Course detail

Descriptive geometry

FAST-AA02Acad. year: 2024/2025

Orthogonal axonometry, skew axonometry, skew projection. Linear perspective, photogrammetry. Helix, developable helicoidal surface, right closed rule helicoidal surface. Surfaces of revolution . Warped surfaces. Lighting. Teoretical designs of roofs. Introduction to topopgraphic surfaces.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

RNDr. Jana Slaběňáková

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

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

Rules for evaluation and completion of the course

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

Aims

After the course the students should understand and know how to use the basics of orthogonal axonometry, skew projection, and linear perspective.
After the course the students should understand and know how to use the basics of orthogonal axonometry, skew projection, and linear perspective.Helix, developable helicoidal surface, right closed rule helicoidal surface. Surfaces of revolution . Warped surfaces. Lighting. Teoretical designs of roofs. Introduction to topopgraphic surfaces.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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)

Recommended literature

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)

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Jana Slaběňáková

Syllabus

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.

Exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Jana Slaběňáková

Syllabus

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.