Czech

4

Not applicable.

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, students 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, arcs using specified elements.

Construction of conics using their focal properties.Perspective collineation, perspectoive affinity, affine image of a circle. Monge projection.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Information is conveyed in the form of lectures and practiced in seminars. Consultation periods are available to students. Assigned work is part of the study activities of the students.

Full-time study programme: Students have to pass two credit tests, submit two drawings and other homework, 100% of attendance.
Followed by an exam with a pass rate of at least 50%.

Lectures
1. Basics of lihting. Technical lighting.
2. Rotation symmetric surfaces, sections of rotation-symmetric surfaces.
3. Lighting of surfaces of revolution .
4. Axonometry – basics.
5. Orthogonal axonometry.
6. Skew axonometry, skew projection.
7. Linear perspective.
8. Linear perspective.
9. Basics of photogrammetry. Reconstruction from a vertical picture.
10. Warped quadrics. Hyperbolic paraboloid. One-sheet hyperboloid.
11. Higher order warped surfaces.Theoretical designe of roofs.
12. Helix, developable helicoidal surface, helicoidal conoid.
13. Topografic surfaces.
Seminars
1. Revision – Monge projection.
2. Technical lighting.
3. Tangent plane of a rotation-symmeric surface, section of a rotation-symmetric surface.
4. Lighting a rotation-symmetric surface.
5. Orthogonal axonometry. Metric problems in coordinate planes.
6. Orthogonal axonometry. Projections of simple bodies and surfaces, their sections and intersections with a straight line.
7. Projecting in skew projection. Projection of a circle in a coordinate plane. Displaying simple bodies and surfaces, their sections and intersections ith a straight line.
8. Linear perspective. Intersection method. Constructing a free perspective.
9. Linear perspective. Method of rotated ground plan. Other methods of projecting a perspective.
10. Linear perspective. Vertical picture. Reconstructing an object from a perpendicular picture.
11. Warped hyperboloid, construction. Hyperbolic paraboloid. Roofing by hyperbolic paraboloid.
12. Higher-order warped surfaces. Theoretic design of roofs.
13. Constructing a helix. Right helicoidal conoid.

Not applicable.

After the course the students should understand and know how to use the basics of orthogonal axonometry, skew projection, and linear perspective.

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

Student can register for the optional subject BA91 in this semester. The contents of the course is an introduction to the issues of the subject of descriptive geometry.

Not applicable.

Piska, R., Medek, V.: Deskriptivní geometrie I.. SNTL Praha, Alfa Bratislava, 1975. (CS)
Piska, R., Medek, V.: Deskriptivní geometrie II.. 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. FAST VUT v Brně, 2004. (CS)

Holáň, S., Holáňová, L.: Cvičení z deskriptivní geometrie II., III.. VUT Brno, 1994. (CS)
Vala, J.: Deskriptivní geometrie I., II.. VUT Brno, 1997. (CS)
Puchýřová, J., Bulantová, J., Prudilová,K., Zrůstová,L.: Úlohy v kosoúhlém promítání (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Puchýřová, J., Bulantová, J., Prudilová,K., Zrůstová,L.: Úlohy o přímkových plochách (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Šafářová, H.: Teoretické řešení střech (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Šafařík, J.: Technické osvětlení (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)

26 hours, compulsory

1. Revision – Monge projection.
2. Projections of a simple bodies and surfaces, their sections and intersections with a straight line. Technical lighting.
3. Tangent plane of a surface of revolution, section of a surface of revolution.
4. Lighting a surface of revolution.
5. Orthogonal axonometry. Metric problems in coordinate planes.
6. Orthogonal axonometry. Projections of simple bodies and surfaces, their sections and intersections with a straight line.
7. Projecting in skew projection. Projection of a circle in a coordinate plane. Displaying simple bodies. Cutting method.
8. Linear perspective. Intersection method. Constructing a free perspective.
9. Linear perspective. Method of rotated ground plan. Other methods of projecting a perspective.
10. Linear perspective. Vertical picture. Reconstructing an object from a perpendicular picture.
11. Warped hyperboloid, construction. Hyperbolic paraboloid. Hyperbolic paraboloid given by skew tetragon. Roofing by hyperbolic paraboloid.
12. Higher-order warped surfaces. Theoretic design of roofs.
13. Constructing a helix. Right helicoidal conoid. Credits.