Course detail

Descriptive geometry

FAST-BAA007Acad. year: 2022/2023

Focal properties of conics. Perspective affinity, affine image of a circle, perspective colineation, colinear image of a circle. Coted projection, application on a topographic surface. Projecting on two perpendicular planes. Basics of orthogonal axonometry, central projection. Linear perspective (perspective of an object using relative and free methods). Stereography projection.

Language of instruction

Czech

Number of ECTS credits

6

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

Students should be able to construct conics from the properties of their foci, perspective colineation, perspective affinity. Understand the basics of projections: coted projection, Monge`s projection, orthogonal axonometry, central projection and perspective projection. Display the basic geometric bodies in each projection. Construct sections of bodies. Project a building using a perspective projection. Topographic surfaces. Stereography projection.

Prerequisites

Basic knowledge of planar and 3D geometry as taught at secondary schools.

Co-requisites

Not required.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

Assesment methods and criteria linked to learning outcomes

Students have to pass two credit tests, submit two/three drawings and other homework.
Followed by an exam with a pass rate of at least 50%.

Course curriculum

1. Extended Euclidean space. Perspective affinity, collineation. Curve affine to a circle.
2. Curve in collineation to a circle. Geodetic curve, developable surfaces. Coted projection.
3. Coted projection.
4. Coted projection. Topographic surfaces.
5. Monge`s projection.
6. Monge`s projection. Sphere. Orthogonal axonometry.
7. Orthogonal axonometry.
8. Central projection.
9. Central projection. Linear perspective projection.
10. Linear perspective projection.
11. Reconstruction of the elements of internal orientation.
12. Stereography projection.
13. Stereography projection.

Work placements

Not applicable.

Aims

Know how to construct conics from the properties of their foci. Understand and apply the principles of perspective colineation and perspective affinity. Understand the basics of coted projection, Monge`s projection and orthogonal axonometry, central projection and perspective projection. Display basic geometric bodies in each projection. Construct sections of bodies by a plane. Constructions in a plane in central projection and the projection of a simple body. Project a building using a perspective projection. Topographic surfaces. Stereography 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

Students can register for the optional subject VAC001. The contents of the course is an introduction to the issues of the subject of descriptive geometry.

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)
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)
ČERNÝ, Jaroslav: Geometry, Vydavatelství ČVUT, Praha 1996. ISBN: 80-01-01535-1 (EN)
KRÁLOVÁ, Alice: Konstruktivní geometrie, Topografické plochy, Mendelova univerzita. http://user.mendelu.cz/balcarko/Top_Plochy.pdf (CS)
ŠAFAŘÍK, Jan: Cvičení z deskriptivní geometrie pro obor Geodézie a kartografie, Fakulta stavební VUT v Brně, 2022. https://mat.fce.vutbr.cz/studium/geometrie/ (CS)
TALANDA, Pavel: Deskriptivní geometrie, Vybrané kapitoly z kartografie pro obor geodezie, Fakulta stavební VUT, Brno 2014. (CS)

Recommended reading

HAVRANOVÁ, Zuzana: Deskriptívna geometria I, Pracovné listy I, Riešenie úloh, Slovenská technická univerzita v Bratislave v Nakladateľstvu STU, Bratislava, 2016. ISBN: 978-80-227-4644-1 (SK)
HAVRANOVÁ, Zuzana: Deskriptívna geometria I, Pracovné listy I, Slovenská technická univerzita v Bratislave v Nakladateľstvu STU, Bratislava, 2015. ISBN: 978-80-227-4496-6 (SK)
KOČANDRLOVÁ, Milada, ČERNÝ, Jaroslav: Konstruktivní geometrie, Česká technika - Nakladatelství ČVUT, Praha 2021. ISBN: 978-80-01-06049-0 (CS)
TALANDA, Pavel: Deskriptivní geometrie pro obor geodezie a kartografie, 3. vydání, Akademické nakladatelství CERM, Brno 1999. ISBN: 80-214-0447-7 (CS)

Classification of course in study plans

  • Programme BPC-GK Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

Mgr. et Mgr. Jan Šafařík, Ph.D.

Syllabus

1. Extended Euclidean space. Perspective affinity, collineation. Curve affine to a circle.
2. Curve in collineation to a circle. Geodetic curve, developable surfaces. Coted projection.
3. Coted projection.
4. Coted projection. Topographic surfaces.
5. Monge`s projection.
6. Monge`s projection. Sphere. Orthogonal axonometry.
7. Orthogonal axonometry.
8. Central projection.
9. Central projection. Linear perspective projection.
10. Linear perspective projection.
11. Reconstruction of the elements of internal orientation.
12. Stereography projection.
13. Stereography projection.

Exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Jana Slaběňáková
Mgr. et Mgr. Jan Šafařík, Ph.D.

Syllabus

1. Focal properties of conics.
2. Perspective collineation, perspective affinity. Constructing an ellipse based on affinity.
3. Collinear image of a n-gonal and a circle.
4. Coted projection.
5. Coted projection. Aplications.
6. Monge´s projection.
7. Monge´s projection. Sphere. Test.
8. Orthogonal axonometry.
9. Central projection.
10. Linear perspective.
11. Test. Linear perspective.
12. Linear perspective.
13. Stereography projection. Seminar evaluation.