Course: Applications of Geometry 1

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Course title Applications of Geometry 1
Course code KMA/APG1
Organizational form of instruction Lecture + Seminar
Level of course Bachelor
Year of study 3
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Bastl Bohumír, Doc. Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Minkowski sum, its basic properties and algorithms, applications. Voronoi diagrams, their properties, algorithms, applications, generalizations. Kinematics. Offset theory - classical and general offsets, classes of curves and surfaces with rational classical and general offsets, applications. Epipolar geometry and its applications (object reconstruction from two or more images). Subdivision curves and surfaces and their application. Quaternions. Isogeometric analysis.

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, E-learning, Students' portfolio
  • Contact hours - 52 hours per semester
  • Preparation for an examination (30-60) - 40 hours per semester
  • Undergraduate study programme term essay (20-40) - 30 hours per semester
  • Presentation preparation (report in a foreign language) (10-15) - 12 hours per semester
prerequisite
professional knowledge
Basic knowledge of linear algebra and basic knowledge of geometry (KMA/G1 or equivalent) is expected. Basic knowledge of differential geometry of curves and surfaces is advantageous.
learning outcomes
Upon completion of the course a student will be able to: - orient in topics and issues of current geometric methods mainly from the field of computational geometry and geometric modeling - understand to theoretical background of studied methods - apply chosen method on problems mainly from technical practice
teaching methods
Lecture supplemented with a discussion
Interactive lecture
E-learning
Students' portfolio
Lecture with practical applications
assessment methods
Combined exam
Seminar work
Individual presentation at a seminar
Recommended literature
  • De Berg, Mark. Computational geometry : algorithms and applications. Berlin : Springer, 1997. ISBN 3-540-61270-X.
  • Goodman, Jacob E.; O'Rourke, Joseph. Handbook of discrete and computational geometry. 2nd ed. Boca Raton : Chapman & Hall/CRC, 2004. ISBN 1-58488-301-4.
  • Ma, Yi. An invitation to 3-D vision : from images to geometric models. New York : Springer, 2004. ISBN 0-387-00893-4.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 3 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 3 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 3 Summer
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 3 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 3 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 3 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 3 Summer
Faculty of Applied Sciences Geomatics (1) Construction industry, geodesy and cartography 1 Summer