Numerické metódy lineárnej algebry / Taťjana Bušinská. Bratislava : Univerzita Komenského, 1993
G. H. Golub, C. F. Van Loan: Matrix Computations, John's Hopkins University Press, 1996
J. W. Demmel: Applied Numerical Linear Algebra, Society for Indrustrial and Applied Mathemaitcs, 1997
C. D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000
Interim evaluation: Programing exercises - 30% of final grade
Final Exam: Oral examination - 70% of final grade
Student need at least half of the maximum number of points to be able to attend the final exam.
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Direct methods for solving a regular system of linear algebraic equations. Solution stability and error estimation. Iterative methods of regular system solution. Least squares problem for singular matrices with complete rank (QR-decomposition) and incomplete rank (pseudoinversion, regularization). Numerical methods for solving partial and complete eigenvalue problems (for symmetric and asymmetric matrices). Stability of eigenvalues problem. Numerical calculation of singular decomposition.
30% homework / 70% final exam
theoretical knowledge and practical experience (through available software and the creation of a separate program) with various numerical methods for solving linear algebra problems; ability to deal with the stability of the solution (analysis of the causes of instability, the limit of the possibility of its elimination) and error estimation
To master the fundamentals of the common language and basic technical terms of particular fields of study; with pre-intermediate students emphasis on reading technical texts and presentations of technical articles, application of French Internet websites.
Capelle Guy, Menand Robert: Le Nouveau taxi 1, Hachette FLE Paris, France 2009, ISBN 978-2-01-155548 - 9
test
French language is taught at two levels: beginner and intermediate. Students opt for one of them depending on whether they wish to obtain the fundamentals of the language or wish to maintain and/or improve previous knowledge of French.
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study; with pre-intermediate students emphasis on reading technical texts and presentations of technical articles, application of French Internet websites.
Capelle Guy, Menand Robert: Le Nouveau taxi 1, Hachette FLE Paris, France 2009, ISBN 978-2-01-155548 - 9
test
The subject continues the program of French language (1) and provides courses of essential and intermediate French language.
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
Appropriate study material is supplied by teacher based on the participants’level of German proficiency.
test
German language is taught at three levels: beginner, intermediate and advanced. Students opt for one of them depending on whether they need to learn the fundamentals or maintain and/or improve their previous knowledge.
This course’s focus is to master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
Appropriate study material is supplied by teacher based on the participants’level of German proficiency
test
German language is taught at two levels: beginner and intermediate. Students opt for one of them depending on whether they wish to obtain the fundamentals of the language or wish to maintain and/or improve previous knowledge of German.
This course’s focus is to to master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
To master the fundamentals of general Russian. The language level is A1.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The textbook: : Точка Ру A1 (Ольга Долматова, Екатерина Новачац), рracovné karty Падежи 1 (Л.С. Безкоровайная, В.Е. Штыленко).
test
To master the fundamentals of general Russian. The language level is A1.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The subject provides a course in Russian language for beginners.
100/0
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
To master the fundamentals of general Russian.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
Textbook: Точка Ру A1 (Ольга Долматова, Екатерина Новачац), рracovné karty Падежи 1 (Л.С. Безкоровайная, В.Е. Штыленко).
test
To master the fundamentals of general Russian.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The subject continues the program of Russian language (1) and provides a course of Russian for beginners.
100/0
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
Krížom- Krážom Slovenčina 1, additional material to further support the covered topics.
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of the basics of the Slovak language for the absolute beginners (A1).
100/0
This course is aimed for foreign students to learn the fundamentals of the Slovak language with the focus on basic communication as well as all other language skills- listening comprehension,reading and writing.
Krížom- Krážom Slovenčina 1, additional material to further support the covered topics
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of the basics of the Slovak language for the absolute beginners (A1) and this course is a follow up course to the Slovak language course 1.
100/0
This course is aimed for foreign students to learn the fundamentals of the Slovak language with the focus on basic communication as well as all other language skills- listening comprehension,reading and writing.
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational English as well as English for specific purposes appropriate for university students. This course is a follow up of the previously taught ESP course.
Appropriate study material is supplied based on the participants’level of English by the lecturer.(Sources- The Guardian, The Herald Morning Sun. The Nine News, The West Australian, BBC News and podcasts, CNN podcasts).
tests, oral presentations, essays
tests, presentations, essays
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
This course’s focus is to broaden spoken/communicational English for students with B2/C1 level of English knowledge.
100/0
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational English as well as English for specific purposes appropriate for university students. This course is a follow up of the previously taught ESP course.
tests
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational/spoken English as well as English for specific purpose appropriate for university students. This course is a follow up of the Conversational English course 1.
Appropriate study material is supplied based on the participants’level of English by the lecturer.(Sources- The Guardian, The Herald Morning Sun. The Nine News, The West Australian, BBC News and podcasts, CNN podcasts).
tests, oral presentations, essays
tests, oral presentations, essays
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
This course’s focus is to broaden spoken/communicational English for students with B2/C1 level of English knowledge( Upper-Intermediate/Lower Advanced).
100/0
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational/spoken English as well as English for specific purpose appropriate for university students. This course is a follow up of the Conversational English course 1.
tests
Improvement of common language, deepening the knowledge of technical terms, reading technical texts, presentations of popular scientific articles.
Capelle Guy, Menand Robert: Le Nouveau taxi 1, Hachette FLE Paris, France 2009, ISBN 978-2-01-155548 - 9
test
The subject provides a course of intermediate French language, covering not only general, but also technical language.
100/0
Improvement of common language, deepening the knowledge of technical terms, reading technical texts, presentations of popular scientific articles.
Menand Robert: Le Nouveau taxi 2, Hachette FLE, Paris, France 2009, ISBN 978-2-01-155551 - 9
test
The subject provides a course of intermediate French covering not only general, but also technical French language.
100/0
Deepening the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
Appropriate study material is supplied by teacher based on the participants’level of German proficiency.
test
The course is a follow-up to the German language (1,2). The subject provides a course of intermediate or advanced German language.
This course’s focus is to deepen the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
100/0
Master the basics of general language and basic professional terminology of individual fields of study (depending on the advanced level of students)
Deepening the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
Appropriate study material is supplied by teacher based on the participants’level of German proficiency.
test
The course is a follow-up to the German language (1-3). It provides a course of intermediate and advanced German language.
This course’s focus is to deepen the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
100/0
Master the basics of general language and basic professional terminology of individual fields of study (depending on the advanced level of students)
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
Точка Ру A2 (Ольга Долматова, Екатерина Новачац) a Short Stories in Russian (Olly Richards, Alex Rowlings)
test
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
The course "Russian for Intermediate Students" is a follow-up to "Russian for Beginners". The subject of the course is general Russian in the range appropriate to the given level.
100/0
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
Точка Ру A2 (Ольга Долматова, Екатерина Новачац) a Short Stories in Russian (Olly Richards, Alex Rowlings)
test
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
The course "Russian for Intermediate Students" is a follow-up to "Russian for Beginners". The subject of the course is general Russian in the range appropriate to the given level.
100/0
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
Krížom-Krážom Slovenčina 2, additional material to further support the covered topics.
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of all the language skills of the Slovak language , and it is a follow up course to the Slovak language course 2.
100/0
This course is aimed for foreign students to better comprehend all the language skills important to enable correct usage of the Slovak language – listening comprehension, reading, writing and speaking.
Krížom-Krážom Slovenčina 2, additional material to further support the covered topics.
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of all the language skills of the Slovak language , and it is a follow up course to the Slovak language course 3.
100/0
This course is aimed for foreign students to better comprehend all the language skills important to enable correct usage of the Slovak language – listening comprehension, reading, writing and speaking.
Pattern classification / Richard O. Duda, Peter E. Hart, David G. Stork. New York : Wiley Interscience, 2001
Classification pattern recognition and reduction of dimensionality / edited by P. R. Krishnaiah, L. N. Kanal. Amsterdam : North-Holland, 1982
Modern multivariate statistical techniques : Regression, classification, and manifold learning / Alan Julian Izenman. New York : Springer, 2008
tests, projects, oral exam
Scale: A 90%, B 80%, C 70%, D 60%, E 50%
The role of classification, feature articles and Syntax Notation.
Selection and pretreatment symptoms.
Classifiers, basic concepts.
