Course detail

Descriptive geometry

FAST-GA02Acad. year: 2013/2014

Focal properties of conics. Perspective affinity, affine image of a circle, perspective colineation, colinear image of a circle. Coted projection. Projecting on two perpendicular planes. Basics of orthogonal axonometry, 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. Ortography projection.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

RNDr. Květoslava Prudilová

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Students should be able to construct conics from the properties of their foci, perspective colineation, perspective affinity. Understand the basics of projections: Monge`s, orthogonal axonometry, central projection and perspective projection. Display the basic geometric bodies in each projection. Construct sections of bodies. Project a building using a perspective projection. Vertical picture, reconstruction of the elements of internal orientation. Ortography projection.

Prerequisites

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

Co-requisites

Not applicable.

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 - lectures, seminars.

Assesment methods and criteria linked to learning outcomes

Full-time study programme: Students have to pass two credit tests, submit two drawings and other homework.
Followed by an exam with a pass rate of at least 50%.
Combined study programme: Students will do 5 texts during the semester and send them to the lecturer. Their successful completion is a condition for getting the credit. An exam with a pass rate of at least 50% will follow.

Course curriculum

Lectures
1. Extended Euclidean space. Perspective affinity, collineation.
2. Curve affine to a circle. Coted projection.
3. Coted projection. Simple bodies and surfaces.
4. Coted projection. Section of a body. Straight line and plane of a given slope.
5. Monge`s projection.
6. Monge`s projection. Spere.
7. Orthogonal axonometry.
8. Central projection.
9. Central projection. Perspective projection. Introduction, projection scheme.
10. Linear perspective.
11. Linear perspective.
12. Linear perspective.
13. Reconstruction of the elements of internal orientation.
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. Basic constructions. Projection of a body.
5. Coted projection. Section of a body by a plane.
6. Monge´s projection. Basic constructions. Projection of a body.
7. Monge´s projection. Sphere. Test.
8. Orthogonal axonometry.
9. Central projection.
10. Linear perspective.
11. Test. Linear perspective.
12. Linear perspective.
13. Vertical picture, reconstruction of the elements of internal orientation. Seminar evaluation.




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 the basics of Monge`s projection and orthogonal axonometry, central projection and perspective projection. Display basic geometric bodies in each projection. Construct sections of bodies by a plane. Constructions in a plane in central projection and the projection of a simple body. Project a building using a perspective projection. Understand the geometric principles of photogrammetry. Vertical picture, reconstruction of the elements of internal orientation.

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 BA91 in the previous semester. The contents of the course is an introduction to the issues of the subject of descriptive geometry.

Prerequisites and corequisites

Not applicable.

Basic literature

R.PISKA, V.MEDEK: Deskriptivní geometrie, II. díl. SNTL Praha, Alfa Bratislava, 1975. (CS)
R.PISKA, V.MEDEK: Deskriptivní geometrie, I. díl. SNTL Praha, Alfa Bratislava, 1975. (CS)
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. (CS)

Recommended reading

HOLÁŇ, Š., HOLÁŇOVÁ, L.: Cvičení z deskriptivní geometrie II. VUT Brno, 1994. (CS)
P. TALANDA: Deskr. geometrie pro obor geodezie a kartografie. VUT Brno, CERM, 1999. (CS)
Hana Kopřivová: Deskriptivní geometrie 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)

Classification of course in study plans

  • Programme B-P-C-GK Bachelor's

    branch G , 1. year of study, winter semester, compulsory

  • Programme B-K-C-GK Bachelor's

    branch G , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

RNDr. Květoslava Prudilová

Syllabus

Lectures
1. Extended Euclidean space. Perspective affinity, collineation.Curve affine to a circle.
2. Curve in collineation to a circle. Geodetic curve, developable surfaces. Coted projection.
3. Coted projection. Plane section af a ball.
4. Coted projection. Straight line and plane of a given slope. Special construction.
5. Monge`s projection.
6. Monge`s projection. Sphere. Orthogonal axonometry.
7. Orthogonal axonometry.
8. Central projection.
9. Linear perspective projection.
10. Linear perspective projection.
11. Reconstruction of the elements of internal orientation.
12. Reconstruction of the snap.
13. Ortography projection.

Exercise

26 hours, compulsory

Teacher / Lecturer

RNDr. Květoslava Prudilová

Syllabus

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. Aplications.
6. Monge´s projection.
7. Monge´s projection. Sphere. Test.
8. Orthogonal axonometry.
9. Central projection.
10. Linear perspective.
11. Test. Linear perspective.
12. Vertical picture, reconstruction of the elements of internal orientation.
13. Ortography projection. Seminar evaluation.