Geometric Algorithms from Coursera

Geometric algorithms are a category of computational methods used to solve problems related to geometric shapes and their properties. These algorithms deal with objects like points, lines, polygons, and other geometric figures.

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.

What's inside

Syllabus

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.

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.

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.

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Explores Geometric Algorithms, which is standard in the robotics, computer graphics, virtual reality, and geographic information systems industries

Provides a strong foundation for learners new to Geometric Algorithms

Applies Geometric Algorithms in practical applications through a mix of videos, readings, and hands-on labs

Reviews summary

Geometric algorithms

According to students, Geometric Algorithms is a good course. While some students found the problems and lectures difficult to follow, others appreciated the interesting subject matter and good content.

Learners found the subject matter interesting.

"The subject is very interesting."

"This a really good course with a lot of good content and good explanations."

The course has good content.

"This a really good course with a lot of good content and good explanations."

Some learners found the course materials difficult to follow.

"Problems and definitions are really hard to understand and follow."

"Unable to follow the lectures unless finding other resources and lectures."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Geometric Algorithms with these activities:

Review calculus basics

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Review basic concepts in calculus to strengthen your foundation for Geometric Algorithms.

Browse courses on Calculus

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Go over your notes from a previous calculus course or textbook
Practice solving basic calculus problems, such as finding derivatives and integrals

Follow an online tutorial on graph terminology

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To become familiar with graph terminology, follow an online tutorial on the topic.

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Search for an online tutorial on graph terminology.
Follow the steps in the tutorial.
Take notes on the key concepts.

Explore resources for Geometric Algorithms

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Seek out tutorials and online resources to enhance your understanding of Geometric Algorithms.

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Search for online tutorials on Geometric Algorithms
Find and read through documentation and articles on Geometric Algorithms
Watch video lectures or demonstrations on Geometric Algorithms

Eight other activities

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Join a study group for geometric algorithms

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To reinforce your knowledge and gain diverse perspectives, join a study group dedicated to geometric algorithms.

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Find a group of classmates who are also taking the course.
Set up a regular meeting time.
Discuss the course material.
Work on practice problems together.

Solve practice problems on geometric algorithms

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To practice applying the techniques and concepts, complete practice problems rooted in geometric algorithms.

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Find a website or textbook with practice problems on geometric algorithms.
Choose a set of problems to solve.
Solve the problems using the techniques and concepts you have learned.
Check your answers against the provided solutions.
Identify any areas where you need additional practice.

Solve practice problems on Geometric Algorithms

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Engage in regular practice by solving problems related to Geometric Algorithms.

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Find practice problems and exercises on Geometric Algorithms
Attempt to solve the problems on your own
Check your solutions against provided answers or consult with others

Participate in study groups or online forums on Geometric Algorithms

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Join study groups or online communities to connect with peers and discuss Geometric Algorithms.

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Find study groups or online forums related to Geometric Algorithms
Attend study sessions or participate in online discussions
Collaborate with peers on solving problems or sharing knowledge

Write a blog post on geometric algorithms

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To solidify your understanding of the principles, try explaining geometric algorithms in a blog post.

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Choose a specific geometric algorithm to write about.
Explain the problem that the algorithm solves.
Describe the steps of the algorithm in detail.
Provide an example of how the algorithm can be used.

Create visual aids for Geometric Algorithms concepts

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Solidify your understanding by creating visual representations of Geometric Algorithms concepts.

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Identify a Geometric Algorithms concept you want to visualize
Choose a visual format, such as a diagram, flowchart, or animation
Create your visual aid using appropriate tools or software

Read "Computational Geometry" by de Berg et al.

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For in-depth knowledge, consider reading the recommended textbook on computational geometry.

View Computational Geometry: Algorithms and... on Amazon

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Purchase or borrow the book.
Read the chapters that correspond to the course material.
Work through the examples and exercises.

Develop a prototype for a geometric algorithm

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To demonstrate your proficiency, build a prototype that showcases a geometric algorithm in practice.

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Choose a geometric algorithm to implement.
Design the prototype.
Develop the prototype.
Test the prototype.
Document the prototype.

Career center

Learners who complete Geometric Algorithms will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians study the properties of numbers, shapes, and other abstract concepts. They use this knowledge to develop new mathematical theories and solve problems in a variety of fields, including science, engineering, and finance. Geometric algorithms are a fundamental part of mathematics, and this course would provide a strong foundation for anyone who wants to pursue a career in mathematics.