Bayesian decision theory, discriminatory and divisive functions hypersurface, the criterion of the minimum error.
Decision trees.
Discriminant analysis, linear classifier.
Mechanisms of support vectors (SVM).
Neural networks.
Uncontrolled classifiers.
Hidden Markov models.
Quality rating classification.
Syntactic recognition, inference grammar. Special types of grammar.
http://www.sccg.sk/~ftacnik/
40/60
Graduates will acquire basic methods of classification.
Large and successful computer graphics projects will be presented. We will focus on a new trends and methodologies in industry.
J. Žára, B. Beneš, P. Felkel, Moderní počítačová grafika, Computer Press, Praha 1998
Project report from journal IEEE Computer and Graphics Applications
http://www.computer.org/portal/web/computingnow/cga
Internet
presentations
A 92%, B 84%, C 76%, D 68%, E 60
Slovak, English
1. Project presentations according to the project report distributed to the students
2. Projects and results done at the department
3. New trends and applications of computer graphics techniques.
https://dai.fmph.uniba.sk/w/Course:Computer_Graphics_Applications/en
100/0
Students will have knowledge of successful design projects and new trends in the application of methods and means of computer graphics.
Displays: fundamentals & applications / Hainich, Rolf R., and Oliver Bimber: AK Peters/CRC Press, 2016.
Augmented reality: principles and practice / Schmalstieg, Dieter, and Tobias Hollerer: Addison-Wesley Professional, 2016.
Eswaran, M., and MVA Raju Bahubalendruni. "Challenges and opportunities on AR/VR
technologies for manufacturing systems in the context of industry 4.0: A state of the art
review." Journal of Manufacturing Systems 65 (2022): 260-278.
Continuing evaluation: project (30%) and exercise assignments (10%).
Exam: written exam (60%).
To successfully complete the course, student has to obtain at least 50% of points and the project and on the exercise assignments and at least 50% on the final exam.
Scale: A 90%, B 80%, C 70%, D 60%, E 50%.
Slovak, English
Definitions and Basic Concepts, Applications in Industry and Culture
Augmented Reality: Definition of Terms, Applications in Industry and Culture
Hardware for Virtual and Augmented Reality (Input and Output Devices)
Case Study of Augmented Reality Application in Industry (Car Design, Data and Process Visualization in
Factories)
Case Study of Virtual Reality Application in Healthcare (Virtual Therapy, Virtual Physiotherapy)
Registration and Tracking in Augmented Reality (Marker, Markerless, RGBD, GPS)
3D Object Reconstruction, Digital Twin
API and Commercial Software for Virtual and Augmented Reality
Modeling and Visualization Software in Virtual Reality
https://dai.fmph.uniba.sk/w/Course:VAR/en
Continuing evaluation/Exam: 40/60.
After graduating, students will understand the theoretical foundations and practical skills in creating the team applications in enhanced and virtual reality.
Ian Goodfellow and Yoshua Bengio and Aaron Courville: Deep learning, MIT Press, Online for free, http://www.deeplearningbook.org/
Michael Nielsen: Neural networks and deep learning, Online for free, http://neuralnetworksanddeeplearning.com/
Adrian Rosebrock: Computer Vision and deep learning, Resource guide
Continuous assessment: homework, project
Examination: oral examination
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Introduction - machine learning basics, classical approaches to feature extraction, data splits and model evaluation, image manipulation basics
Classification - k-nearest neighbors method, linear classifier, loss functions, gradient optimization, regularization
Fully-connected NNs - computational graphs, vectorized computation, backpropagation, loss functions, automatic differentiation software, augmentation, dropout, stochastic optimization
Convolutional NNs - convolution, pooling, vanishing gradients, batch normalization, weight initialization, transfer learning, architectures
Recurrent NNs - sequential data, hidden states, LSTM, GRU, training regimes
Transformers - self-attention, transformers in NLP tasks, combinations with CNNs, transformers in computer vision
Object detection and segmentation - one and two stage object detectors, expansion of object detectors to segmentation, segmentation architectures, data annotation
Generative models - GAN, VAE
CNN visualization and understanding - learned features, style transfer, deep dream, adversarial examples, activation maps
Scientific and ethical problems of computer vision - data collection, privacy issues, computational dominance, method interpretability, safety, undesirable social effects, model bias, illusion of algorithmic objectivity
60/40
Upon completion the student will have a good understanding of the theoretical background of various types of neural networks used in computer vision for classification, localization and object detection tasks as well as generative models. The student will also be able to create, implement, train and evaluate such networks with the use of hardware on PCs or in the cloud.
L. N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM, 1997
P-G. Martinsson, J. A. Tropp: Randomized Numerical Linear Algebra: Foundations & Algorithms
Carl D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2001
Gene Golub, Charles Van Loan: Matrix Computations, John Hopkins, 2012
1-MAT-530 Numerical Methods of Linear Algebra
Semester: homework
English, Slovak
Spectral theory: eigenvalue problems, Schur factorization, power method, QR-algorithm, eigenvalue problems for symmetric matrices - Min-max theorem, QR-algorithm for symmetric matrices, Rayleigh-Ritz projection, subspace iterations, Krylov methods, GMRES , Arnoldi and Lanczos iteration, Golub-Kahan-Lanczos bidiagonalization.
Randomized numerical linear algerba: current algorithms for big data processing based on a randomized sampling, accuracy estimates, parallelization of calculations, etc.
http://thales.doa.fmph.uniba.sk/niepel/MC/matice3.html
100/0
Students will get acquainted with theoretical foundations of advanced techniques in numerical linear algebra and at the same time gain practical experience with programming computational algorithms.
To provide students with fundamental techniques in computer graphics.
Eugen Ružický, Andrej Ferko: Počítačová grafika a spracovanie obrazu, Bratislava: Sapientia, 1995
Jiří Žára a kol.: Moderní počítačová grafika, Computer Press, 2004
Allan Watt: 3D computer graphics (3rd edition), Addison Wesley, 1999
Philip Schneider, David Eberly: Geometric Tools for Computer Graphics, Morgan Kaufmann, 2003
Donald Hearn, Pauline Baker, Warren Carithers: Computer Graphics with Open GL (4th Edition), Pearson, 2010
Steve Marschner, Peter Shirley: Fundamentals of Computer Graphics (5th Edition), A K Peters/CRC Press 2021
projects
For the semester, the student can get 50% for exercises and 50% for the final exam. To successfully pass the final exam, the student must obtain at least half of the points for the exercises. The final exam is written (50% of rating) and oral (50% of rating), continuous assessment is in the form of projects and homework.
Evaluation: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
1. Affine transformations in 2D and 3D space.
2. Representation and modeling of 3D objects.
3. Determining the visible surface of objects in a 3D scene.
4. Projection from 3D to 2D space.
5. Calculation of intersection of basic objects.
6. Clipping basic primitives with respect to window, convex and non-convex shapes.
7. Rasterization of lines and selected quadratic curves, filling of raster shapes.
8. Antialiasing methods in 2D discrete space, supersampling and image filtering.
9. Phases of the imaging process (3D graphics channel).
https://flurry.dg.fmph.uniba.sk/webog/sk/bohdal-vyucba/52-bohdal/467-pocitacova-grafika-1
Students will gain knowledge about algorithmic solutions to basic computer graphics problems. They will learn the principles of working on the creation of simple graphics applications using computer graphics algorithms. They will be able to evaluate them in terms of efficiency, time and memory requirements.
exam
To provide students with the knowledge of techniques for fotorealistic computer graphics.
Eugen Ružický, Andrej Ferko: Počítačová grafika a spracovanie obrazu, Bratislava: Sapientia, 1995
Jiří Žára a kol.: Moderní počítačová grafika (2. vydání), Computer Press, 2004
Samuel Buss: 3-D Computer Graphics - A Mathematical Introduction with OpenGL. Cambridge University Press, 2003
John Hughes, Andries van Dam, et al: Computer Graphics: Principles and Practice. Addison-Wesley, 2013
Tomas Akenine-Möller, Eric Haines, et al: Real-Time Rendering (4th Edition), A K Peters, 2018
Matt Pharr, Wenzel Jakob, Greg Humphreys: Physically Based Rendering: From Theory to Implementation (3rd Edition). Morgan Kaufmann, 2016
Steve Marschner, Peter Shirley: Fundamentals of Computer Graphics (5th Edition), A K Peters/CRC Press 2021
projects
For the semester, the student can get 40% for exercises and 60% for the final exam. To successfully pass the final exam, the student must obtain at least half of the points for the exercises. The final exam is only oral, continuous assessment is in the form of projects and homework.
