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Lecturer(s)
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Urban Luděk, prof. Ing. CSc.
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Course content
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1-2 Introduction, Typical problems and methods, a mathematical overview, Algorithm complexity and robustness. Algorithm Transformation of algorithms 3-4 Data representation, coordinate systems, homogeneous coordinates, affine and projective spaces, Principle of duality and applications, Geometric transformation in E2 and E3 5-6 Plucker and barycentric coordinates, typical problems. GPU based computational methods 7-8 Fundamentals of geometric algebra and conformal algebra. Geometric transformations of geometric elements in E2 and E3 in the frame of geometric algebra. 9-10 Interpolation of ordered and un-ordered data sets in the Euclidean and non-Euclidean space. 11 Application of geometrical algebra and conformal algebra in computer graphics and computer games, data visualization and virtual reality systems. 12 Invited talk. 13 Final course overview
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Learning activities and teaching methods
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Lecture supplemented with a discussion
- Contact hours
- 65 hours per semester
- Presentation preparation (report) (1-10)
- 10 hours per semester
- Preparation for an examination (30-60)
- 30 hours per semester
- Graduate study programme term essay (40-50)
- 45 hours per semester
- Preparation for comprehensive test (10-40)
- 15 hours per semester
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| prerequisite |
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| Knowledge |
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| Knowledge of fundamentals of computer graphics (level of KIV/ZPG is an advantage), practical knowledge of procedural and object-oriented programming, basic knowledge of graphical interfaces. |
| Skills |
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| can select or design algorithms and data structures for solving a given geometrically formulated problem |
| can estimate the complexity of an algorithm or measure it based on its implementation and testing |
| can implement and test the proposed solution of a geometrically formulated problem |
| can assess the advantages and disadvantages of the algorithm |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| Student of the course will gain: - knowledge of advanced methods used in computer graphics, data visualization, 3D game engines - understanding of relevant mathematical background - ability to design and implement programming tools - basic knowledge of working in a team |
| Skills |
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| analyze the given problem in terms of methods of their solution |
| to suggest the use of appropriate methods for solving geometric problems |
| use of the apparatus of geometric algebra and projective extension of Euclidean space |
| analysis of computational complexity and stability of numerical solutions |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture supplemented with a discussion |
| Skills |
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| Lecture |
| Competences |
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| Lecture |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Skills |
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| Oral exam |
| Combined exam |
| Competences |
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| Combined exam |
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Recommended literature
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Blinn,J. Jim Blinn's Corner - A Trip Down the Graphics Pipeline. Morgan Kaufmann Publ, 1996.
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David Salomon. The Computer Graphics Manual. 978-0-85729-885-0, 2011. ISBN 978-0-85729-885-0.
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Guo, Hongyu. Modern mathematics and applications in computer graphics and vision. 2014. ISBN 978-981444932-8.
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Hartley, Richard; Zisserman, Andrew. Multiple view geometry in computer vision. Cambridge : Cambridge University Press, 2001. ISBN 0-521-62304-9.
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John Vince. Geometric Algebra for Computer Graphics. 2008. ISBN 1846289963.
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Lengyel, Eric. Mathematics for 3D game programming and computer graphics. 2nd ed. Hingham : Charles River Media, 2004. ISBN 1-58450-277-0.
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Lichtenbelt, Barthold; Crane, Randy; Naqvi, Shaz. Introduction to volume rendering. Upper Saddle River : Prentice Hall, 1998. ISBN 0-13-861683-3.
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Penna,M.A., Patterson,R.R. Projective Geometry and its Application to Computer Graphics. Prentice Hall, 1986.
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Shirley,Peter. Fundamentals of computer graphics.
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Vince, John. Essential mathematics for computer graphics fast. London : Springer, 2001. ISBN 1-85233-380-4.
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