UIN3034 Comp. Geometry and Computer Graphics I

Faculty of Philosophy and Science in Opava
Winter 2023
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
doc. RNDr. Luděk Cienciala, Ph.D. (lecturer)
doc. RNDr. Luděk Cienciala, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Luděk Cienciala, Ph.D.
Institute of Computer Science - Faculty of Philosophy and Science in Opava
Thu 8:05–9:40 B2
  • Timetable of Seminar Groups:
UIN3034/A: Thu 9:45–11:20 B3b, L. Cienciala
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
Course objectives
Content of the course is a computer graphics in 2D, basic algorithms, basic of geometry used in computer graphics.
Learning outcomes
After completing the course the student will be able to:
- recognize the main characteristics of vector and raster graphics;
- describe the image processing flow;
- describe the main types of raster image representation, recognizing the advantages and disadvantages of each type;
- apply algorithms for rendering geometric primitives;
  • 1. Introduction - computer graphics, vector and raster graphics, technical resources for computer graphics, colors, color models, additive color model, subtractive color model, RGB, RGBA, CMY, CMYK, HSV, HLS, YUV, YCbCr, pallets - 3 -3-2, 7-12-3, adapted color palette, graphic systems.
    2. The image and its representation, digitization, quantization, sampling, Fourier transform, forward and inverse Fourier transform, Shannon sampling theorem and frequency-limited functions, reconstruction of continuous functions, alias, antialising, delete the alias, with a higher frequency sampling, filtering, stochastic sampling.
    3. All representations raster image matrix index mode, quad tree, raster image compression, RLE, Huffman coding, LZW, fractal compression, examples of raster formats, PCX, GIF, PNG, TGA, TIFF formats to MPEG animated sequences, other formats , BMP, DICOM, JPEG.
    4. Computer graphics in two-dimensional space, rasterization lines, DDA algorithm, Bresenham algorithm, drawing dashed lines, drawing thick lines, rasterization circle, drawing a circle using line segments, Bresenham algorithm for drawing circles, ellipses rasterization.
    5. Curves - expression and basic properties of curves, modeling curves, rational curves, irrational curves, interpolation, curve fitting, cubic Ferguson, Bezier curves, Casteljau algorithm, Beierová cubic B-spline curves, Coons cubic, NURBS curves, continuity
    6. Generation brands, characters, font, font line, raster, problems with the aesthetic appearance of the rendered text, area, filling polygonal areas, filling line, filling pattern, shading, filling the borders drawn in the grid, 4spojitá, 8spojitá area, simple Seed filling, Seed filling line, filling the area raster pattern, shading raster area, filling line with a list of active edges, inverse filling, filling in templates.
    7. Transformation window size, cropping, trimming lines, trimming with area codes, sequential halving lines, parametric trimming, cropping polygon, Sutherland-Hodgmanův algorithm, Weiler-Athertonův algorithm
    8. Transformation color halftone, distractions, randomly dispersed, matrix dispersion, distribution rounding errors, color palette
    9. mapping, forward mapping, reverse mapping, separable operations, resampling, convolution, geometric transformations linear, nonlinear, changing resolution, nearest neighbor interpolation, bilinear interpolation, Parzenovo window rotation discrete image histogram, a lookup table operation, frequently used operation - thresholding, bounded thresholding, gamma correction, equalization.
    10. Geometry - affine space, Euclidean space Cartesian coordinate system, consistent view of Euclidean space, in conformity E2, E3 conformity, similar views Euclidean space, scale and complex transformations, coordinate systems and transformations, vector size and distance of a pair of points, scalar product, cross product of vectors, mixed product of vectors, distance of a point from a line in the plane, distance of a point from a line in space, position point to a line segment, the position of the point to the circle and sphere, distance of a point from the plane, the position of point to polygon Circle with three points, 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 lecture
Lecture with a video analysis
Assessment methods
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 registation 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 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 1993, Winter 1994, Winter 1995, Winter 1996, Winter 1997, Winter 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022.
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