CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Constructive Geometry

Code Completion Credits Range Language
101KOGG Z,ZK 5 2P+2C Czech
Garant předmětu:
Hana Lakomá
Lecturer:
Hana Lakomá
Tutor:
Hana Lakomá, Petra Vacková
Supervisor:
Department of Mathematics
Synopsis:

In the first part the course contains the basics and principles of projections of the space. It applies and practices this knowledge when displaying solids, surfaces, geodetic curves, the reference sphere with meridians and parallels, when using cartographic projections and in the constructive photogrammetry. The 3D program SketchUp is used for visualization and solving geometric problems. In the second part, the course presents the basics of spherical trigonometry and its use in mathematical geography and astronomy.

Requirements:

Mandatory active participation in classes, a maximum of 3 excused absences.

Submission of graphic works within the prescribed period and quality (see Moodle).

Completion of the credit test.

Completion of the written exam work.

Syllabus of lectures:

1. Reference surfaces. Solids and surfaces, their nets, developments, geodesics.

2. Projection as a representation of space onto a plane. Parallel projection - basic properties and relationships.

3. Orthographic projection with the spot heights and its applications.

4. Azimuthal cartographic projections I. - Orthographic projection.

5. Oblique projection and orthogonal axonometry.

6. Parallel projection of the geographical net on the reference sphere.

7. Central projection - basic properties and relations, ratios.

8. Geometric basics of photogrammetry.

9. Azimuthal cartographic projection II. - Gnomonic projection.

10. Azimuthal cartographic projection III. - Stereographic projection.

11. Spherical trigonometry: Basic concepts and formulas.

12. Application of spherical trigonometry I. - Mathematical geography.

13. Application of spherical trigonometry II. - Astronomical coordinate systems.

Syllabus of tutorials:

1. Basic constructions of an ellipse, elliptical coordinates. Affinity, affine image of a circle.

2. Projection of surfaces and solid groups. Top, front and side view of objects.

3. Solids and geodesics in the orthographic projection with the spot heights

4. Orthographic projection.

5. Solids and geodesics in the oblique projection.

6. Parallel projection of the meridians and parallels on the reference sphere.

7. Central projection - ratios.

8. Constructive photogrammetry.

9. Gnomonic projection.

10. Stereographic projection.

11. Spherical trigonometry: Basic concepts and formulas.

12. Application of spherical trigonometry I. - Mathematical geography.

13. Application of spherical trigonometry II. - Astronomical coordinate systems.

Study Objective:

The first aim is to increase students' competence in techniques of space projection. The second aim is to present the sphere, parametric, cartographic and geodetic curves on the sphere with regard to their use in cartographic and geodetic applications.

Study materials:

Černý J., Kočandrlová M.: Konstruktivní geometrie, 2021, ISBN 978-80-01-06049-0

Linkeová I.:Constructive Geometry, 2019, ISBN 978-80-01-05879-4

Pyšek J.: Kartografie, kartometrie a matematická geografie v příkladech, 2000, ISBN 80-7082-680-0

Pottmann H.: Architectural Geometry, 2007, ISBN 978-1-934493-04-5

Švercl J.: Technické kreslení a deskriptivní geometrie pro školu a praxi, 2003, ISBN 80-7183-297-9

SketchUp - learning materials for beginners, http://cadtutorial.cz/sketchup/

Note:
Further information:
https://mat.fsv.cvut.cz/vyuka/bakalari/zs/KOGG/
Time-table for winter semester 2023/2024:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomTH:C-21712:00–13:50(lecture parallel1)Thákurova 7 (budova FSv)C217 roomTH:B-25514:00–15:50(lecture parallel1parallel nr.102)Thákurova 7 (budova FSv)B255roomTH:B-25516:00–17:50(lecture parallel1parallel nr.101)Thákurova 7 (budova FSv)B255 roomTH:B-47114:00–15:50(lecture parallel1parallel nr.103)Thákurova 7 (budova FSv)B471
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-07-15
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet24157205.html