Evaluation: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
1. Spherical coordinates and direction (vector) in 3D, basic concepts of radiometry and photometry.
2. Interaction of light with the surface, BRDF definition, reflection equation, reflectance.
3. BRDF models, empirical models, physically based models, models based on measured data.
4. Shading methods, Gouraud, Phong and Blinn-Phong illumination model.
5. Ray casting, ray tracing, forward vs backward tracing, CSG and ray tracing.
6. Intersection of ray with parametric and algebraic surfaces.
7. Acceleration methods for ray tracing - bounding objects/volumes.
8. Acceleration methods for ray tracing - dividing the scene space.
9. Distributed ray tracing.
10. Monte Carlo integration and the reflection equation, integral estimation (estimator).
11. Monte Carlo integration and sampling, samples generation methods.
12. Multiple importance sampling and combined estimator.
13. Rendering equation, global vs local illumination.
14. Path tracing and bidirectional path tracing.
15. From rendering equation to radiosity, form-factor calculation.
16. Textures, texture mapping, texture filtering, procedural textures.
17. Shadows, shadows calculation methods.
https://flurry.dg.fmph.uniba.sk/webog/en/bohdal-teaching/52-bohdal/418-computer-graphics-2
Students will gain the necessary theoretical foundations and the ability to work with basic and advanced techniques of photorealistic computer graphics in 3D.
exam
Preliminary assessment: homework
Final assessment: oral exam
Grading: A 90%, B 80%, C 70%, D 60%, E 50%
- ideals and varieties in affine space, Hilbert's basis theorem
- Nullstellensatz
- elements of algebraic geometry:
- Zariski topology,
- coordinate rings, morphisms and rational maps
- computational methods of algebraic geometry: Gröbner bases, resultants
- Sturm sequences (calculations in real algebraic geometry)
The student gains an overview of the basic concepts of algebraic geometry as well as the most common computational methods there.
To expose basic data structures. To present methods of evaluation for algorithm and data structures efficiency. To describe basic techniques for effective algorithms design.
Aho, Hopcroft, Ullman: The design and analysis of computer algorithms, Adison Wesley 1974.
Niklaus Wirth: Algoritmy a štruktúry údajov, Alfa 1987.
Cormen, Leiserson, Rivest: Introduction to Algorithms, MIT Press 1990.
test
An introduction into problem area.
Mathematical foundations (asymptotic notation, standard notations and common functions).
Analysis of algorithms (heapsort, quicksort, sorting in linear time).
Data structures (elementary data structures, hashing tables, binary tries, balanced tries).
40/60
examination
Analytická a diferenciální geometrie / Bruno Budinský. Praha : Státní nakladatelství technické literatury, 1983
Lectures on classical differential geometry / Dirk J. Struik. Cambridge : Addison-Wesley Press, 1950
Electronic texts by the teacher, published on the WWW page of the subject.
Homeworks (written solutions of problems and their consulting 20%), final exam (oral exam with written preparation 80%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Curves: Torsion of a curve, the Frenet formulas. Envelopes of a one-parameter family of curves. Singular points of plane curves. The oriented curvature of plane curves. Some special curves (evolutes, evolvents, equidistants).
Surfaces: Developable ruled surfaces. The first fundamental form of a surface and measuring on a surface. Mappings of surfaces. The Dupin indicatrix, directions at a point. Principal directions and principal curvatures. The Gaussian curvature. Geodesics. Semi-geodesic coordinates. Extremal properties of geodesics. Surfaces of constant Gaussian curvature.
20/80
By completing this subject, the students will deepen the knowledge of curves in Euclidean plane and Euclidean 3-space, as well as the knowledge of surfaces, needed in advanced computer graphics, geometric modeling and their applications.
The understanding of the basic principles of the image processing, regarding the filtration, segmentation, recognition and reconstruction and methods of its enconding, especially for transmission.
Kódovaní / Jiří Adámek. Praha : Státní nakladatelství technické literatury, 1989
Vybrané metódy kompresie dát : Kódovanie obrazov / Jaroslav Polec, Tatiana Karlubíková, Miloš Oravec a kol.. Bratislava : Fakulta matematiky, fyziky a informatiky UK, 2000
Digital image processing / Rafael C. Gonzalez, Richard E. Woods. Beijing : Pearson education Asia : Publishing House of Electronics Industry, 2010
Digital study materials by the lecturer, published online at the class web-page.
tests
Slovak and English
Signals, systems and Discrete Fourier Transform. Z-transformation, impulse response, filters with finite and infinite impulse response. Discrete orthogonal transformations, PCA. Evaluation of the spectrum, correlation models of the image. Human visual system, color systems. Enhancement of the image: contrast, dynamic range, noise reduction, edge detection. Reconstruction of the image: homomorphic systems, reduction of additive noise, reduction of multiplicative noise. Spectral analysis, reduction of combined noises, reduction of noise depending on the signal. Image interpolation: median, mean, spline methods, convolution interpolation, polynomial interpolation, interpolation by the discrete orthogonal transformations. Image segmentation. Losless image encoding – the principle and basic methods. Lossy image encoding – the principle and basic methods. Some problems connected with the errors of the transmissed encoded image.
40/60
examination
Teorie aproximací / N. I. Achijezer. Praha : Nakladatelství Československé akademie věd, 1955
Aproximacia funkcií / Arnold Dávid, Ľudomír Šlahor. Bratislava : Univerzita Komenského, 1978
Aproximačné a kvadratúrne metódy / Adela Fillová, Anna Valková. Bratislava : MFF UK, 1986
Electronics materials of the lecturer published on the web page of the course.
Preliminary assessment: continuous assessment 4x individual tasks 10 point each, tests 50%
Final assessment: oral examination 10%
Indicative assessment scale: A 90%; B 80%; C 70%; D 60%; E 50%
Slovak and English
Polynomial functions and trigonometric polynomial functions. The Bernstein operator, the Bezier representation (the polar form of a polynomial). The Weierstrass theorem. The Lagrange interpolator. Jackson and Whitney’s theorems. The spline approximation for functions of one variable. B-splines, polar forms. Advantages of the spline approximation.
90/10
The students obtain an overview of the results used in approximations and interpolations of functions of one real variable.
Fundamentals of computer aided geometric design / Josef Hoschek, Dieter Lasser ; translated by Larry L. Schumaker. Wellesley : A. K. Peters, 1993
Curves and Surfaces for computer-Aided geometric design : A practical Guide / Gerald E. Farin. San Diego : Academic Press, 1997
Cohen, Elaine; Riesenfeld, Richard F.; Elber, Gershon Geometric modeling with splines: an introduction. (English) Zbl 0980.65016 Natick, MA: A. K. Peters. xxii, 616 p. (2001).
The electronic materials of the teacher published via the web-page of the subject.
Homeworks (written solutions of problems and their consulting 40%), final exam (oral exam with written preparation 60%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Bézier curves. Polar forms of polynomial curves.
Simple interpolation schemes. Spline curves.
B-spline functions and curves, NURBS curves.
Selected subdivision curve schemes.
40/60
The students should know, theoretically and practically, basic principles and techniques of construction of piecewise polynomial/rational curves, their properties and some ways of modifications of such curves in computer aided geometric design.
Engelking, Ryszard: General topology. Rev. and compl. ed. Sigma Series in Pure Mathematics, 6. Berlin: Heldermann Verlag. viii, 529 p. ,1989.
Ladislav Mišík: Funkcionálna analýza / . Bratislava : Alfa, 1989
Glen E. Bredon: Topology and geometry / . New York : Springer, 1993
Vlastné elektronické texty vyučujúceho predmetu zverejňované prostredníctvom web stránky predmetu.
Preliminary assessment: 0% Final assessment: Final evaluation exam 100% (A 90%; B 80%; C 70%; D 60%; E 50%)
Slovak, English
Metric topology. Topological spaces. Continuous mappins. Basic constructions of topological spaces. Countability axioms. Separation axioms (T1 – T4). Nets and convergence. Connectedness. Compactness. Topological manifolds and their discrete representations.
