Lecturer(s)


Skala Václav, Prof. Ing. CSc.

Course content

12 Introduction, Typical problems and methods, a mathematical overview, Algorithm complexity and robustness. Algorithm Transformation of algorithms 34 Data representation, coordinate systems, homogeneous coordinates, affine and projective spaces, Principle of duality and applications, Geometric transformation in E2 and E3 56 Plucker and barycentric coordinates, typical problems. GPU based computational methods 78 Fundamentals of geometric algebra and conformal algebra. Geometric transformations of geometric elements in E2 and E3 in the frame of geometric algebra. 910 Interpolation of ordered and unordered data sets in the Euclidean and nonEuclidean 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

Learning activities and teaching methods

Lecture supplemented with a discussion
 Preparation for comprehensive test (1040)
 15 hours per semester
 Contact hours
 65 hours per semester
 Presentation preparation (report) (110)
 10 hours per semester
 Preparation for an examination (3060)
 30 hours per semester
 Graduate study programme term essay (4050)
 45 hours per semester

prerequisite 

professional knowledge 

Knowledge of fundamentals of computer graphics at the level of KIV/ZPG, practical knowledge of procedural and objectoriented programming, basic knowledge of graphical interfaces OpenGL and/or Direct X 
learning outcomes 

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 
teaching methods 

Lecture supplemented with a discussion 
assessment methods 

Combined exam 
Recommended literature


Blinn,J. Jim Blinn's Corner  A Trip Down the Graphics Pipeline. Morgan Kaufmann Publ, 1996.

Hartley, Richard; Zisserman, Andrew. Multiple view geometry in computer vision. Cambridge : Cambridge University Press, 2001. ISBN 0521623049.

Lengyel, Eric. Mathematics for 3D game programming and computer graphics. 2nd ed. Hingham : Charles River Media, 2004. ISBN 1584502770.

Lichtenbelt, Barthold; Crane, Randy; Naqvi, Shaz. Introduction to volume rendering. Upper Saddle River : Prentice Hall, 1998. ISBN 0138616833.

Penna,M.A., Patterson,R.R. Projective Geometry and its Application to Computer Graphics. Prentice Hall, 1986.

Shirley,Peter. Fundamentals of computer graphics.

Vince, John. Essential mathematics for computer graphics fast. London : Springer, 2001. ISBN 1852333804.
