Course detail

# Descriptive Geometry

FAST-BAA015Acad. year: 2022/2023

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

4

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

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.

Prerequisites

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

Co-requisites

Not required.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Information is conveyed in the form of lectures and practiced in seminars. Consultation periods are available to students. Assigned work is part of the study activities of the students.

Assesment methods and criteria linked to learning outcomes

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%.

Course curriculum

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.

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

Students can register for the optional subject VAC001. The contents of the course is an introduction to the issues of the subject of descriptive geometry.

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)
ŠAFAŘÍK, Jan: Technické 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 (EN)

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 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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.