept15m

Data Structures for Plane Sweep Algorithms20m

Line Sweep: missing parts20m

Line Sweep Algorithms15m

Semana

Semana 2

7 horas para completar

Voronoi 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.

7 horas para completar

8 videos (Total 45 minutos)

8 videos

Voronoi Diagrams4m

Voronoi Diagrams: Structure4m

Complexity of Voronoi Diagrams4m

Delaunay Triangulations5m

Angle-Optimal Triangulations6m

Legal Triangulations5m

Randomized Incremental Construction4m

Randomized Incremental Construction: Analysis10m

4 ejercicios de práctica

Voronoi15m

Triangulations15m

Randomized incremental construction20m

Voronoi Diagrams and Delaunay triangulations15m

Semana

Semana 3

4 horas para completar

Orthogonal 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.

4 horas para completar

6 videos (Total 43 minutos)

6 videos

Introduction to Range Searching4m

1D Range Searching6m

KD Trees5m

Queries in KD-Trees7m

Range Trees7m

Range Trees: Extensions10m

3 ejercicios de práctica

KD-trees20m

Range Trees20m

KD and range trees30m

Preguntas Frecuentes

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Este Curso no otorga crédito universitario, pero algunas universidades pueden aceptar los Certificados del curso para obtener crédito. Consulta con tu institución para obtener más información. Los Títulos en línea y los Certificados Mastertrack™ de Coursera brindan la oportunidad de obtener créditos universitarios.

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