Course detail

Descriptive geometry

FAST-MA02Acad. year: 2024/2025

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

Mode of study

Not applicable.

Guarantor

RNDr. Jan Vondra, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

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

Rules for evaluation and completion of the course

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

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.

Study aids

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 literature

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 hod., 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 hod., 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.