Final evaluation exam 100% (A 90%; B 80%; C 70%; D 60%; E 50%)
The student masters basic constructions and fundamental facts from set-theoretic topology for nonspecialists.
1. Gary R. Jensen, Emilio Musso, Lorenzo Nicolodi: Surfaces in Classical Geometries, Springer 2016
2. Marcel Berger, Bernard Gostiaux: Differential Geometry: Manifolds, Curves, and Surfaces, Springer, GTM 115, 1988
3. Philipp Grohs, Martin Holler, Andreas Weinmann: Handbook of Variational Methods for Nonlinear Geometric Data, Springer, 2020
4. Tristan Needham: Visual Differential Geometry and Forms, Princeton University Press, 2021
5. Web materials created by the lecturer
Homeworks (written solutions of problems and their consulting 60%), final exam (oral exam with written preparation 40%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
Basic notions of Lie group, bundle theory on varieties, spherical and hyperbolic geometries. The notions are illustrated on examples and applications in the are of geometry processing and visualization. As topics serve canal surfaces, minimum surfaces, hull surfaces and further constructions of curves and surfaces in Euclidean, elliptic and hyperbolic type of spaces.
60/40
The student masters basic techniques of approximation of curves, surfaces and its differential-geometric characteristics, their local of global optimization applied on areas of geometric processing.
Szeliski, R.: Computer Vision: Algorithms and Applications, 2010 (on-line)
Šikudová E., et al.:Počítačové videnie. Detekcia a rozpoznávanie objektov., Wikina
Reinhard Klette: Concise Computer Vision: An Introduction into Theory and Algorithms, Springer-Verlag London 2014
R. Hartley, A. Zisserman: Multiple View Geometry in Computer Vision, 2nd Edition, Cambridge University Press 2004
Electronic study materials
Preliminary assessment: Homework programming exercises - 40% of the final grade.
Final assessment: Written and oral examination - 60% of the final grade.
Student needs at least half of points from homework projects to be able to attend the final exam.
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Fourier transformation, feature points, edge filters, mathematical morphology, segmentation, finite projective camera model, epipolar geometry, projective and metric reconstruction
40% exercises/60 final exam
Graduates will know the advance techniques of machine vision and image processing, their mathematical background and geometric techniques for 3D reconstruction
Systematic acquaintance with geometry of the projective space.
Projektívna geometria / Štefan Solčan. Bratislava : MFF UK, 1995
The real projective plane / Harold Scott MacDonald Coxeter. Toronto : McGraw-Hill book company, Inc., 1949
Foundations of Projective Geometry / Robin Hartshorne, New York: W. A. Benjamin, 1967, dostupne aj na http://filebox.vt.edu/users/jabrunso/Math/Hartshorne.pdf , marec 2014
Electronic texts of the lecturer published via the web-site of the course.
--- available also at http://filebox.vt.edu/users/jabrunso/Math/Hartshorne.pdf , March 2014
tests
Slovak and English
n-dimensional projective space over a field, homogeneous coordinates. Subspaces, joins and intersections and their equations. Collineations. Cross ratio. Axioms of the projective plane and the projective space. Desarguesian and pappian planes. Coordinatization of a desarguesian plane. Finite projective and affine planes.
The graduate learns the fundamentals of projective plane geometry, some consequences of the axioms of projective plane a understands the independence of Desargues's and Pappus's assertions with respect to these axioms. The graduate masters the Principle of duality in projective and also in Desarguesian and Pappian planes and is able to apply it. The graduate learns the synthetic definition and some properties of projective mappings and knows solutions of problems via synthetic and analytic methods.
To become familiar with methods of parallel and central projections. Algorithmic access to construction and description of geometric objects by methods of analytic geometry.
Konštruktívna geometria pre technikov / Václav Medek, Jozef Zámožík. Bratislava : Alfa, 1978
Osobný počítač a geometria / Václav Medek, Jozef Zámožík. Bratislava : Alfa, 1991
Základy počítačovej grafiky / Jozef Zámožík, Edita Vranková, Mária Mišútová, Iveta Markechová,STU Bratislava,1999
Zobrazovací metódy I, II / Emil Kraemer, SPN Praha, 1991
Electronic texts by the teacher, published on the WWW page of the subject.
tests
Continuous assessment: tests, individual work
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
1. Fundamental principles of parallel projection, affine transformations, perspective afinity.
2. Hierarchy of methods of parallel projection – orthogonal (Monge, axonometry), oblique (basic, degenerative axonometry).
3. Analytic access to methods of parallel projection to display the surfaces (of revolution, helical surfaces, translational surfaces).
4. Central projection, linear perspective projection, principle of stereo images, analytic access to central projection.
100/0
To become familiar with methods of parallel and central projections. Algorithmic access to construction and description of geometric objects by methods of analytic geometry.
William Sherman, Alan Craig: Understanding Virtual Reality: Interface, Application, and Design, (2nd edition). Morgan Kaufmann, 2019
Robert Bohdal: Zariadenia pre rozšírenú a virtuálnu realitu. Knižničné a edičné centrum FMFI UK Bratislava, 2020
Róbert Bohdal: Architektúra grafických zariadení pre PC. https://flurry.dg.fmph.uniba.sk/webog/en/bohdal-vyucba/83-architektura.html, 2020
For the semester, the student can get 100% for the final exam. The final exam is only oral.
Evaluation: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
1. Displaying devices (monitors and displays).
2. Devices displaying 3D images (stereoscopical and volume displays).
3. Projector technology (LCD, DLP, LCoS, ...).
4. Scanners – types and the principle of their operation.
5. Touch screens, digitizers and tablets.
6. Printers and plotters.
7. Input devices for computer graphics.
8. Devices for virtual reality (headup displays, haptic devices, treadmills).
9. Devices for augmented reality (smart glasses, projection see-through displays).
10. Position and motion sensors.
11. Graphics cards functions.
12. OpenGL, DirectX, SDL – API overview.
https://flurry.dg.fmph.uniba.sk/webog/en/bohdal-vyucba/52-bohdal/83-architektura-grafickych-zariadeni
0/100
After completing the course, students will know how some of the graphics peripherals of computers (2D and 3D monitors, touch screens and tablets, printers, graphics cards, etc.) work. Students will also familiarize themselves with the devices for augmented, virtual, and mixed reality.
Overview of fractal geometry and its application in computer graphics.
Peitgen, H.-O., Saupe D.: The Science of Fractal Images, Springer Verlag
Benoit B. Mandelbrot: The Fractal Geometry of Nature, W. H. Freeman
Fractals everywhere / Michael F. Barnsley. San Francisco : Morgan Kaufmann, 1993
Digital study materials by the lecturer, published online at the class web page.
tests
Continuous assessment: tests, midterm and final. For the semester, the student can get 40% for the midterm, 60% for the final test. The student must obtain at least half of the points for both tests in order to pass the course.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
Mathematical background. Deterministic fractals (Koch, Peano, Sierpiński). IFS (iterated functions system, attractors, chaos game). Fractal compression. L-systems (modeling of plants, trees,…). Julia sets, Mandelbrot set, Newton fractals. Strange attractors (dynamical systems).
Overview of fractal geometry and its applications in computer graphics.
Jiří Špaček, Michal Spielmann: AutoCAD – Názorný průvodce pro verze 2019 a 2020, Computer Press, 2020
Lydia Cline: SketchUp for Interior Design. John Wiley & Sons, 2014
Aidan Chopra: SketchUp For Dummies. John Wiley & Sons, 2020
Tutorial Books: FreeCAD 0.19 Learn by doing: Sketcher, Part Design, Assemblies, Technical Drawings Paperback. 2021
Róbert Bohdal: CAD systémy, https://flurry.dg.fmph.uniba.sk/webog/sk/bohdal-vyucba/52-bohdal/85-cad-systemy, 2020
For the semester, the student can get 100% for continuous assessment in the form of independent work on individual projects.
Evaluation: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
1. Drawing basic shapes (lines, rectangles, arcs, polygons) in QCAD.
2. Dimensioning, hatching, creating blocks and manipulating blocks, working with layers.
3. Advanced QCAD functions - trimming, smooth arc joining, working with text, editing dimension marks, and more.
4. Basics of working in SketchUp. Description of the application layout and settings (toolbar layout). Using push, move and rotate tools to create simple 3D objects.
