Constructive Geometry
Code  Completion  Credits  Range  Language 

101KOGG  Z,ZK  5  2P+2C  Czech 
 Course guarantor:
 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 9788001060490
Linkeová I.:Constructive Geometry, 2019, ISBN 9788001058794
Pyšek J.: Kartografie, kartometrie a matematická geografie v příkladech, 2000, ISBN 8070826800
Pottmann H.: Architectural Geometry, 2007, ISBN 9781934493045
Švercl J.: Technické kreslení a deskriptivní geometrie pro školu a praxi, 2003, ISBN 8071832979
SketchUp  learning materials for beginners, http://cadtutorial.cz/sketchup/
 Note:
 Further information:
 https://mat.fsv.cvut.cz/vyuka/bakalari/zs/KOGG/
 Timetable for winter semester 2024/2025:

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
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Geodézie a kartografie (compulsory course)
 Geodézie a kartografie (compulsory course)