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Terminated in academic year 2019/2020

Geometry with Computer

Type of study Bachelor
Language of instruction English
Code 714-0556/03
Abbreviation GP
Course title Geometry with Computer
Credits 5
Coordinating department Department of Mathematics and Descriptive Geometry
Course coordinator Mgr. František Červenka

Subject syllabus

The program of lectures
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1 Basic geometric objects (point, line, plane), terms and constructions
2 Planimetry - properties of triangles
3 Planimetry - basic constructions of triangles (altitudes, medians, angles)
4 Planimetry - advanced constructions of triangles (identity mappings, inscribed circle, add to trapezium)
5 Planimetry - homothety (tangent of two circles, triangle inscribed to square)
6 Conics - derived from right circular conical surface, the definition of an ellipse
7 Conics - construction of an ellipse of the specified elements
8 Conics - definition and construction of a hyperbola
9 Conicc - definition and construction of a parabola
10 Kinematic Geometry - elliptical and cadioidical motion
11 Kinematic Geometry - conchoidical and cyclical movements
12 Stereometry - cuts of a cube
13 Stereometry - cuts of other solids
14 Reserve


Program of exercises and seminars + individual students' work
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1 Introduction to PovRAY, basic elements of the scene (camera, light, background)
2 Basic solids (sphere, cylinder, cone, cuboid)
3 Colors, textures
4 Transformations (translation, rotation, scaling)
5 Set operations (union, intersection, difference)
6 Practical Workshop - creating of a realistic static scene
7 PovRay programming (variables, while loop)
8 Implicit surfaces (BLOB)
9 Programming in PovRay (mathematical function)
10 Practical Workshop - creating dynamically generated static scene
11 Animation (clock variables and framenumber)
12 Animation (controlling of animated objects trajectories)
13 Practical Workshop - realistic animation of static scene
14 Practical Workshop - Preparation of semestral project

Literature

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.

Advised literature

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.