Course detail

Descriptive geometry

FAST-MA02Acad. year: 2021/2022

Focal properties of conics. Perspective affinity, affine properties of a circle, perspective colineation, colinear image of a circle. Coted projection.Monges´s projection. Basics of orthogonal axonometry.Basics of central projection.Linear perspective (perspective of an object using relative and free methods). Basics of photogrammetry. Vertical picture, reconstruction of the elements of internal orientation.

Language of instruction

Czech

Number of ECTS credits

5

Guarantor

RNDr. Jan Vondra, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Basic knowledge of planar and 3D geometry as taught at secondary schools.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Lectures
1. Extended Euclidean space. Perspective affinity, collineation.
2. Curve affine to a circle. Coted projection.
3. Coted projection. Projection of a solid.
4. Coted projection. Section of a body.Line and plane of a given slope.
5. Monge`s projection.
6. Monge`s projection. Sphere.
7. Orthogonal axonometry.
8. Central projection.
9. Central projection. Perspective projection.
10. Perspective projection.
11. Perspective projection.
12. Perspective projection. Basics of photogrammetry. Vertical picture - reconstruction of the elements of internal orientation.
13. Reconstruction of the elements of internal orientation.

Work placements

Not applicable.

Aims

Know how to construct conics from the properties of their foci. Understand and apply the principles of perspective colineation and perspective affinity. Understand and know the basics of coted and Monge`s projection and orthogonal axonometry, central projection and perspective projection. Display basic geometric bodies in each projection.Construct sections of elementary bodies by a plane in coted and Monge´s projection. Sphere in Monge´s projection. Constructions in a plane in central projection and the projection of a simple body. Project a building using a perspective projection. Understand the geonmetric principles of photogrammetry.

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

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BULANTOVÁ,J.,HON,P.,PRUDILOVÁ,K.,PUCHÝŘOVÁ,J.,ROUŠAR,J.,ROUŠAROVÁ,V.,SLABĚŇÁKOVÁ,J.,ŠAFAŘÍK,J.: Deskriptivní geometrie, multimediální CD-ROM. FAST VUT v Brně, 2012. ISBN 978-80-7204-787-1. (CS)

Recommended reading

PISKA,R.; MEDEK,V.: Deskriptivní geometrie, II. díl. SNTL Praha, Alfa Bratislava, 1975. (CS)
PISKA,R.; MEDEK,V.: Deskriptivní geometrie, I. díl. SNTL Praha, Alfa Bratislava, 1975. (CS)
Kopřivová,H.: Deskriptivní geometrie I,II. Vydavatelství ČVUT Praha, 1999. (CS)
Černý J., Kočandrlová M.: Konstruktivní geometrie 10 (sbírka příkladů). ČVUT Praha, 2002. (CS)
Černý J., Kočandrlová M.: Konstruktivní geometrie. ČVUT Praha, 2003. (CS)

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

RNDr. Jan Vondra, Ph.D.

Syllabus

Lectures 1. Extended Euclidean space. Perspective affinity, collineation. 2. Curve affine to a circle. Coted projection. 3. Coted projection. Projection of a solid. 4. Coted projection. Section of a body.Line and plane of a given slope. 5. Monge`s projection. 6. Monge`s projection. Sphere. 7. Orthogonal axonometry. 8. Central projection. 9. Central projection. Perspective projection. 10. Perspective projection. 11. Perspective projection. 12. Perspective projection. Basics of photogrammetry. Vertical picture - reconstruction of the elements of internal orientation. 13. Reconstruction of the elements of internal orientation.

Exercise

26 hours, compulsory

Teacher / Lecturer

RNDr. Jan Vondra, Ph.D.

Syllabus

Seminars 1. Focal properties of conics. 2. Perspective collineation, perspective affinity. Constructing an ellipse based on affinity. 3. Collinear image of a n-gonal and a circle. 4. Coted projection. 5. Coted projection. 6. Monge´s projection. 7. Monge´s projection. Sphere. Credit test. 8. Orthogonal axonometry. 9. Central projection. 10. Linear perspective. 11. Linear perspective. Credit test. 12. Linear perspective. 13. Vertical picture - reconstruction of the elements of internal orientation. Credits.