Czech

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Institute of Mathematics and Descriptive Geometry (MAT)

Students should be able to construct conics using their focus properties, perspective colineation and affinity. Understand and get the basics of projection: coted, Monge`s projection, orthogonal axonometry, and linear perspective. They should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. In a linear perspective, they should be able to draw a building. They construct a helix using specified elements, an orthogonal closed rule right helicoidal surface. They construct a hyperbolic paraboloid, circle and parabolic conoid using specified elements.

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

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

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. Projection of circle. The third projection plane.
4.Monge`s projection. Projection of surfaces and its plane sections.
5.Orthogonal axonometry. Basic problems. Construction in coordinate planes, circle in coordinate plane. Position problems.
6.Orthogonal axonometry. Surfaces. Plane sections for surfaces with base in horizontal plane. Cuting method.
7.Basic parts of central projection. Perspective projection and its methods. Intersecting method.
8.Perspective projection. Method of revolved ground plan. The true shape of a line segment. Free perspective.
9.Perspective projection. Circle in horizontal and vertical plane.
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.

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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: coted, 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.

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

HOLÁŇ, Š., HOLÁŇOVÁ, L.: Cvičení z deskr.geometrie II,III. VUT Brno, 1994. (CS)
Pare, Loving, Hill: Descriptive geometry. London, 1965. (EN)
VALA, J.: Deskriptivní geometrie I,II. VUT Brno, 1997. (CS)