Course detail

# Constructive Geometry

Perspective collineation and affinity,circle in affinity. Monge`s projection, topographic surfaces, theoretical solution of the roofs, orthogonal axonometry and linear perspective.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Basics of plane and 3D geometry a stereometrie as taught at secondary schools.

Rules for evaluation and completion of the course

Full-time study programme: Students have to pass two credit tests, submit two drawings and other homework.
Followed by an exam with a pass rate of at least 50%.
Combined study programme: Students will do 6 tests during the semester and send them to the lecturer. Their successful completion is a condition for getting the credit. An exam with a pass rate of at least 50% will follow.

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

Aims

Students should be able to construct conics using their focus properties, understand the principles of perspective colineation and affinity using such properties in solving problems, understand and get the basics of projection: Monge`s projection, orthogonal axonometry, and linear perspective. They should develop 3D visualization and be able to solve simple 3D problems, display simple geometric bodies and surfaces in each type of projection, their section with a plane and intercestions with a straight line. In a linear perspective, they should be able to draw a building. They should learn the basics of the theoretical solution of roofs and topographic surfaces.

Students should be able to construct conics using their focus properties, perspective colineation and affinity. Understand and get the basics of projection: coted, Monge`s projection, orthogonal axonometry, and linear perspective. They should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. In a linear perspective, they should be able to draw a building. They should be theoretically able to solve the roof and solve the location of the construction object in the terrain, both in coted projection.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Deskriptivní geometrie, multimediální CD-ROM, verze 4.0; BULANTOVÁ,J.,HON,P.,PRUDILOVÁ,K.,PUCHÝŘOVÁ,J.,ROUŠAR,J.,ROUŠAROVÁ,V.,SLABĚŇÁKOVÁ,J.,ŠAFAŘÍK,J. FAST VUT v Brně, 2012 (CS)

Descriptive geometry ČERNÝ, Jaroslav, KOČANDRLOVÁ, Milada ČVUT, Praha, 1996 (EN)
Konstruktivní geometrie Černý J., Kočandrlová M ČVUT Praha. 2003 (CS)
Deskriptivní geometrie I Drábek K., Harant F.,Setzer O SNTL Praha, 1978 (CS)
Deskriptivní geometrie I, II PISKA, Rudolf, MEDEK, Václav SNTL, 1976 (CS)
Deskriptivní geometrie I,II VALA, Jiří VUT Brno, 1997 (CS)
Cvičení z deskr.geometrie II,III HOLÁŇ, Štěpán, HOLÁŇOVÁ, Libuše VUT Brno, 1994 (CS)
Descriptive geometry Pare, Loving, Hill: London, 1965 (EN)
Sbírka řešených příkladů z konstruktivní geometrie, Autorský kolektiv ÚMDG FaSt VUT v Brně https://mat.fce.vutbr.cz/studium/geometrie/ (CS)

Classification of course in study plans

• Programme B-K-C-SI (N) Bachelor's

branch VS , 1. year of study, summer semester, compulsory

• Programme B-P-C-SI (N) Bachelor's

branch VS , 1. year of study, summer semester, compulsory

• Programme B-P-C-MI (N) Bachelor's

branch MI , 1. year of study, summer semester, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction - principles of parallel and central projection. Perspective collineation and affinity-basic properties. 2. System of basic problems, examples. Monge`s projection. Basic problems. 3. Monge`s projection. Basic problems. 4. Monge`s projection. Coted projection. 5. Orthogonal axonometry. 6. Orthogonal axonometry. 7. Basic parts of central projection. Linear perspective. 8. Linear perspective. 9. Linear perspective. Topographic surfaces (basic concepts and constructions). 10. Topographic surfaces. 11. Topographic surfaces. Theoretical solution of the roofs. 12. Theoretical solution of the roofs. 13. Questions.

Exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Focus properties of conic sections of an ellipse. Construction of an ellipse on the basis of affinity – Rytz´s and trammel construction. 2. Perspective collineation, perspective affinity. Curve affine to the circle. 3. Monge`s projection. Basic problems. 4. Monge`s projection. 5. Monge`s projection. 6. Test. Orthogonal axonometry. 7. Orthogonal axonometry. 8. Linear perspective. 9. Linear perspective. 10. Linear perspective. Topographic surfaces. 11. Test. Topographic surfaces. 12. Topographic surfaces. Theoretical solution of the roofs. 13. Theoretical solution of the roofs. Credits.