5. Using other SketchUp tools to create more complex 3D models.
6. Overview of some interesting SketchUp extensions for creating complex objects. Create simple animations and create a virtual tours.
7. Basics of working in Sweet Home 3D. Creating walls, rooms, adding and placing windows and doors and furniture; setting materials, resizing of models.
8. Sweet Home 3D Extensions. Creating sloping walls and multi-storey buildings, work with lights, importing your own textures and new objects.
9. Basics of working in FreeCAD. Layout description, creation of simple objects.
https://flurry.dg.fmph.uniba.sk/webog/en/bohdal-vyucba/52-bohdal/85-cad-systemy
100/0
Students will get familiar with free CAD applications QCAD, SketchUp, Sweet Home 3D and FreeCAD. They will learn to create technical 2D drawings, model more complex 3D objects and use their own and publicly available 3D models when designing the interior of a house or apartment.
Fundamentals of interactive computer graphics / James D. Foley, Andries van Dam. Reading : Addison-Wesley, 1983
Real-time rendering / Tomas Akenine-Möller, Eric Haines, Naty Hoffman. Wellesley : A. K. Peters, 2008
• Selection of recent papers in the field of research in geometric modeling, computer graphics and vision as well as selected applications.
The seminar content does not belong to state exam topics.
Continuous assessment: active participation in seminars, presentations and discussion.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
English and Slovak
The recent results of doctoral students and seminar guests are discussed.
Weight of interim / final evaluation: Interim evaluation 100%.
The graduate of the seminar in the given semester will master the latest published results of the participants and guests of the seminar as a specification of the methodology of scientific work.
Continuous assessment: paper presentation, active participation in the seminar.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
English and Slovak
The latest results of doctoral students and seminar guests are discussed.
Weight of interim / final evaluation: Interim evaluation 100%.
The graduate of the seminar in the given semester will master the latest published results of the participants and guests of the seminar as a specification of the methodology of scientific work. The seminar form will also enable him to achieve a recognizable position in the scientific debate on given topics.
Ratcliffe, JG. Foundations of hyperbolic manifolds. Springer 2006.
The latest relevant monographs and articles in world magazines.
Active participation in discussions and 1-2 papers per semester for doctoral students are expected at this departmental scientific seminar.
Recommended inclusion in the master's study plan
mMPGa / k computer graphics and geometry (conversion program) 2 / W
mMPG computer graphics and geometry 1 / W
mMPGa computer graphics and geometry 1 / W
mMPGa / k computer graphics and geometry (conversion program) 2 / W
English and Slovak
Own research. Paper preparation. Presentation at a seminar.
Interim evaluation: presentation of a paper at a seminar
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Weight of the intermediate / final evaluation: 100/0
The graduate will be able to present mathematical results in front of a professional audience, as well as expert discussion on the referenced topics.
Ratcliffe, JG. Foundations of hyperbolic manifolds. Springer 2006.
The latest relevant monographs and articles in world magazines.
Active participation in discussions and 1-2 papers is expected at this scientific seminar of the workplace
per semester for doctoral students.
Recommended inclusion in the master's study plan
mMPGa / k computer graphics and geometry (conversion program) 4 / S
mMPG computer graphics and geometry 3 / S
mMPGa computer graphics and geometry 3 / S
mMPGa / k computer graphics and geometry (conversion program) 4 / S
English and Slovak
Own research. Paper preparation. Presentation at a seminar.
Weight of the mid-term / final evaluation: Interim evaluation: presentation of the paper
at the seminar
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Weight of the intermediate / final evaluation: 100/0
The graduate will be able to present mathematical results in front of a professional audience, as well as expert discussion on the referenced topics.
Presentation on the seminar.
100/0
Presentation on the seminar.
100/0
Vybrané metódy kompresie dát : Kódovanie obrazov / Jaroslav Polec, Tatiana Karlubíková, Miloš Oravec a kol.. Bratislava : Fakulta matematiky, fyziky a informatiky UK, 2000
Polec, Jaroslav - Pavlovičová, Jarmila - Karlubíková, Tatiana: Medzinárodné štandardy pre kompresiu obrazu II : H.261, MPEG-1, MPEG-2, H.263, MPEG-4. - Bratislava : FEI STU, 2002. - 151 s. - ISBN 80-227-1784-3
Slovak and English
Lossless coding: the Huffman coding, the Huffman shift coding, the Ziv – Lempel – Welch coding, Run – length encoding, bit plane coding (PDQ, DDC).
Arithmetic coding. Data compression using prediction. Block coding (BTC, IBTC), vector quantization (VQ), sub-band coding. Transform coding: discrete orthogonal transforms: Karhunen – Loeve transformation, SVD transformation, data approximation using functions of discrete orthogonal transforms, zonal filtering, JPEG, combined transform coding (CTC). Wavelet transforms and their use in transform coding of images. Image segmentation: coding with non-rectangular blocks. Hybrid coding: intra-picture and inter-picture – compression of moving images, motion vector. Video compression standards. Digital television.
100/0
The students will master the fundamentals of the data compression for static and dynamic images.
Szirmay-Kalos, L. Theory of 3D Computer Graphics. Akademiai Kiado 1995. PDF online at http://sirkan.iit.bme.hu/~szirmay/book.html
Fundamentals of interactive computer graphics / James D. Foley, Andries van Dam. Reading : Addison-Wesley, 1983 (Third edition by Hughes et al. 2013.CG Principles and Practice.)
Spatial Augmented Reality - Merging Real and Virtual Worlds / Bimber O., Raskar R. , A K Peters, 2005, PDF online at the class web page.
Počítačová grafika a spracovanie obrazu / Eugen Ružický, Andrej Ferko. Bratislava : Sapientia, 1995
Moderní počítačová grafika / Jiří Žára, Bedřich Beneš, Petr Felkel. Praha : Computer Press, 1998
Digital study materials by the lecturer, published online at the class web page.
For the semester, the student can get 50% for exercises, 20% for midterm and the final written exam has a weight of 30%. The student must obtain at least half of the points for the exercises as well as for the project in order to pass the final written exam.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
ISO standardization and extensions for virtual and augmented reality (Bimber-Raskar). Computer game or mobile application design, modeling, interaction, and usability evaluation. Real-time rendering issues.
Computer animation (Szirmay-Kalos). Animation languages and procedural animation. Animating articulated structures: forward and inverse kinematics. Key-frame animation.
Geometry processing, special triangulations and levels of detail.
Textures for rendering, object movies and cultural heritage digitization. Visualizing of multidimensional data.
Váha priebežného / záverečného hodnotenia: Priebežné hodnotenie 20% (midterm)/ + 50% projekt 30% záverečna skúška.
Advanced modeling and rendering methods and their applications to multidimensional data presentations.
To make students acquaint with basic problems of computational geometry and with their effective solutions.
Zložitosť geometrických algoritmov / Pavel Chalmovianský, Andrej Ferko, Roman Galbavý. Bratislava : Univerzita Komenského, 2001
Boissonnat, Jean-Daniel; Yvinec, Mariette Algorithmic geometry. Translated from the 1995 French original by Hervé Brönnimann. (English) Zbl 0917.68212 Cambridge: Cambridge University Press. xxii, 519 p.(1998).
Okabe, Atsuyuki Author Profile; Boots, Barry; Sugihara, Kokichi; Chiu, Sung Nok Spatial tessellations. Concepts and applications of Voronoi diagrams. With a foreword by D. G. Kendall. 2nd ed. (English) Zbl 0946.68144 Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. Chichester: Wiley. xii, 671 p. (2000).
individual tasks
Homeworks (written solutions of problems and their consulting 40%), final exam (oral exam with written preparation 60%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Basic data structures of computational geometry.
Geometric searching.
Constructions of convex hull of finite set of points and modifications.
Proximity problems. Triangulations.
Intersection of polygons and polyhedra.
