Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |

Subject guarantor | Mgr. František Červenka | Subject version guarantor | Mgr. Jana Bělohlávková |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | English | ||

Year of introduction | 2016/2017 | Year of cancellation | |

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

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

Login | Name | Tuitor | Teacher giving lectures |

BEL10 | Mgr. Jana Bělohlávková |

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

Form of study | Way of compl. | Extent |

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

• to train development of space abilities
• to handle by different types of projection methods, to understand to their principles, to be familiar with their properties, advantages and disadvantages
• to acquaint with geometric characteristics of curves and surfaces that are used in technical practice of a given specialization

Lectures

Individual consultations

Tutorials

Focus properties of conic sections. The two-plane method. Perspective affinity.
Orthogonal axonometry. Orthogonal image of circle. Prismatic surface.
Cylindrical surface. Pyramidal surface. Conical surface. Central collineation.
Spherical surface. Surfaces of rotation. Quadrics of rotation. One-sheet
hyperboloid of rotation. Circular helix. Spiral surfaces.

Černý, J.: Geometry. Vydavatelství ČVUT,Praha 1996,ISBN 80-01-01535-1
Kargerová, M.: Geometry and Computer Graphics. Praha 1998, ISBN 80-01-01816-4

1/ Plocková, E. - Řehák, M.: Sbírka řešených příkladů z DG a KG, díl 3. -
Mongeovo promítání. Skriptum VŠB - TU, Ostrava 1995.
2/ Stejskalová, J. - Vrbenská, H.: Sbírka řešených příkladů z DG a KG, díl 4. -
Axonometrie. Skriptum VŠB - TU, Ostrava 1995.
3/ Urban, A.: Deskriptivní geometrie I, II, Praha, SNTL, 1967.
4/ Doležal, M. - Poláček, J. - Tůma, M.: Sbírka řešených příkladů z DG a KG,
díl 5. - Rotační a šroubové plochy. Skriptum VŠB - TU, Ostrava 1995.

Course credit
========================================================
To obtain a credit the student has to submit 3 drawings. Student can get 12 points for attendance of the lectures and another 8 points for properly solved homework. A maximum of 20 points.
Exam
========================================================
Written part of an exam is classified by 0 - 60 points. The part is successful if student obtains at least
25 points.
Oral part of the exam is classified by 0 - 20 points. The part is successful if student obtains
at least 5 points.
Point quantification in the interval 100 - 91, 90 - 81, 80 - 71, 70 - 61, 60 - 51, 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
A set of topics for the theoretical part of the exam
========================================================
1) Monge projection – position tasks.
2) Monge projection - metric tasks.
3) Orthogonal axonometry - basic position tasks.
4) Orthogonal projection of a circle (Rytz construction).
5) Monge projection - views of a circle in a general plane.
6) Prism surface – cut by a plane.
7) Cylindrical surface – cut by a plane.
8) Pyramid surface – cut by a plane.
9) Construction of a sphere, cut of a sphere by a plane, intersection of line and solid.
10) Focal properties of conics - ellipse, hyperbola, parabola.
11) Construction of conics.
12) Surfaces of revolution - development, application, construction of the tangent plane.
13) Surfaces of revolution - quadrics - development, application, construction of the tangent plane.
14) Intersections of surfaces of revolution.
15) Intersections of quadrics.
16) Design and layout of helix.
17) Screw ruled surfaces - the classification, tangent plane.

www.studopory.vsb.cz

There are no more requirements.

Subject has no prerequisities.

Subject has no co-requisities.

The program of lectures
=================
1 Introduction to constructive geometry, axial affinity
2 Monge projection – position tasks
3 Monge projection - metric tasks
4 Orthogonal axonometry - basic position tasks
5 Orthogonal projection of the circle (trammel construction, Rytz construction)
6 Views of circle in the projection plane (ax.) and in a general plane (MP)
7 Prism surface, cylindrical surface – cut by a plane
8 Central collineations, pyramid surface – cut by a plane
9 Conical surface, sphere – cut by a plane perpendicular to the projection plane.
10 Intersections of a line and solids
11 Helix, screw surfaces
12 Surfaces of revolution - creation, application
13 Intersections of surfaces of revolution
14 Reserve
Program of exercises and seminars + individual students' work
================================================== ======
1 A focal properties of conic sections - ellipse, hyperbola, parabola
2 Construction of elements of the conics
3 Basic position tasks in Monge projection
4 Basic metric tasks in Monge projection
5 Basic position tasks at orthogonal axonometry
6 Views of circle; constructions of a prism and pyramid out from given elements
7 Construction of a sphere, cylinder and cone from given elements
8 Cuts of a prism, pyramid, and cylinder by a plane
9 Cut of a sphere by a plane, intersection of line and the solid
10 Design and layout of helix
11 Screw ruled surfaces - the classification, tangent plane
12 Surfaces of revolution - the development, construction of the tangent plane
13 Intersections of surfaces of revolution
14 Reserve

Conditions for completion are defined only for particular subject version and form of study

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

2018/2019 | (B2341) Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B2341) Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (B2341) Engineering | P | English | Ostrava | 1 | Compulsory | study plan |

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

ECTS - MechEng - Bachelor Studies | 2019/2020 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2018/2019 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block |