# 714-0375/06 – Constructive Geometry (KG)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Mgr. František Červenka Subject version guarantor Mgr. Dagmar Dlouhá, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2010/2011 Year of cancellation 2018/2019 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
BEL10 Mgr. Jana Bělohlávková
CER0007 Mgr. František Červenka
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DOL75 Mgr. Jiří Doležal
VAV14 RNDr. Eva Vavříková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 12+4

### 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

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

### Další požadavky na studenta

No more requirements.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Lectures: I Introduction to constructive geometry, axial affinity, Monge projection – position tasks, Monge projection - metric tasks II Orthogonal axonometry - basic position tasks, Orthogonal projection of the circle (trammel construction, Rytz construction) III Views of circle in the projection plane (ax.) and in a general plane (MP), Prism surface, cylindrical surface – cut by a plane IV Central collineations, pyramid surface – cut by a plane V Conical surface, sphere – cut by a plane perpendicular to the projection plane, Intersections of a line and solids VI Helix, screw surfaces, Surfaces of revolution - creation, application, Intersections of surfaces of revolution

### 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 K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner