230-0241/01 – Descriptive Geometry (BcDg)

Gurantor departmentDepartment of MathematicsCredits5
Subject guarantorMgr. Dagmar Dlouhá, Ph.D.Subject version guarantorMgr. Dagmar Dlouhá, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2018/2019Year of cancellation
Intended for the facultiesFASTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
CER0007 Mgr. František Červenka
DOL75 Mgr. Jiří Doležal
POL12 RNDr. Jiří Poláček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

• to train development of space abilities • to handle by different types of projection methods, to understand to their principles, to be familiar with their properties, advantages and disadvantages • to acquaint with geometric characteristics of curves and surfaces that are used in technical practice of a given specialization

Teaching methods

Individual consultations
Other activities


The basic properties of the projection. Central collineation, perspective affinity. The mapping projection, the Monge’s projection, the orthogonal axonometry. Elementary surfaces and solid. Circular helix and moving trihedral. Surfaces of revolution, quadrics of revolution. The ruled surfaces, the evelopable and especially the skew ruled surfaces. Spiral surfaces.

Compulsory literature:

Vavříková, E.: Descriptive Geometry. VŠB-TU, Ostrava 2005. ISBN 80-248-1006-9. Watts,E.F. - Rule,J.T.: Descriptive Geometry, Prentice Hall Inc., New York 1946. http://mdg.vsb.cz/portal/dg/DeskriptivniGeometrie.pdf

Recommended literature:

Ryan, D. L.: CAD/CAE Descriptive Geometry. CRC Press 1992. Pare, Loving, Hill: Deskriptive geometry, London, 1965. http://mdg.vsb.cz/portal/

Way of continuous check of knowledge in the course of semester

assing the course, requirements Course-credit -participation on tutorials is obligatory, -elaborate programs, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points. Point quantification in the interval 100 - 86 85 - 66 65 - 51 50 - 0 National grading scheme excellent very good satisfactory failed 1 2 3 4 List of theoretical questions: 1. Parallel projection - basic characteristics. 2. Ellipse - definition, the focal properties, trammel construction. 3. Hyperbola - definition, the focal properties. 4. Parabola - definition, the focal properties. 5. Theoretical solutions of roofs - basic notions and constructions. 6. Monge projection - principles and basic notions. 7. Orthogonal axonometry - principles and basic notions. 8. The notch method in orthogonal axonometry. 9. Displaying of circle in Monge projection and axonometry (in a coordinate or parallel plane). 10. Curves - the creation, distribution, movement frame. 11. Helix - the creation, basic concepts, movement frame. 12. Surfaces - the creation, distribution, tangent plane and normal. 13. Surfaces of revolutions - the creation, basic notions, tangent plane. 14. Rotating quadrics - the creation, distribution. 15. Skew hyperboloid of two sheets - the creation, characteristics, application. 16. Ruled surfaces - the creation, distribution, types of straight line on surface. 17. Developable ruled surfaces- distribution, application. 18. Skew ruled surfaces, the creation, characteristics. 19. Hyperbolic paraboloid - the creation, characteristics, applications. 20. Conoids - the creation, examples, applications. 21. Examples of the skew ruled surfaces in the building practices (surface of diagonal pass, surface of Stramberk Tower, Montpellier and Marseille arc). 22. Screw surfaces - the creation, basic notions, distribution. 23. Stair surface, coiled column - the creation, applications.


http://www.studopory.vsb.cz http://mdg.vsb.cz (in Czech language)

Other requirements

At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1. Parallel projection. Improper objects. Axial affinity in plane. 2. Monge projection: representation of point, line and plane, the basic position problems. 3. Monge projection: the basic metric problems, displaying of circle. 4. Orthogonal axonometry: principles and representation of point, line and plane, the basic position problems. 5. Orthogonal axonometry: object in coordinate or parallel plane, notch method. 6. Curves - the creation, distribution, movement frame. Circular helix. 7. Surfaces: describing, classification, tangent plane and normal. 8. Screw surfaces - ruled, cyclical. 9. Surfaces of revolution. Second degree surfaces of revolution. 10. Ruled surfaces. Developable and skew ruled surfaces. 11. One-sheet hyperboloid of rotation. 12. Hyperbolic paraboloid. Conoids. 13. Other surfaces suitable for civil engineering. 14.Reserve.

Conditions for subject completion

Full-time form (validity from: 2018/2019 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 30
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (B3607) Civil Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3607) Civil Engineering P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner