230-0241/06 – Descriptive Geometry (BcDg)

Gurantor departmentDepartment of MathematicsCredits4
Subject guarantorMgr. Dagmar Dlouhá, Ph.D.Subject version guarantorMgr. Dagmar Dlouhá, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFASTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BEL10 Mgr. Jana Bělohlávková
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
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

Questions: Center projection - basic properties. Parallel projection - basic properties. Ellipsis - definition, focal properties, strip construction. Hyperbola - definition, focal properties. Dish - definition, focal properties. Theoretical solution of roofs - basic terms and constructions. Listed projection - principle and basic terms. Monge's projection - principle and basic terms. Rectangular axonometry - principle and basic terms. Angular projections - principle and basic terms. Linear perspectives - principle and basic terms. Cut a prism. Display a circle in projections. Helix - creation, basic terms, accompanying triangular. Rotational surfaces - creation, basic terms, tangent plane. Rotational quadratic surfaces - creation, distribution. Helical surfaces - creation, basic terms, classification. Stair surface - creation, use. Wound post - creation, use. Rotary warped hyperboloid - creation, properties, use. Developable linear surfaces - classification, use. Warped line faces - creation, properties. Conoids - control units, examples, applications. Examples of warped surfaces in construction practice (oblique passage area, Štramberk trumpet, Montpellier and Marseilles) arc). Requirements for granting the credit and exam Conditions for granting the credit: - participation in exercises (20% of absences can be excused), -submission of credit work in the required quality. The student receives 5 points for attendance and submission of credit work. Additional points (0 to 30) can be obtained by elaborating homework in the given term. In total, it is possible to get a maximum of 35 points. The minimum number of points for credit is 5. Exam: Combined Practical part max. 55 points. Theoretical part max. 10 points. Total max. 65 points. Students must pass in each part of the combined exam: In the practical part they must obtain at least 25 points, in the theoretical part at least 5 points. Score is obtained by adding points from exercises (max. 35) and exam (max. 65) and graded: Earned points Score 86 - 100 excellent 66 - 85 very well 51 - 65 well 0 - 50 failed


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

Other requirements

At least 80% attendance at the exercises. Absence, up to a maximum of 20%, 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:

Syllabus of lectures: 1. Dimensioned projection - principle, depiction of basic figures, positional problems. 2. Dimensional projection - metric problems, circle representation. 3. Dimensioned projection - terrain solution. 4. Monge projection - principle and depiction of basic figures. 5. Rectangular axonometry and angular projections - principle and mapping of basic figures. 6. Constrained perspectives - principle and depiction of basic formations. 7. Cut prism by plane, mesh of body. 8. Curves - creation, distribution, accompanying triangular. Helix. 9. Surfaces - creation, distribution, tangent plane and normal. Rotating surfaces. Rotary quadrics. 10. Helical surfaces - straight, cyclic. 11. Line surfaces. Developable and undevelopable linear surfaces. 12. Conoids. 13. Conusoids. 14. Reserve. Program of exercises and seminars + individual work of students 1. Theoretical solution of roofs. 2. Dimensional projection - basic tasks. 3. Dimensioned projection - metric problems, circle projection. 4. Dimensioned projection - terrain solution. 5. Monge projection - basic problems. 6. Rectangular axonometry and angular projections - roof representation. 7. One-point perspective of a room, two-point perspective of a building. 8. Cut prism by plane, mesh of body. 9. Projection of circle and helix. 10. Rotational quadrics. 11. Screw surfaces - stair surface, wound post. 12. Rotary warped hyperboloid. Hyperbolic paraboloid. 13. Conoids and conusoids. 14. Reserve.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 35  5
        Examination Examination 65 (65) 30 3
                Písemná zkouška Written examination 55  25
                Ústní zkouška Oral examination 10  5
Mandatory attendence participation: 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

Conditions for subject completion and attendance at the exercises within ISP: Mandatory participation in the course is not required. Other conditions for subject completion will respect the individual needs of the student.

Show history

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (B0732A260002) Civil Engineering P English Ostrava 1 Compulsory study plan
2023/2024 (B0732A260002) Civil Engineering P English Ostrava 1 Compulsory study plan
2022/2023 (B0732A260002) Civil Engineering P English Ostrava 1 Compulsory study plan
2021/2022 (B0732A260002) Civil Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (B0732A260002) Civil Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (B0732A260002) Civil Engineering P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

Předmět neobsahuje žádné hodnocení.