Geometry with Computer

Type of study	Bachelor
Language of instruction	Czech
Code	230-0442/03
Abbreviation	GP
Course title	Geometry with Computer
Credits	5
Coordinating department	Department of Mathematics
Course coordinator	Mgr. Dagmar Dlouhá, Ph.D.

Osnova předmětu

1. Basic geometric objects (point, line, plane), terms and constructions
2. Planimetry - properties and constructions of triangles (altitudes, medians, angles, identity mappings, inscribed circle, add to trapezium), homothety (tangent of two circles, triangle inscribed to square)
3. Conics - derived from right circular conical surface, the definition and construction of an ellipse, a hyperbola and a parabola
4. Kinematic Geometry - elliptical and cadioidical motion, conchoidical and cyclical movements
5. Stereometry - cuts of a cube and other solids
6. Introduction to PovRAY, basic elements of the scene (camera, light, background)
7. Basic solids (sphere, cylinder, cone, cuboid)
8. Colors, textures
9. Transformations (translation, rotation, scaling)
10. Set operations (union, intersection, difference)
11. Creating of a realistic static scene
12. PovRay programming (variables, while loop, mathematical function), Implicit surfaces (BLOB)
13. Creating dynamically generated static scene
14. Animation (clock variables and framenumber, controlling of animated objects trajectories), Realistic animation of static scene

E-learning

http://www.studopory.vsb.cz
http://mdg.vsb.cz
(in Czech language)

Povinná literatura

Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1.
Vavříková, Eva: Descriptive Geometry, VŠB – TUO, Ostrava 2005.
Foley, J., van Dam, A., Feiner, S., Hughes, J.: Computer Graphics-Principles and Practise. 2nd ed., Addison-Wesley, Reading, Massachusetts, 1990.
Stillwell, J.: Geometry of surfaces. New York: Springer, 1992. ISBN 0-387-97743-0.

Advised literature

Kreyszig, E.: Differential geometry. New York: Dover Publications, 1991. ISBN 0-486-66721-9.
Kobayashi, S.: Transformation groups in differential geometry. Berlin: Springer, 1972. Classics in mathematics. ISBN 3-540-05848-6.
Umehara, M. and Yamada, K.: Differential geometry of curves and surfaces. Kaiteiban. Translate Rossman, W.. Singapore: World Scientific, 2017. .
Falconer, K. J. Fractal geometry: mathematical foundations and applications. 3rd ed. Chichester: Wiley, 2014. ISBN 978-1-119-94239-9.

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