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 | 2 | Semester | summer |

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 |

Full-time | Credit and Examination | 2+2 |

• 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
- 70% absence attendance can be excused
- elaboration of assigned homework
0-15 points
Term project
creating a 3D model according to the assignment
- Up to 2 members can work on one model
- Creation means modeling in appropriate modeling software
division into individual printable parts, optimization in terms of quality and quantity of material,
3D printing itself
creating a realistic scene
- rated: appropriate choice of geometric objects, level of their execution
external appearance, use of set operations CSG, realization of more
the same or similar objects using the programmer directives (using cycles, conditions, etc.)
source code clarity (use of notes), parameterization
objects in the scene (appropriate parameter names), resulting animation
- Overall, the idea is: the idea of using as many as possible
objects and options, use of unobstructed 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
- plane geometry - elaboration of given examples 0-30 points
- spatial modeling - elaboration of given examples or defense of semester project 0-30 points
theoretical test 0-20 points
Scoring
- Practical part of the exam is evaluated by max. 60 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.

Program of lectures
=================
Week Lecture content
-------------------------------------------------- -----------------------------
1 Basic geometric objects (point, line, plane), concepts and constructions
2 Planimetry - properties of triangles, construction of basic triangles (height, center of gravity, angles)
3 Planimetry - construction of triangles advanced, uniformity (tangent of two circles, triangle inscribed in squares)
4 Conic sections - derivation from a rotational conical surface, definition and construction of an ellipse
5 Conics - definition and construction of a hyperbola
6 Conic sections - definition and construction of a dish
7 Kinematic geometry - elliptic and cardioid motion, conchoidal and cyclic movements
8 Stereometry - cube sections, slices of other bodies
9 Modeling and 3D Printing - Introduction to 3D Modeling and 3D Printing (Technology, Materials)
10 Modeling and 3D Printing - Basic Bodies (Spheres, Cylinders, Cones, Blocks)
11 Modeling and 3D Printing - Transform (Shift, Rotate, Scale)
12 Modeling and 3D Printing - Set Operations (Unification, Intersection, Difference)
13 Modeling and 3D Printing - Visual Programming (Mathematical Functions, Cycles)
14 Reserve
Exercise and seminar program + individual student work
================================================== ======
Week Content of seminars and seminars
-------------------------------------------------- -----------------------------
1 Basic geometric objects (point, line, plane), concepts and constructions
2 Planimetry - properties of triangles, construction of basic triangles (height, center of gravity, angles)
3 Planimetry - construction of triangles advanced, uniformity (tangent of two circles, triangle inscribed in squares)
4 Conic sections - derivation from a rotational conical surface, definition and construction of an ellipse
5 Conics - definition and construction of a hyperbola
6 Conic sections - definition and construction of a dish
7 Kinematic geometry - elliptic and cardioid motion, conchoidal and cyclic movements
8 Stereometry - cube sections, slices of other bodies
9 Modeling and 3D Printing - Introduction to 3D Modeling and 3D Printing (Technology, Materials)
10 Modeling and 3D Printing - Basic Bodies (Spheres, Cylinders, Cones, Blocks)
11 Modeling and 3D Printing - Transform (Shift, Rotate, Scale)
12 Modeling and 3D Printing - Set Operations (Unification, Intersection, Difference)
13 Modeling and 3D Printing - Visual Programming (Mathematical Functions, Cycles)
14 Reserve

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 |

Písemná zkouška | Written examination | 60 | 25 |

Ústní zkouška | 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 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (B2110) Geological Engineering | (2101R004) Geoscience and Industrial Tourism | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (B2110) Geological Engineering | (2101R004) Geoscience and Industrial Tourism | P | Czech | Most | 2 | Optional | study plan | ||||

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

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

2019/2020 | (B1088A330001) Geoscience and Industrial Tourism | P | Czech | Most | 3 | Optional | study plan | |||||

2019/2020 | (B1088A330001) Geoscience and Industrial Tourism | P | Czech | Ostrava | 3 | Optional | study plan | |||||

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

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

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

2019/2020 | (B2102) Mineral Raw Materials | (3904R028) Environmental Biotechnology | P | Czech | Ostrava | 2 | Optional | study plan |

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