40/60
To acquaint the students with basic problems of computational geometry and their effective solutions.
exam
Fundamentals of interactive computer graphics / James D. Foley, Andries van Dam. Reading : Addison-Wesley, 1983
Real-time rendering / Tomas Akenine-Möller, Eric Haines, Naty Hoffman. Wellesley : A. K. Peters, 2008
Curves and Surfaces for computer-Aided geometric design : A practical Guide / Gerald E. Farin. San Diego : Academic Press, 1997
Recent papers on the geometric modeling research, computer graphics, computer vision and selected applications, especially from kesen.realtimerendering.com
Interim evaluation: papers, presentations and discussion.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
Introductory lectures on scientific methodology in general, and in geometry and graphics in particular (observation, experiment etc.).
The language of synthetic, analytic and iterative geometry, ruptures of the mathematics language (Kvasz), the Erlangen program, change of paradigm, Copernican revolution, Occam’s razor, axiomatic method, algorithmic strategies, Raskar’s hexagon, the role of errors, scientometry, open problems.Graphics in 2D and 3D, GUI, computational geometry, geometric modeling, computer vision, applications with scientific methodology. The seminar talks are about the most recent results , including talks at CESCG and Students‘ Scientific Conference.
Weight of interim / final evaluation: Interim evaluation 100%.
In a seminar-talk, the student discusses a selected article containing the most recent results on modeling, simulation or visualization, mainly from the SIGGRAPH conference. The student gets also an overview on selected open problems in processing of visual information.
Michael Barnsley: Fractals everywhere. Morgan Kaufmann, 1993
Benoit Mandelbrot: The Fractal Geometry of Nature. Echo Point Books & Media, 2021
David Ebert at al: Texturing and Modeling. A procedural approach (3rd edition). Morgan Kaufmann, 2002
Andrzej Katunin: A Concise Introduction to Hypercomplex Fractals. CRC Press, 2017
Tanya Short, Tarn Adams: Procedural Generation in Game Design. A K Peters/CRC Press, 2017
For the semester, the student can get 100% for the final exam. The final exam is only oral.
Evaluation: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
1. Generators of pseudorandom and random sequences.
2. Procedural creation of geometric objects.
3. Noises and turbulences.
4. Fractals and their procedural modeling.
5. Modeling of georelief, cities and facades.
6. Reaction diffusion, diffusion limited aggregation, biological mechanisms of exodermal pattern formation.
7. Cellular automata, demographic models and their use in simulations of various processes.
8. Procedural textures, projection of textures on 3D objects.
9. Particle systems.
10. Genetic and evolutionary algorithms.
https://flurry.dg.fmph.uniba.sk/webog/sk/bohdal-vyucba/52-bohdal/405-proceduralne-modelovanie
0/100
After completing the course, students will know how to use the methods of procedural modeling for creating complex objects and large scenes using predefined functions or rules.
Fundamentals of computer aided geometric design / Josef Hoschek, Dieter Lasser ; translated by Larry L. Schumaker. Wellesley : A. K. Peters, 1993
Curves and Surfaces for computer-Aided geometric design : A practical Guide / Gerald E. Farin. San Diego : Academic Press, 1997
Cohen, Elaine; Riesenfeld, Richard F.; Elber, Gershon Geometric modeling with splines: an introduction. (English) Zbl 0980.65016 Natick, MA: A. K. Peters. xxii, 616 p. (2001).
The electronic materials of the teacher published via web of the subject.
Homeworks (written solutions of problems and their consulting 40%), final exam (oral exam with written preparation 60%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Bézier quadrangular and triangular patches and their polar forms.
B-spline surfaces, NURBS-surfaces. Coons quadrangle and triangle interpolation surfaces.
Selected subdivision schems of surface constructions.
The students should know, theoretically and practically, basic principles and techniques of construction of piecewice polynomial/rational surfaces, their properties and some ways of modifications of such curves in computer aided geometric design.
Fundamentals of computer aided geometric design / Josef Hoschek, Dieter Lasser ; translated by Larry L. Schumaker. Wellesley : A. K. Peters, 1993
Wavelets for Computer Graphics: Theory and Applications. Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. Morgan Kaufmann, San Francisco, 1996.
Computing in Euclidean Geometry, Ding-Zhu Du,Frank Hwang, World Scientific, 1995, 492 strán
The electronic materials of the teacher published via web of the subject.
Final exam (oral exam with written preparation 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Forms of continuity of curves and surfaces. Necessary and suffiecient conditions of continuity of curves and surfaces. DMS splines. Geometry of meshes and refinement schemes.
The student gets more involved with topics of CAGD based on individual studium as well as lecturing of current monographic and scientific journal works and he approaches advanced techniques of geometric modeling. His final work is evaluated from professional as well as pedagogical point of view. The lectured topics and the topics of the evaluated exam are linked in extended context.
Fundamentals of computer aided geometric design / Josef Hoschek, Dieter Lasser ; translated by Larry L. Schumaker. Wellesley : A. K. Peters, 1993
Wavelets for Computer Graphics: Theory and Applications. Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. Morgan Kaufmann, San Francisco, 1996.
Computing in Euclidean Geometry, Ding-Zhu Du,Frank Hwang, World Scientific, 1995, 492 strán
The electronic materials of the teacher published via web of the subject.
Final exam (oral exam with written preparation 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Curves and surfaces constructed with refinement schemes. Wavelets. Modeling using implicitely defined curves and surfaces. Variational modeling of curves and surfaces. Selected numerical algorithms used for computing of curves and surfaces in CAGD.
0/100
The student gets more involved with topics of CAGD based on individual studium as well as lecturing of current monographic and scientific journal works and he approaches advanced techniques of geometric modeling. His final work is evaluated from professional as well as pedagogical point of view. The lectured topics and the topics of the evaluated exam are linked in extended context.
Zložitosť geometrických algoritmov / Pavel Chalmovianský, Andrej Ferko, Roman Galbavý. Bratislava : Univerzita Komenského, 2001
Algorithmics for hard problems : Introduction to combinatorial optimization, randomization, approximation, and heuristics / Juraj Hromkovič. Berlin : Springer, 2003
Approximation algorithms / Vijay V. Vazirani. Berlin : Springer, 2001
Assessment: evaluation
Preliminary assessment: Continuous assessment, individual work, paper. For attending the final examination, the student should have at least 50% of the points from the continuous assessment.
Final assessment: 50% Final evaluation examination (written, oral)
Slovak and English
- Problems and algorithms. Basic computational models and complexity measures.
- Complexity classes, their fundamental characteristics and hierarchies.
- Reduction and completness in the complexity classes. NP-complete problems.
- Methods of solving (computationally) hard problems – deterministic methods, heuristics,
approximation algorithms, probabilistic algorithms.
50/50
The students acquire a basic knowledge of complexity theory. They will know basic models and their relation to the characterization of complexity of real problems, with emphasis on hard problems. They will grasp the methods used to analyse and solve hard algorithmic problems and they will be able to apply them.
Preliminary assessment: homework
Grading: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
- Projective space.
- Special algebraic varieties: Veronese varieties, Segre varieties, Grassman varieties and Plücker coordinates, Fano varieties. Determinantial varieties. Bundles of varieties.
- Tangent space. Tangent cone. Regular and singular points.
- Dimension of algebraic variety. Hilbert's polynomial.
- Criteria for parameterization of curves. Genus of the curve.
- Schemes (introduction to theory).
The graduate of the course has deeper knowledge of algebraic geometry. They know the basics of the theory of singularities. They are familiar with frequently used classes of algebraic varieties.
Emil Vitásek : Numerické metody , SNTL, Praha, 1987
Golub, Ortega: Scientific Computing and Differential Euations – An Introduction to Numerical Methods, Academic Press, 1992
Holmes: Introduction to Numerical Methods in Differential Equations, Spriger, 2007
Burden, Faires: Numerical Analysis, 9th Edition, Cengage Learning, 2011
Preliminary assessment: 2 written tests 10 points each, project 20 points
Final examination: written exam for 50 points and oral exam for 10 points
Grading scheme: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Computational model in numerical mathematics. Numerical stability and robustness, error analysis. Numerical solution of initial value and boundary values problems for ordinary differential equations, discretization methods, shooting method, variational approach – finite element method.
Partial differential equations – the finite difference method for parabolic, hyperbolic and elliptic equations in 2D, explicit and implicit methods, stability, the alternating direction method. Applications of the numerical methods in physical and biological problems. Implementation numerical algorithms in Matlab.
40/60
Students become familiar with methods and tools in numerical computing used in higher computer graphics (physical modeling and animation, global illumination problem, special modeling).