See salaries and explore the career path for Mathematician

Software Engineer

Software Engineers design, develop, and maintain software systems. They use their knowledge of computer science to create software that is reliable, efficient, and user-friendly. Geometric algorithms, such as those used in Computational Geometry, are used in a variety of software applications, including computer graphics, robotics, and data visualization.

See salaries and explore the career path for Software Engineer

Computer Vision Engineer

Computer Vision Engineers develop computer systems that can interpret and understand images and videos. This may include tasks such as object recognition, tracking, and segmentation. Familiarity with geometric algorithms, such as Plane Sweep Algorithms and Voronoi diagrams, allows Computer Vision Engineers to develop more efficient and accurate systems.

See salaries and explore the career path for Computer Vision Engineer

Robotics Engineer

Robotics Engineers design, build, and maintain robots. They use their knowledge of mechanical engineering, electrical engineering, and computer science to create robots that can perform a variety of tasks, from manufacturing to healthcare. Geometric algorithms, such as those used in Path Planning, are used to help robots navigate their environment and avoid obstacles.

See salaries and explore the career path for Robotics Engineer

Transportation Engineer

Transportation Engineers plan, design, and maintain transportation systems. They use their knowledge of civil engineering and traffic engineering to create transportation systems that are safe, efficient, and environmentally friendly. Geometric algorithms, such as those used in Network Analysis, are used to help Transportation Engineers to design and optimize transportation systems.

See salaries and explore the career path for Transportation Engineer

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve problems in a variety of fields, including business, healthcare, and government. Geometric algorithms, such as those used in Plane Sweep Algorithms, can help Operations Research Analysts to develop more efficient and effective solutions to problems.

See salaries and explore the career path for Operations Research Analyst

GIS Analyst

GIS Analysts use geographic information systems (GIS) to create and analyze maps and other data. GIS is used in a variety of fields, including planning, environmental science, and marketing. Geometric algorithms, such as those used in Orthogonal range searching, can help GIS Analysts to identify patterns and trends in data more efficiently.

See salaries and explore the career path for GIS Analyst

Surveyor

Surveyors measure and map the Earth's surface. They use their knowledge of geometry and trigonometry to determine the location of property boundaries, roads, and other features. Geometric algorithms, such as those used in Delaunay triangulation, are used to create accurate maps and other visualizations of the Earth's surface.

See salaries and explore the career path for Surveyor

Geographer

Geographers study the Earth's surface, climate, and human and animal life. They use this knowledge to solve problems and make recommendations for land use, conservation, and other issues. Geometric algorithms, such as Delaunay triangulation, are used to create maps and other visualizations that help Geographers to understand and communicate their findings.

See salaries and explore the career path for Geographer

Data Analyst

Data Analysts clean, analyze, and interpret large amounts of data to identify patterns and trends. They use this information to make recommendations for businesses and organizations. Geometric algorithms, such as those used in Orthogonal range searching, can help Data Analysts to identify patterns and trends in data more efficiently.

See salaries and explore the career path for Data Analyst

Geologist

Geologists study the Earth's physical structure and history. They use this knowledge to find and extract natural resources, such as oil and gas. Geometric algorithms, such as those used in Voronoi diagrams, are used to create models of the Earth's subsurface, which can help Geologists to identify potential drilling sites.

See salaries and explore the career path for Geologist

Cartographer

Cartographers plan, research, compile, and produce maps for use in traveling, planning and land and resource management as well as in engineering, education, business and other activities requiring accurate locational data. Familiarity with geometric algorithms, such as Delaunay triangulation, is a major component of map production, so taking this course would be a valuable addition to a Cartographer's skill set.

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Product Designer

Product designers create and develop new products. They use their knowledge of design, engineering, and marketing to create products that are both functional and appealing to consumers. Geometric algorithms, such as those used in Voronoi diagrams, can help Product Designers to create products that are more efficient and aesthetically pleasing.

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Information Scientist

Information Scientists design and manage information systems. They use their knowledge of information technology and data analysis to help organizations make better decisions. Familiarity with geometric algorithms, such as those used in Orthogonal range searching, allows Information Scientists to develop more efficient and accurate information systems.

See salaries and explore the career path for Information Scientist

Civil Engineer

Civil Engineers design and supervise the construction of roads, bridges, dams, airports, buildings and other structures. They also plan and manage water and wastewater systems and other infrastructure. Knowledge of geometric algorithms allows Civil Engineers to ensure that structures are stable and efficient. This course would be a beneficial addition to the skill set of a Civil Engineer.

See salaries and explore the career path for Civil Engineer