Course detail

Descriptive geometry

FAST-GA06Acad. year: 2022/2023

Focal properties of conics. Perspective affinity, affine image of a circle, perspective colineation, colinear image of a circle. Coted projection. 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: Monge`s, 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. Stereography projection.

Prerequisites

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

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. 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. Plane section af a ball.

4. Coted projection. Straight line and plane of a given slope. Special construction.

5. Monge`s projection.

6. Monge`s projection. Sphere. Orthogonal axonometry.

7. Orthogonal axonometry.

8. Central projection.

9. Linear perspective projection.

10. Linear perspective projection.

11. Linear perspective projection.

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 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. Understand the geometric principles of photogrammetry. 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

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)
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 (CS)
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

Not applicable.

Classification of course in study plans

  • Programme B-P-C-GK Bachelor's

    branch GI , 1 year of study, winter semester, compulsory

  • Programme B-K-C-GK Bachelor's

    branch GI , 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. Plane section af a ball.

4. Coted projection. Straight line and plane of a given slope. Special construction.

5. Monge`s projection.

6. Monge`s projection. Sphere. Orthogonal axonometry.

7. Orthogonal axonometry.

8. Central projection.

9. Linear perspective projection.

10. Linear perspective projection.

11. Linear perspective projection.

12. Stereography projection.

13. Stereography projection.

Exercise

26 hod., compulsory

Teacher / Lecturer

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. Vertical picture, reconstruction of the elements of internal orientation.

13. Stereography projection. Seminar evaluation.