Course Details

Descriptive Geometry

Academic Year 2023/24

AA002 course is part of 1 study plan

​ B-P-C-APS (N) / APS Winter Semester 1st year

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.

Credits

4 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

RNDr. Jana Slaběňáková

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

Entry Knowledge

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

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.

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

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.

Prerequisites

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

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/273893

Lecture

13 weeks, 2 hours/week, elective

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

13 weeks, 2 hours/week, compulsory

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.