FPFVA020 Computational geometry and computer graphics I

Faculty of Philosophy and Science in Opava
Winter 2020
Extent and Intensity
0/1/0. 5 credit(s). Type of Completion: z (credit).
doc. RNDr. Luděk Cienciala, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Luděk Cienciala, Ph.D.
Faculty of Philosophy and Science in Opava
Basic PC skills, fundamentals of analytical geometry within the range of secondary school mathematics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 22 fields of study the course is directly associated with, display
Course objectives
Content of the course is a computer graphics in 2D, basic algorithms, basic of geometry used in computer graphics.
Learning outcomes
- Student will get acquaint with the typical problems of computational geometry and computer graphics in 2D.
- Student will understand the existing solutions and their applications in computer graphics in 2D.
- Student will get deeper knowledge of mathematics.
- Student will learn the principles of geometric algebra including its application in graphics and vision related tasks.
- Student will practice programming, problem solving and defence of a small project.
  • 1. Introduction - computer graphics, colours, colour models, pallets, graphics systems
    2. The image and its representation
    3. Representations of raster image, raster image compression, examples of raster formats, formats for animated sequences
    4. Computer graphics in two-dimensional space, rasterization of lines, circles, ellipses
    5. Curves
    6. Generation of brands, marks, fonts
    7. Regions - fill
    8. Window and shape transformation. Crop
    9. Colours transformation
    10. Mapping, resampling, interpolation, rotation of discrete image. Frequently used operation - thresholding, bounded thresholding, gamma correction, equalization
    11. Geometry - Euclidean space, Cartesian coordinate system, similar views in Euclidean space, scale and complex transformations, coordinate systems and transformation.
    12. Geometry - vectors, distances, the relative position, analytic geometry.
    recommended literature
  • Klawonn, F. Introduction to Computer Graphics: Using Java 2D and 3D. Springer, 2012. ISBN 9781447127321. info
  • Sarfraz, M. Interactive Curve Modeling: With Applications to Computer Graphics, Vision and Image Processing. Springer, 2010. ISBN 9781849966634. info
  • Mark de Berg a kol. Computational Geometry: Algorithms and Applications. Springer, 2008. ISBN 9783540779735. info
  • Agoston, K., M. Computer Graphics and Geometric Modelling: Implementation & Algorithms. Springer, 2005. ISBN 9781852338183. info
  • Egerton, P. A., Hall, W. S. Computer Graphics - Mathematical first steps. Pearson Education, 1999. info
  • ŽÁRA, J., BENEŠ, B., FENKEL, P. Moderní počítačová grafika. Brno Computer Press, 1998. ISBN 80-7226-049-9. info
  • Hudec, J. Algoritmy počítačové grafiky. Praha, ČVUT, 1997. info
  • Granát, L., Selechovský, H. Počítačová grafika. Praha, ČVUT, 1995. info
  • Drs, L., Ježek, F., Novák, J. Počítačová grafika. Praha, ČVUT, 1995. info
  • Sobota, B. Počítačová grafika a jazyk C. České Budějovice, KOOP, 1995. info
  • Žára, J., Sochor, J. Algoritmy počítačové grafiky. ČVUT Praha, 1993. info
  • Skála, V. Světlo, barvy a barevné systémy v počítačové grafice. Praha, ČVUT, 1993. info
  • Drdla, J. Metody modelování křivek a ploch v počítačové geometrii. Olomouc, UP, 1992. info
  • Slavík, P. Metody zpracování grafické informace. Praha, ČVUT, 1992. info
  • Poláček, J., Ježek, G., Kopincová, E. Počítačová grafika. Praha, 1991. info
  • Heinz-Otto Leitgen, Peter H. Richter. The Beauty of Fractals. Springer, 1986. ISBN 9783540158516. info
  • Drs, L. Plochy ve výpočetní technice. Praha, ČVUT, 1984. info
Teaching methods
interactive lectures, homework
Language of instruction
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Credit: full-time students wrote the exercises two credit tests scored more than 30 points per test. Tests consist of three parts: a theoretical part (10 points), the numerical part (10 points) and a practical part (10 points). A necessary condition for the exam is registration to the date of the final test at: http://axpsu.fpf.slu.cz/ ~ cie10ui/index.php. The students can get bonus points (maximum 10 points) - for submission of practical tasks the day of the exercise, to which the job is submitted or for solving complex computational problems. Each student prepares a specified project, which is rated up to 30 points. Submission of the project is a necessary condition for the granting of credit. On the selected project can sign a maximum of two full-time students the second week of the semester of the academic year and at: http://axpsu.fpf.slu.cz/ ~ cie10ui/index.php. The deadline of submission of the project is midterm week of the semester. For every further week, the maximum number of points that a student can get for the project, reduced by 50 percent. The project includes a user manual, which describes the procedures used, algorithms. The credit is necessary to obtain total (2 + test project) 55 points.
Exam: The exam can get 70 points. For the successful completion you need to get at least 35 points. Mark is determined by adding the points for the exam and points that the student earned during the semester.
The course is also listed under the following terms Winter 2017, Winter 2018, Winter 2019, Summer 2020, Summer 2021, Winter 2021, Summer 2022, Winter 2022, Summer 2023.
  • Enrolment Statistics (Winter 2020, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2020/FPFVA020