Course Details

Constructive Geometry

Academic Year 2024/25

BAA013 course is part of 5 study plans

​ BPC-SI / VS Summer Semester 1st year

​ BPC-MI Summer Semester 1st year

​ BPC-EVB Summer Semester 1st year

​ BKC-SI Summer Semester 1st year

​ BPA-SI Summer Semester 1st year

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

Credits

5 credits

Language of instruction

Czech, English

Semester

summer

Course Guarantor

Mgr. Hana Boháčková, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

Entry Knowledge

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

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.

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)

Recommended Reading

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)

Offered to foreign students

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/281389

Lecture

13 weeks, 2 hours/week, elective

Syllabus

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

Exercise

13 weeks, 2 hours/week, compulsory

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. Coted projection.
  • 6. Test. Orthogonal axonometry.
  • 7. Orthogonal axonometry.
  • 8. Linear perspective.
  • 9. Linear perspective.
  • 10. Test. Linear perspective.
  • 11. Topographic surfaces.
  • 12. Topographic surfaces. Theoretical solution of the roofs.
  • 13. Theoretical solution of the roofs. Credits.