Czech

5

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Student should be able to construct conics, perspective colineation and affinity. Understand and get the basics of projection: Monge`s, orthogonal axonometry, linear perspective. He should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. In a linear perspective, he should be able to draw a building. He constructs a helix, an helicoidal surface, a hyperbolic paraboloid, circle and parabolic conoid, arcs using specified elements.

Basics of plane and 3D geometry a stereometrie as taught at secondary schools.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

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 6 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.

1.Introduction - principles of parallel and central projection. Perspective collineation and affinity-basic properties.
2.System of basic problems, examples. Monge`s projection. Basic problems.
3.Monge`s projection. Basic problems.
4.Monge`s projection.
5.Axonometry.
6.Axonometry.
7.Basic parts of central projection. Perspective projection.
8.Perspective projection.
9.Perspective projection.
10.Theory of curves and surfaces. Helix.
11.Closed ruled right helicoidal surface. Warped surfaces. Warped surfaces of the second degree. Warped hyperboloid.
12.Hyperbolic paraboloid. Circle and parabolic conoid.
13.Questions.

Not applicable.

Students should be able to construct conics using their focus properties, understand the principles of perspective colineation and affinity using such properties in solving problems, understand and get the basics of projection: Monge`s projection, orthogonal axonometry, and linear perspective. They should develop 3D visualization and be able to solve simple 3D problems, display simple geometric bodies and surfaces in each type of projection, their section with a plane and intercestions with a straight line. In a linear perspective, they should be able to draw a building. They should learn the basics of the theory of curves and surfaces, construct a helix using specified elements as well as an orthogonal closed rule right helicoidal surface. They should learn the basics of the theory of warped surfaces, construct a hyperbolic paraboloid, circle and parabolic conoid using specified elements.

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

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.

Not applicable.

R. Piska, V. Medek: Deskriptivní geometrie I, II. SNTL, 1976. (CS)
Jaroslav Černý: Descriptive geometry. ČVUT, Praha, 1996. (EN)

Pare, Loving, Hill: Descriptive geometry. London, 1965. (EN)
HOLÁŇ, Š., HOLÁŇOVÁ, L.: Cvičení z deskr.geometrie II,III. VUT Brno, 1994. (CS)
VALA, J.: Deskriptivní geometrie I,II. VUT Brno, 1997. (CS)
BULANTOVÁ,J.,HON,P.,PRUDILOVÁ,K.,PUCHÝŘOVÁ,J.,ROUŠAR,J.,ROUŠAROVÁ,V.,SLABĚŇÁKOVÁ,J.,ŠAFAŘÍK,J.: Deskriptivní geometrie, multimediální CD-ROM, verze 4.0. FAST VUT v Brně, 2012. (CS)

26 hours, compulsory

1. Focus properties of conic sections.
2. Perspective collineation, perspective affinity. Curve affine to the circle.
3. Construction of an ellipse using affinity. Monge´s projection.
4. Monge´s projection.
5. Monge´s projection.
6. Test. Orthogonal axonometry.
7. Orthogonal axonometry. Oblique projection.
8. Linear perspective.
9. Linear perspective.
10. Linear perspective.
11. Test. Helix. Closed ruled right helicoidal surface.
12. Building and technical surfaces.
13. Credits.