Course content

Computer Geometry

Code:

33496

Abbreviation:

B12A01

Higher education institution:

Faculty of Geodesy

ECTS credits:

5.0

Load:

30(L) + 30(E)

Issuing teachers:

Senior Lecturer Nikol Radović, MSc

Course contractors:

Senior Lecturer Nikol Radović, MSc (L, E)

Course description:

The goal of course Computational geometry is the renewal and replenishment secondary education of geometry, using the dynamic geometry (Geometer's Sketchpad 5.03HR) as a tool for drawing / design, with particular emphasis on applications in geodesy and geoinformatics. Learning outcomes at the level of the programme to which the course contributes <ul><li>To know theoretical principals, procedures of computer processing and visualisation of surveying data. <li>To understand the mathematical methods and physical laws applied in geodesy and geoinformatics. <li>To apply the knowledge in mathematics and physics for the purpose of recognizing, formulating and solving problems in the field of geodesy and geoinformatics, <li>To use information technology in solving geodetic and geoinformation tasks. <li>To plan the continuation of academic education in the field of geodesy and geoinformatics, or related disciplines, and to develop the lifelong learning attitude.</ul> Learning outcomes expected at the level of the course <ul><li>Troubleshoot and draw constructive task of applying the transformation plane / space using dynamic geometry Sketchpad 5:03CRO <li>To construct geometric figures by animation using the dynamic geometry sketchpad 5:03 <li>To solve constructive tasks by iteration method <li>The basics of mathematical (geometric) model and apply them <li>Ability to formulate problems of geodesy on geometric (mathematical) language as well as their analysis and resolution <li>Demonstrate skills geometric reasoning</ul> Course content broken down in detail by weekly class schedule (syllabus) <ul><li>A brief history of geometry / Computer geometry (1 hour) <li>Transformation of the plane (translation, symmetry, rotation, slide symmetry). (3 hours) <li>Solving constructive tasks by methods of plane transformation s. (4 hours) <li>Solving constructive tasks using as the locus of points. (4 hours) <li>The composition of plane transformations and symmetry groups and their display using the dynamic geometry (4 hours) <li>Basic concepts of fractal geometry and structure fractal iteration method using dynamic geometry (2 hours) <li>Visualization of projective planes (2 hours) <li>Display plane curves 2 and a higher degree with the program dynamic geometry as tool for for drawing (2 hours) <li>Animation as the foundation of computer graphics, construction geometric figure animation (2 hours) <li>The use of dynamic geometry (2 hours) <li>Non-Euclidean geometry (4 hours)</ul> Screening student work <ul><li>Class attendance - 0.5 ECTS <li>homeworks - 1 ECTS <li>Tests - 1.2 <li>Oral exam - 1.2 <li>Written exam - 1.1</ul>

Mandatory literature:

3. A. Barager: A Survey of Classical and Modern Geometries with Computer Activities, Prentice-Hall, 2001.

4. B. E. Reynolds, W. E. Fenton: College Geometry Using The Geometer's Sketchpad, Key College Publishing, 2006.

8. L. C. Kinsey, T. E. Moore: Symmetry, Shape and Space with the Geometer's Sketchpad, Key Curriculum Press, 1001.

9. C. V. Sanders: Geometric Graphic, Key Curriculum Press, Emeryville, 2003.

Recommended literature:

2. R. Dixon: Mathograpies, Dover Publications, Inc, New York, 1991.

5. L. S. Leff: Geometry - The Easy Way, Barron's Education Series, New York, 1997.

6. V. Gutenmacher, N. B. Vasilyev: Lines and Curves A Practical Geometry Handbook, Birkhauser Boston Inc., 2004.

7. J. Vince: Geometry for Computer Graphic, Springer - Verlag, 2006.

Course in study programme:

Code	Name of study	Level of study	Semester	Required/Elective
71	Geodesy and Geoinformatics	undergraduate	2	required

* the course is not taught in that semester

Legend

E - Exercises

L - Lectures