This course represents an introduction to computational geometry – a branch of algorithm theory that aims at solving problems about geometric objects. Its application areas include computer graphics, computer-aided design and geographic information systems, robotics, and many others. You will learn to apply to this end various algorithmic approaches, and asses their strong and weak points in a particular context, thus gaining an ability to choose the most appropriate method for a concrete problem.
Computational Geometry
Saint Petersburg State UniversityAbout this Course
12,879 recent views
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Basic knowledge of at least one programming language (loops, recursion, input/output). Basic math: proof by induction, proof by contradiction.
Approx. 19 hours to complete
English
Subtitles: English
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Basic knowledge of at least one programming language (loops, recursion, input/output). Basic math: proof by induction, proof by contradiction.
Approx. 19 hours to complete
English
Subtitles: English
Offered by
Saint Petersburg State University
Санкт-Петербургский государственный университет (СПбГУ) — старейший вуз России, основанный в 1724 году. Университет сегодня — научный, образовательный и культурный центр мирового значения, неизменно входящий во все международные рейтинги вузов. В номинации взаимодействие с работодателями QS Graduate Employability 2018 СПбГУ занимает 20 место среди 400 ведущих вузов мира и является лучшим в России.
Syllabus - What you will learn from this course
4 hours to complete
Point inclusion in a polygon
How can it be determined whether you have selected a particular region on an interactive map? This problem is an excellent starting point to get introduced to computational geometry and a variety of its applications!
4 hours to complete
9 videos (Total 41 min)
9 videos
1.2 Problem statement4m
1.3 Testing point inclusion in a polygon3m
1.4 Algorithmic details3m
1.5 Degenerate cases2m
1.6 Putting everything together3m
1.7 Convex polygons4m
1.8 Testing point inclusion in a convex polygon6m
1.9 Star-shaped polyogns4m
3 practice exercises
Preliminaries20m
Geometric computing
Polygon hierarchy
4 hours to complete
Convex hulls
Algorithmic processing of finely shaped objects may be computationally expensive. Can they be reasonably approximated, so as to decrease the handling costs? Convex hulls will come at hand!
4 hours to complete
9 videos (Total 54 min)
9 videos
2.2 A naïve algorithm5m
2.3 Modified Graham's algorithm10m
2.4 Graham's scan6m
2.5 Jarvis march3m
2.6 Divide and conquer10m
2.7 Incremental algorithms3m
2.8 Quick hull3m
2.9 Chan's algorithm7m
3 practice exercises
Basic observations
Alternative algorithmic approaches
Refinements
4 hours to complete
Intersections
Geographic information systems typically store a vast amount of data in the form of various maps. How can be those efficiently combined to provide an adequate response to our requests? Get acquainted with the key algorithmic aspects underlying map overlay!
4 hours to complete
6 videos (Total 52 min)
6 videos
3.2 Plane sweep10m
3.3 Data structures6m
3.4 An algorithm for intersecting line segments11m
3.5 The algorithm complexity9m
3.6 Polygon intersection8m
3 practice exercises
Intersections and plane sweep
Implementation details
Intersecting polygons
4 hours to complete
Polygon triangulation
In computer graphics, 3D-scenes are commonly represented by complex polygonal models. Do you wonder how those can be processed efficiently? Triangulation stays behind!
4 hours to complete
7 videos (Total 40 min)
7 videos
4.2 Traingulation: definition and properties5m
4.3 A naïve algorithm2m
4.4 Graph dual to a triangulation6m
4.5 An ear-cutting algorithm4m
4.6 Monotone polygons4m
4.7 Triangulating a monotone polygon11m
3 practice exercises
Polygon triangulations: basic properties
Dual graphs
Monotone polygons
Frequently Asked Questions
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?
You will be eligible for a full refund until two weeks after your payment date, or (for courses that have just launched) until two weeks after the first session of the course begins, whichever is later. You cannot receive a refund once you’ve earned a Course Certificate, even if you complete the course within the two-week refund period. See our full refund policy.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You’ll be prompted to complete an application and will be notified if you are approved. Learn more.
Will I earn university credit for completing the Course?
This Course doesn't carry university credit, but some universities may choose to accept Course Certificates for credit. Check with your institution to learn more. Online Degrees and Mastertrack™ Certificates on Coursera provide the opportunity to earn university credit.
More questions? Visit the Learner Help Center.
