Course detail

Descriptive Geometry

FAST-AA002Acad. year: 2024/2025

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

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

RNDr. Jana Slaběňáková

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. Monge´s projection.

Rules for evaluation and completion of the course

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 orthogonal axonometry, skew projection, and linear perspective.
After the course the students should understand and know how to use the basics of orthogonal axonometry, skew projection, and linear perspective.Helix, developable helicoidal surface, right closed rule helicoidal surface. Surfaces of revolution . Warped surfaces. Lighting. Teoretical designs of roofs. Introduction to topopgraphic surfaces.

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, 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)
ŠAFAŘÍK, Jan: Techniské osvětlení, Fakulta stavební VUT v Brně, 2022. https://mat.fce.vutbr.cz/studium/geometrie/ (CS)

Recommended reading

Not applicable.

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Jana Slaběňáková

Syllabus

1. Basics of lihting. Technical lighting.

2. Surfaces of revolution, sections of surfaces of revolution.

3. Lighting of surfaces of revolution .

4. Axonometry – basics.

5. Orthogonal axonometry.

6. Skew axonometry, oblique projection.

7. Linear perspective.

8. Linear perspective.

9. Basics of photogrammetry. Reconstruction from a vertical picture.

10. Warped quadrics. Hyperbolic paraboloid. One-sheet hyperboloid.

11. Higher order warped surfaces. Theoretical designe of roofs.

12. Helix, developable helicoidal surface, helicoidal conoid.

13. Topographic surfaces.

Exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Jana Slaběňáková

Syllabus

1. Revision – Monge projection.

2. Projections of a simple bodies and surfaces, their sections and intersections with a straight line. Technical lighting.

3. Tangent plane of a surface of revolution, section of a surface of revolution.

4. Lighting of a surface of revolution.

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. Warped hyperboloid, construction. Hyperbolic paraboloid. Hyperbolic paraboloid given by skew tetragon. Roofing by hyperbolic paraboloid.

12. Higher-order warped surfaces. Theoretic design of roofs.

13. Constructing a helix. Right helicoidal conoid. Credits.