Gurantor department | Department of Mathematics | Credits | 5 |

Subject guarantor | Mgr. Dagmar Dlouhá, Ph.D. | Subject version guarantor | Mgr. František Červenka |

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 3 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | HGF | Intended for study types | Bachelor |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

CER0007 | Mgr. František Červenka | ||

DLO44 | Mgr. Dagmar Dlouhá, Ph.D. | ||

DOL75 | Mgr. Jiří Doležal |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Part-time | Credit and Examination | 16+0 |

• to solve planimetric and stereometric tasks with the help of computer
• to know how to characterize geometric curves and surfaces by synthetic and also analytic way
• to acquaint with geometric and physical principles of 3D modeling

Lectures

Individual consultations

Tutorials

Project work

Other activities

The course combines geometric and computer disciplines - planimetry, stereometry, analytic geometry, 3D modeling, computer graphics and programming.
In the exercise there is used free software GeoGebra and POV-Ray.

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.

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. ISBN 978-981-4740-23-4.
Falconer, K. J. Fractal geometry: mathematical foundations and applications. 3rd ed. Chichester: Wiley, 2014. ISBN 978-1-119-94239-9.

Credit and test requirements
Conditions for granting credit
- participation in seminars
Term project
- Creating an animated movie of your own using POV-Ray
- the theme is, if possible, a real scene with several objects in a suitable composition
- Up to 2 members can work on one subject
- Creation in POV-Ray environment is evaluated: suitable choice of geometric objects, level of execution of their external appearance, use of set operations CSG, realization of more identical or similar objects by means of programming directives (use of cycles, conditions, etc.), transparency of source code (use of notes), parameterization of objects in the scene (suitable parameter names), resulting animation
- overall: the idea, using as many objects and options as possible, using unexplored objects and options (own initiative)
Exam
- The exam will be divided into two parts and can be completed in one regular and two correction terms
- practical part - defense of semester project
- theoretical question
Scoring
- Practical part of the exam is evaluated by max. 80 points, minimum 25 points are required
- at the theoretical part it is possible to reach max. 20 points, at least it is necessary to have at least 5 points
- The overall rating is based on a standard table
points mark
86-100 1 excellent
66-85 2 very good
51-65 3 well
0-50 4 failed

They are no other requests fo students.

Subject has no prerequisities.

Subject has no co-requisities.

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

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 20 | 5 |

Examination | Examination | 80 (80) | 30 |

Written test | Written test | 60 | 25 |

Oral exam | Oral examination | 20 | 5 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2021/2022 | (B2110) Geological Engineering | (2101R003) Geological Engineering | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2021/2022 | (B1316) Geodesy, Cartography and Geoinformatics | (3646R006) Geoinformatics | K | Czech | Ostrava | 3 | Choice-compulsory | study plan | ||||

2021/2022 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2020/2021 | (B2110) Geological Engineering | (2101R003) Geological Engineering | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B1316) Geodesy, Cartography and Geoinformatics | (3646R006) Geoinformatics | K | Czech | Ostrava | 3 | Choice-compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Most | 2 | Choice-compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (3902R064) System Engineering in Industry | K | Czech | Most | 2 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (B2110) Geological Engineering | (2101R003) Geological Engineering | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2019/2020 | (B1316) Geodesy, Cartography and Geoinformatics | (3646R006) Geoinformatics | K | Czech | Ostrava | 3 | Choice-compulsory | study plan | ||||

2019/2020 | (B2102) Mineral Raw Materials | (3902R064) System Engineering in Industry | K | Czech | Most | 2 | Compulsory | study plan | ||||

2019/2020 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Most | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (B2102) Mineral Raw Materials | (3904R022) Waste Treatment and Disposal | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (B2102) Mineral Raw Materials | (3904R022) Waste Treatment and Disposal | K | Czech | Most | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | K | Czech | Ostrava | 2 | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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