Course detail

Descriptive Geometry

FAST-BAA015Acad. year: 2025/2026

Orthogonal axonometry, skew axonometry, oblique projection. Linear perspective, basics of photogrammetry. Helix, right closed rule helicoidal surface. Surfaces of revolution . Warped surfaces. Lighting. Teoretical designs of roofs.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

Mgr. et Mgr. Jan Šafařík, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Construction of conics using their focal properties.Perspective collineation, perspectoive affinity, affine image of a circle.

Rules for evaluation and completion of the course

Students have to pass two credit tests, submit two drawings and other homework, 100% of attendance.
Followed by an exam with a pass rate of at least 50%.


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

Aims

After the course the students should understand and know how to use the basics of Monge projection, orthogonal axonometry, skew projection, and linear perspective.


Students should be able to construct conics using their focus properties, basics of stereometry, perspective colineation and affinity. Understand and get the basics of projection: Monge`s projection, axonometry and linear perspective. They should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. Students should be able to draw an object in a linear perspective. They construct a helix using specified elements, an orthogonal closed rule right helicoidal surface, circle and parabolic conoid, arcs.

Study aids

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, 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)
ČERNÝ, Jaroslav: Geometry, Vydavatelství ČVUT, Praha 1996. ISBN: 80-01-01535-1 (EN)
ŠAFAŘÍK, Jan: Technické osvětlení, Fakulta stavební VUT v Brně, 2022. https://mat.fce.vutbr.cz/studium/geometrie/ (CS)

Recommended reading

KOČANDRLOVÁ, Milada, ČERNÝ, Jaroslav: Konstruktivní geometrie, Česká technika - Nakladatelství ČVUT, Praha 2021. ISBN: 978-80-01-06049-0 (CS)

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Mgr. et Mgr. Jan Šafařík, Ph.D.

Syllabus

  • 1. Monge projection.
  • 2. Monge projection of simple surfaces, their sections and intersections with a straight line.
  • 3. Surfaces of revolution, thein tangent plane and plane sections.
  • 4. Basics of lighting. Technical lighting.
  • 5. Orthogonal axonometry.
  • 6. Orthogonal axonometry.
  • 7. Oblique projection.
  • 8. Linear perspective projection.
  • 9. Linear perspective projection.
  • 10. Linear perspective projection.
  • 11. Theoretical solution of roofs.
  • 12. Higher order warped surfaces, arcs.
  • 13. Helix, helicoidal conoid.

Exercise

26 hod., compulsory

Teacher / Lecturer

Mgr. et Mgr. Jan Šafařík, Ph.D.

Syllabus

  • 1. Monge projection.
  • 2. Projections of a simple bodies and surfaces, their sections and intersections with a straight line.
  • 3. Tangent plane of a surface of revolution, section of a surface of revolution.
  • 4. Lighting, technical lighting.
  • 5. Orthogonal axonometry. Metric problems in coordinate planes.
  • 6. Orthogonal axonometry. Projections of simple bodies and surfaces, their sections and intersections with a straight line.
  • 7. Projecting in oblique projection. Projection of a circle in a coordinate plane. Displaying simple bodies. Cutting method.
  • 8. Linear perspective. Intersection method. Constructing a free perspective.
  • 9. Linear perspective. Method of rotated ground plan. Other methods of projecting a perspective.
  • 10. Linear perspective. Vertical picture. Reconstructing an object from a perpendicular picture.
  • 11. Theoretical solutions of the roofs.
  • 12. Higher-order warped surfaces.
  • 13. Constructing a helix. Right helicoidal conoid. Credits.