Course Details

Descriptive geometry

Academic Year 2023/24

GA06 course is part of 1 study plan

​ B-P-C-GK / GI Winter Semester 1st year

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.

Credits

6 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

Mgr. et Mgr. Jan Šafařík, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

Entry Knowledge

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

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.


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.

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, 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)
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)
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)
ČERNÝ, Jaroslav: Geometry, Vydavatelství ČVUT, Praha 1996. ISBN: 80-01-01535-1 (cs)

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.

Prerequisites

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

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

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

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/271676

Lecture

13 weeks, 3 hours/week, elective

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

13 weeks, 2 hours/week, compulsory

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.