Course Details

Basics of Descriptive Geometry

Academic Year 2025/26

VAC001 course is not part of any programme in the faculty

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.

Credits

2 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

Entry Knowledge

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

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.


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.

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, 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)

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/294937

Lecture

13 weeks, 2 hours/week, elective

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.