Course detail

Basics of Descriptive Geometry

FAST-VAC001Acad. year: 2022/2023

Euclidean constructions in plane, identical and similarity transforms in plane, construction of ellipse by focus properties, basics of solid geometry, basics of parallel and central projection, perspective affinity, perspective collineation, circle in affinity, coted projection, orthogonal axonometry.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

Mgr. et Mgr. Jan Šafařík, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

The students should be able to construct ellipse by focus properties, the principles of perspective affinity, perspective collineation. They will get the basics of projection: coted projection, orthogonal axonometry, basic problems and be able to solve simple 3D problems, display simple geometric solids and surfaces in each type of projection.

Prerequisites

Basic knowledge of planar and 3D geometry as taught at secondary schools and basic skills of work with a ruler and pair of compasses.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Constructions of basic figures in plane (euclidean constructions in plane, identical and similarity transforms). Extended Euclidean space. Construction of ellipse by focus properties.

2. Central and parallel projection. Perspective affinity, perspective collineation, examples.

3. Circle in affinity. Basic of solid geometry. Simple solids (pyramid, prism, cone, cylinder,sphere). System of basic problems. Coted projection

4. Coted projection.

5. Coted projection. Projection of circle.

6. Coted projection. Constructional problems.

7. Coted projection. Projection of a solid.

8. Orthogonal axonometry. Basic problems.

9. Orthogonal axonometry. Position problems.

10. Seminar evaluation.

Work placements

Not applicable.

Aims

Students should be able to construct: Euclidean constructions in plane, identical and similarity transforms in plane, ellipse by focus properties, understand the principles of perspective affinity, perspective collineation, using such properties in solving problems, understand and get the basics of projection: coted projection, orthogonal axonometry. They should develop 3D visualization and be able to solve simple 3D problems, display simple geometric solids and surfaces in each type of projection.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BULANTOVÁ, Jana, HON, Pavel, PRUDILOVÁ, Květoslava, PUCHÝŘOVÁ, Jana, ROUŠAR, Josef, ROUŠAROVÁ, Veronika, SLABĚŇÁKOVÁ, Jana, ŠAFAŘÍK, Jan, ŠAFÁŘOVÁ, Hana, ZRŮSTOVÁ, Lucie: Deskriptivní geometrie, verze 4.0 pro I. ročník Stavební fakulty Vysokého učení technického v Brně, Soubor CD-ROMů Deskriptivní geometrie, Fakulta stavební VUT v Brně, 2012. ISBN 978-80-7204-626-3. (CS)
BULANTOVÁ, Jana, MENCÁKOVÁ, Kristýna, MORÁVKOVÁ, Blanka, RÝPAROVÁ, Lenka, ŠAFAŘÍK, Jan, ZRŮSTOVÁ, Lucie: Sbírka řešených příkladů z konstruktivní geometrie, Fakulta stavební VUT v Brně, 2021. https://www.geogebra.org/m/ejhn4jay (CS)

Recommended reading

BULANTOVÁ, Jana, PRUDILOVÁ, Květoslava, PUCHÝŘOVÁ, Jana, ROUŠAR, Josef, ROUŠAROVÁ, Veronika, SLABĚŇÁKOVÁ, Jana, ŠAFAŘÍK, Jan, ŠAFÁŘOVÁ, Hana, ZRŮSTOVÁ, Lucie: Sbírka řešených příkladů z deskriptivní geometrie pro I. ročník Stavební fakulty Vysokého učení technického v Brně, Fakulta stavební VUT v Brně, 2006. https://mat.fce.vutbr.cz/studium/geometrie/ (CS)
BULANTOVÁ, Jana, PRUDILOVÁ, Květoslava, ROUŠAR, Josef, ŠAFAŘÍK, Jan, ZRŮSTOVÁ, Lucie: Sbírka zkouškových příkladů z deskriptivní geometrie pro I. ročník Stavební fakulty Vysokého učení technického v Brně, Fakulta stavební VUT v Brně, 2009. https://mat.fce.vutbr.cz/studium/geometrie/ (CS)

Classification of course in study plans

  • Programme BPC-VP Bachelor's 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Mgr. et Mgr. Jan Šafařík, Ph.D.

Syllabus

1. Constructions of basic figures in plane (euclidean constructions in plane, identical and similarity transforms). Extended Euclidean space. Construction of ellipse by focus properties.

2. Central and parallel projection. Perspective affinity, perspective collineation, examples.

3. Circle in affinity. Basic of solid geometry. Simple solids (pyramid, prism, cone, cylinder,sphere). System of basic problems. Coted projection

4. Coted projection.

5. Coted projection. Projection of circle.

6. Coted projection. Constructional problems.

7. Coted projection. Projection of a solid.

8. Orthogonal axonometry. Basic problems.

9. Orthogonal axonometry. Position problems.

10. Seminar evaluation.