714-0375/07 – Constructive Geometry (KG)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorMgr. František ČervenkaSubject version guarantorMgr. Jana Bělohlávková
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageEnglish
Year of introduction2016/2017Year of cancellation
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BEL10 Mgr. Jana Bělohlávková
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

Lectures
Individual consultations
Tutorials

Summary

Focus properties of conic sections. The two-plane method. Perspective affinity. Orthogonal axonometry. Orthogonal image of circle. Prismatic surface. Cylindrical surface. Pyramidal surface. Conical surface. Central collineation. Spherical surface. Surfaces of rotation. Quadrics of rotation. One-sheet hyperboloid of rotation. Circular helix. Spiral surfaces.

Compulsory literature:

Černý, J.: Geometry. Vydavatelství ČVUT,Praha 1996,ISBN 80-01-01535-1 Kargerová, M.: Geometry and Computer Graphics. Praha 1998, ISBN 80-01-01816-4

Recommended literature:

1/ Plocková, E. - Řehák, M.: Sbírka řešených příkladů z DG a KG, díl 3. - Mongeovo promítání. Skriptum VŠB - TU, Ostrava 1995. 2/ Stejskalová, J. - Vrbenská, H.: Sbírka řešených příkladů z DG a KG, díl 4. - Axonometrie. Skriptum VŠB - TU, Ostrava 1995. 3/ Urban, A.: Deskriptivní geometrie I, II, Praha, SNTL, 1967. 4/ Doležal, M. - Poláček, J. - Tůma, M.: Sbírka řešených příkladů z DG a KG, díl 5. - Rotační a šroubové plochy. Skriptum VŠB - TU, Ostrava 1995.

Way of continuous check of knowledge in the course of semester

Course credit ======================================================== To obtain a credit the student has to submit 3 drawings. Student can get 12 points for attendance of the lectures and another 8 points for properly solved homework. A maximum of 20 points. Exam ======================================================== Written part of an exam is classified by 0 - 60 points. The part is successful if student obtains at least 25 points. Oral part of the exam is classified by 0 - 20 points. The part is successful if student obtains at least 5 points. Point quantification in the interval 100 - 91, 90 - 81, 80 - 71, 70 - 61, 60 - 51, 50 - 0 ECTS grade A B C D E F Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0 National grading scheme excellent very good satisfactory failed A set of topics for the theoretical part of the exam ======================================================== 1) Monge projection – position tasks. 2) Monge projection - metric tasks. 3) Orthogonal axonometry - basic position tasks. 4) Orthogonal projection of a circle (Rytz construction). 5) Monge projection - views of a circle in a general plane. 6) Prism surface – cut by a plane. 7) Cylindrical surface – cut by a plane. 8) Pyramid surface – cut by a plane. 9) Construction of a sphere, cut of a sphere by a plane, intersection of line and solid. 10) Focal properties of conics - ellipse, hyperbola, parabola. 11) Construction of conics. 12) Surfaces of revolution - development, application, construction of the tangent plane. 13) Surfaces of revolution - quadrics - development, application, construction of the tangent plane. 14) Intersections of surfaces of revolution. 15) Intersections of quadrics. 16) Design and layout of helix. 17) Screw ruled surfaces - the classification, tangent plane.

E-learning

www.studopory.vsb.cz

Další požadavky na studenta

There are no more requirements.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

The program of lectures ================= 1 Introduction to constructive geometry, axial affinity 2 Monge projection – position tasks 3 Monge projection - metric tasks 4 Orthogonal axonometry - basic position tasks 5 Orthogonal projection of the circle (trammel construction, Rytz construction) 6 Views of circle in the projection plane (ax.) and in a general plane (MP) 7 Prism surface, cylindrical surface – cut by a plane 8 Central collineations, pyramid surface – cut by a plane 9 Conical surface, sphere – cut by a plane perpendicular to the projection plane. 10 Intersections of a line and solids 11 Helix, screw surfaces 12 Surfaces of revolution - creation, application 13 Intersections of surfaces of revolution 14 Reserve Program of exercises and seminars + individual students' work ================================================== ====== 1 A focal properties of conic sections - ellipse, hyperbola, parabola 2 Construction of elements of the conics 3 Basic position tasks in Monge projection 4 Basic metric tasks in Monge projection 5 Basic position tasks at orthogonal axonometry 6 Views of circle; constructions of a prism and pyramid out from given elements 7 Construction of a sphere, cylinder and cone from given elements 8 Cuts of a prism, pyramid, and cylinder by a plane 9 Cut of a sphere by a plane, intersection of line and the solid 10 Design and layout of helix 11 Screw ruled surfaces - the classification, tangent plane 12 Surfaces of revolution - the development, construction of the tangent plane 13 Intersections of surfaces of revolution 14 Reserve

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng - Bachelor Studies 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Bachelor Studies 2018/2019 Full-time English Choice-compulsory 301 - Study and International Office stu. block