Introduce the processes in digital photography from the artistic and technical point of view, then extend the subject with the computational photography state-of-the-art.
Fundamentals of interactive computer graphics / James D. Foley, Andries van Dam. Reading : Addison-Wesley, 1983
Spatial Augmented Reality - Merging Real and Virtual Worlds / Bimber O., Raskar R. , A K Peters, 2005, PDF online na predmetovej stránke.
Electronic texts by the teacher, published on the WWW page of the subject.
assignments
Slovak and English
: Camera and optics, light sources, special capturing devices, ideal pinhole camera. Calibration, suppressing image distortions due to optics. Omnidirectional sensing, stitching and panoramas. Visual perception, creative photography, image exposition and composition. Editing of digital photography, digital effects in artistic photography. Simple and multiple view photogrammetry. Generalized sensor/optics, ray processing. Image morphing/warping, HDR (high dynamic range), image based illumination. Texture synthesis, matting. Selected parts from the theory of image processing. Refocusing, deblurring, depth detection using flash. Synthetic aperture, confocal imaging, bracketing, time-lapse photography and image fusion.
Introduce the processes in digital photography from the artistic and technical point of view, then extend the subject with the computational photography state-of-the-art.
• Image processing, analysis, and machine vision / Milan Sonka, Vaclav Hlavac, Roger Boyle. [Stamford] : Cengage Learning, 2008
• Digital image processing / Rafael C. Gonzalez, Richard E. Woods. Beijing : PEARSON; 4th edition, 2018
• Computer Vision: Algorithms and Applications, Richard Szeliski, The University of Washington, 2nd ed. 2021
• Color in computer vision : Fundamentals and applications / Theo Gevers ... [et al.]. Hoboken : Wiley, 2012
• Digital color image processing / Andreas Koschan, Mongi Abidi. Hoboken, N.J. : Wiley, 2008
It is necessary to obtain at least 90% of the points to obtain A grade, at least 80% of points to grade B, at least 70% of points to grade C, at least 60% to grade D and at least 50% to grade E.
The course assessment consists of three parts: exercises (25%), project (25%) and final exam (50%). Students should get at least 30 points (out of 50) from exercises and project to meet the minimum condition for admission to the final written exam.
Slovak and English
• Color science (human visual system, colorimetry)
• Color models, color quantization, and palette determination.
• Color morphology.
• Edge search (multi-dimensional gradient, vector order statistics)
• Color image filtering (debluring, defocusing, Fast Filtering)
• Color image segmentation and editing (GMM, graph cut, grab cut)
• Convert a color image to grayscale and vice versa
• Color fastness for one (white patch retinex, gray world assumption) and multiple light sources
• Highlights
• Color space mapping
• Multisprectral image acquisition and processing (IR and UV images)
50/50
After completing the subject, the student will master advanced techniques of the colour-image processing.
Electronic texts, scripts and other materials published on the teacher's website.
https://www.latex-project.org/help/documentation/
https://maxima.sourceforge.io/documentation.html
https://home.csulb.edu/~woollett/mbe.html
The student can obtain 100% of the grade during the semester. The student prepares assignments of various types in various digital tools, he / she needs at least half of the available points to successfully obtain the final grading.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
1. LaTeX: Typing mathematical formulae in LaTeX. Drafting texts in LaTeX. Additional document settings in LaTeX, more advanced typesetting concepts (document settings, templates, custom environment definitions, etc.). LaTeX presentations.
2. wxMaxima: Introduction to the environment. Setup and control. Basic programming concepts (variable, cycle, condition, data structures). Basic mathematical concepts and structures (matrices, equations, maps). Rendering and visualization in plane and space (polygons, curves, surfaces). Animation and visualization of processes.
3. Methodology of writing professional texts: basic thought procedures for creating longer professional texts.
Preliminary assessment 100% (homework assignments) / 0% final exam
1. The graduate will acquire advanced skills needed to work in the LaTeX typographic system.
2. The graduate will acquire basic skills in the computer algebra system wxMaxima. Learns the basic structures and procedures of the environment's language, learns to write simple scripts and generate visualizations of basic mathematical and geometric concepts.
3. The graduate will get acquainted with the methodological procedures of writing longer professional texts, from the stage of preparation to the finalization of the text.
Preparation of diploma thesis project and diploma thesis text.
According to specifications of diploma thesis tutor.
individual task
Slovak and English
Problem specification and its analysis.
Overview of the given area.
Methodics of problem solving.
Project decision.
Plan of the work and its checking.
Software realization.
Numerical experiments.
Structure of diploma thesis text.
Realization of diploma thesis project and diploma thesis text.
According to specifications of diploma thesis tutor.
individual task
Slovak and English
Diploma thesis text writing.
Obtain and train professional skills and experience for individual and cooperative research work for medium size projects.
According to requirements of thesis advisor.
Fundamentals of interactive computer graphics / James D. Foley, Andries van Dam. Reading : Addison-Wesley, 1983
Curves and Surfaces for computer-Aided geometric design : A practical Guide / Gerald E. Farin. San Diego : Academic Press, 1997
Počítačová grafika a spracovanie obrazu / Eugen Ružický, Andrej Ferko. Bratislava : Sapientia, 1995
Ako písať vysokoškolské a kvalifikačné práce : Ako písať seminárne práce, ročníkové práce, práce študentskej vedeckej a odbornej činnosti, diplomové práce, záverečné a atestačné práce, dizertácie / Dušan Katuščák. Bratislava : Stimul, 1998
oral and web presentations
Assessment: evaluation
Interim evaluation: presentations and discussion.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
An overview on technology of scientific methodology and research work on medium size projects.
Scientific writing. Requirements and conventions.
Student presentations of their diploma projects and work in progress.
Weight of interim / final evaluation: Interim evaluation 100%.
Obtain and train professional skills and experience for individual and cooperative research work for medium size projects.
Obtain and train professional skills and experience for individual and cooperative research work for large size projects.
According to requirements of thesis advisor.
According to requirements of thesis advisors.
Zložitosť geometrických algoritmov / Pavel Chalmovianský, Andrej Ferko, Roman Galbavý. Bratislava : Univerzita Komenského, 2001
Ako písať vysokoškolské a kvalifikačné práce : Ako písať seminárne práce, ročníkové práce, práce študentskej vedeckej a odbornej činnosti, diplomové práce, záverečné a atestačné práce, dizertácie / Dušan Katuščák. Bratislava : Stimul, 1998
Master’s thesis relevant selection of recent research papers.
oral and web presentations
Assessment: evaluation
Preliminary assessment: 100% Continuous asessment, oral and WWW presentations
Final assessment: 0% Final evaluation exam
A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Student presentations of their diploma projects and work in progress.
100/0
Obtain and train professional skills and experience for individual and cooperative research work for large size projects.
Assessment: State Examination
Preliminary assessment: 0%
Final assessment: 100%
A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Topics of the examination are taken from the following subjects: Computer Graphics (1), (2), (3); Computer Vision; Algorithms and Data Structures; Procedural Modelling; Image Processing and Encoding; Virtual and Extended Reality; Complexity Theory.
The students answer questions from the subjects that they have completed.
100/0
The students demonstrate their ability to deal effectively with the facts and methods of geometrically oriented subjects of their study. The expected result is that the student passes the final state-exam in the subject of Computer Graphics.
Assessment: State Examination
Preliminary assessment: 0%
Final assessment: 100%
A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Topics of the examination are taken from the following subjects: Differential Geometry; Algebraic Geometry (1); Computational Geometry; Topology and Functional Analysis; Modelling of Curves and Surfaces (1), (2); Numerical Mathematics for Graphic Designers; Modelling of Curves and Surfaces (3), (4).
100/0
The students demonstrate their ability to deal effectively with the facts and methods of geometrically oriented subjects of their study. The expected result is that the student passes the final state-exam in the subject of Geometric Modelling.
Ako písať vysokoškolské a kvalifikačné práce : Ako písať seminárne práce, ročníkové práce, práce študentskej vedeckej a odbornej činnosti, diplomové práce, záverečné a atestačné práce, dizertácie / Dušan Katuščák. Bratislava : Stimul, 1998
Assessment: State Examination - Thesis Defence
Preliminary assessment: 0%
Final assessment: 100%
Slovak and English
Individual work by the student, under the guidance of the diploma thesis supervisor. Writing and submitting a diploma thesis. Defense of the diploma thesis.
