Czech

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

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.

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

Not applicable.

Not applicable.

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

Lectures
1. Extended Euclidean space. Affine ratio. Perspective affinity, collineation.
2. Curve affine to a circle. Coted projection. Positional problems.
3. Coted projection. Metric problems. Projection of a circle, simple bodies and surfaces.
4. Coted projection. Section of a body. Straight line and plane of a given slope.
5. Monge`s projection. Introduction, basics problems.
6. Monge`s projection. Projection of a circle. Introducing an auxiliary plane. Spere.
7. Orthogonal axonometry. Introduction. Metric problems in coordinate planes, positional problems.
8. Central projection. Introduction. Basic problems.
9. Central projection. Projection of simple bodies. Perspective projection. Introduction, projection scheme. Principle of intersection method.
10. Linear perspective. Lengths of line segments. Constructions in the ground plane with inaccessible neutral point. Constructing the perspective of an object by free method.
11. Linear perspective. Methods of projecting a perspective. Circles in a horizontal and vertical plane.
12. Basics of photogrammetry. Vertical picture, reconstruction of the elements of internal orientation.
13. Reconstruction of a vertical picture.
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. Section of a sphere, intersection of a sphere with a straight line.
8. Orthogonal axonometry. Metric problems in coordinate planes.
9. Central projection. Constructions in a plane, projection of a body.
10. Linear perspective.
11. Linear perspective.
12. Linear perspective. Vertical picture, reconstruction of the elements of internal orientation.
13. Vertical picture, reconstruction of the elements of internal orientation. Seminar evaluation.

Not applicable.

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.

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

Not applicable.

Not applicable.

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

Černý J., Kočandrlová M.: Konstruktivní geometrie. ČVUT Praha, 2003. (CS)
Černý J., Kočandrlová M.: Konstruktivní geometrie 10 (sbírka příkladů). ČVUT Praha, 2002. (CS)
Hana Kopřivová: Deskriptivní geometrie II. Vydavatelství ČVUT Praha, 1999. (CS)
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)