100/0
The students write, submit and defend their diploma theses, and thus gain several competences specified in the graduate’s characteristic in this study programme.
Basic practicing and improvement of locomotion skills in various selected sports: aerobics, basketball, volleyball, football, floorball, hockey, badminton, tennis, table tennis, swimming, body building, trampoline jumping, paddling. Development of a harmonic personality in the sense of “kalokagatia” – to cultivate the students´ mental and physical values.
Slovak, English
Practicing of the students´ game skills in collective sports: basketball, volleyball, football, floorball and hockey. Mastering of the basic technique of a particular sport discipline in other sports. In paddling, basic training on still and slightly flowing water. Development of coordination skills, improvement of articular mobility and cardiovascular system.
100/0
Grades: A 90%, B 80%, C 70%, D 60%, E 50%
The condition for the award of 1 or 2 credits is the completion of a multi-day course in its full scope, or the completion of one-day courses in the scope of 4 days. Candidates can apply to the leaders of individual courses. From the presented offer of courses, you can choose the one that suits your interests, abilities and deadlines.
Slovak
KTVŠ does not rent ski equipment.
The student can sign up for the outdoor sports courses offered by the department: skiing, snowboarding. The lessons in the courses are focused on the development of basic and special movement skills and mastering the techniques needed for the sports.
Acquisition and development of basic motor skills and abilities in selected sports: skiing and snowboarding. Mastering the correct technique of performing individual movements, which are necessary for skiing and snowboarding.
Grades: A 90%, B 80%, C 70%, D 60%, E 50%.
The condition for the award of 1 or 2 credits is the completion of a multi-day course in its full scope, or the completion of one-day courses in the scope of 4 days. Candidates can apply to the leaders of individual courses. From the presented offer of courses, you can choose the one that suits your interests, abilities and deadlines.
Slovak
KTVŠ will provide sports equipment.
The student can sign up for the outdoor sports courses offered by the department: water tourism - river rafting, windsurfing, beach volleyball, hiking and other hobby sports. The lessons in the courses are focused on the development of basic and special movement skills and, mastering the techniques needed for the sports.
Creating a positive and lasting relationship with physical activity. Acquisition and mastery of basic motor skills and abilities in outdoor sports: windsurfing, beach volleyball, water tourism - river rafting, hiking and other sports according to interest. Training and improving the technique needed for the sports.
Improvement training in a selected sport aimed at enhancing locomotion skills in the selected sport. To improve the students´ resistance against various vices, stresses and risk factors.
Slovak, English
Practicing of offensive and defensive game combinations and playing with modified rules in collective sports such as basketball, volleyball, football, floorball, hockey. Command of elements of higher difficulty in locomotion skills (swimming - crawl stroke, breast stroke, butterfly stroke, trampoline jumping and aerobics – practicing of areobics compositions, bodybuilding – development of the main muscle groups, paddling on running water. Testing of the level of physical fitness and coordination skills.
100/0
Russell S., Norwig P. (2010). Artificial Intelligence: A Modern Approach, (3rd ed.), Prentice Hall. Available in faculty library.
Marsland S. (2015). Machine Learning: An Algorithmic Perspective, (2nd ed.), CRC Press.
Passing the online course https://course.elementsofai.com/ (in Enlish or Slovak version).
Slovak or English
The course consists of 20 numerical and 5 text-based tasks. Numerical tasks are checked automatically, text-based tasks are evaluated anonymously by students.
1. What is artificial intelligence: related areas, AI philosophy.
2. Troubleshooting and UI: Browsing and troubleshooting, browsing and games
3. Probability and chance, Bayes' theorem, naive Bayesian classification.
4. Machine learning: nearest neighbor classifier, regression.
5. Neural networks: basics, creation, modern techniques.
6. Consequences: on predicting the future, the effects of AI on society, summary.
The student will get acquainted with selected basic concepts of artificial intelligence and their use in solving various practical tasks.
Russell S., Norwig P. (2010). Artificial Intelligence: A Modern Approach, (3rd ed.), Prentice Hall. Available in faculty library.
Marsland S. (2015). Machine Learning: An Algorithmic Perspective, (2nd ed.), CRC Press.
Passing the online course https://course.elementsofai.com/ (in Enlish or Slovak version).
Slovak or English
The course consists of 20 numerical and 5 text-based tasks. Numerical tasks are checked automatically, text-based tasks are evaluated anonymously by students.
1. What is artificial intelligence: related areas, AI philosophy.
2. Troubleshooting and UI: Browsing and troubleshooting, browsing and games
3. Probability and chance, Bayes' theorem, naive Bayesian classification.
4. Machine learning: nearest neighbor classifier, regression.
5. Neural networks: basics, creation, modern techniques.
6. Consequences: on predicting the future, the effects of AI on society, summary.
The student will get acquainted with selected basic concepts of artificial intelligence and their use in solving various practical tasks.
- Teachers' own electronic study materials published on the course website or in the Moodle system
- Gavora, Peter a kol. 2010. Elektronická učebnica pedagogického výskumu. [online]. Bratislava : Univerzita Komenského, 2010. Dostupné na: http://www.e-metodologia.fedu.uniba.sk/ ISBN 978–80–223–2951–4.
- Tharenou, P., Donohue, R. and Cooper, B., 2007. Management research methods. Cambridge University Press.
- Topping, A., 2015: The Quantitative-Qualitative Continium. In: Gerrish, K. and Lathlean, J., The Research Process in Nursing, p. 159-172
- Williamson, K. and Johanson, G. eds., 2017. Research methods: Information, systems, and contexts. Chandos Publishing.
Continuous assessment: active participation in research in an international student team (25%), presentation of work in a workshop (25%), scientific article (50%)
Indicative evaluation scale: A 90 %, B 80 %, C 70 %, D 60 %, E 50 %
English
- Research methodology
- Design and implementation of a research project in an international group (preferably interdisciplinary)
- Methods and tools for collaboration in virtual space, collaboration in science and practice
- Academic writing, presentation of research results through scientific articles; objectives, content and structure of scientific articles; forms of academic publication, publication forums and evaluation of their quality
- Quality assurance and feedback - peer review
- Communication of results through posters or conference presentations
100/0
Students will learn in the team to agree on a common research topic, formulate research questions, determine research methods for the problem, collect and evaluate data, discuss their findings, present research results to the professional public, analyze and evaluate the scientific work of their colleagues, prepare a scientific article suitable for publication
2/1 (lecture / individual work)
Clark, Timothy R., et al. Business Model Generation. Wiley, 2010
The condition for admission to the exam is active participation in at least 80% of the lessons.
The final assessment consists of a presentation of the semester project. To successfully complete the course, it is necessary to achieve at least 50% of the overall score.
Slovak
1. Commercialization of scientific research.
2. Fundamentals of entrepreneurship and startup terminology.
3. Identification of problems and customer needs analysis (design thinking).
4. Technology transfer. Technology Readiness Levels (TRL).
5. Intellectual property and its protection.
6. Market, customer, and market potential of a technological solution.
7. Business Model Canvas. Revenue models.
8. Sources of financing for technological projects.
9. Pitching and communication of the solution.
10. Fundamentals of management and leadership.
11. Innovation support and incubation structures at national and international levels.
0/100
After completing the course, students can describe the possibilities for commercialization of scientific and technological research. They can identify market needs, assess the market potential of a technological solution, and are familiar with the terminology of entrepreneurship, technology transfer, and intellectual property protection. They understand the overall structure of a business plan and the main forms of financing for technological projects. They are familiar with the principles of communication, teamwork, and team leadership and can apply them appropriately in project work and its presentation.
To improve the students´ physical fitness, health and sport performance through sport.
Slovak, English
To improve offensive and defensive game combinations in collective sports. Practicing of tactical and technical elements in individual sports. Compensatory exercises to correct wrong body posture. Stretching. Competition rules in sport disciplines.
100/0
To strengthen the procedural aspect of university sport, stressing its health and psychological importance. To improve the students´ physical fitness.
Slovak, English
Sport training for Faculty Championships in a selected sport with modified rules. Selection of sport-talented students into teams of the Faculty Sport League, University League of Bratislava Faculties, and participation in sport events of the Faculty and University.
100/0