|Abbreviation: B12A01||Load: 30(L)
|Lecturers in charge: ||v. pred. mr. sc. Nikol Radović
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
- To know theoretical principals, procedures of computer processing and visualisation of surveying data.
- To understand the mathematical methods and physical laws applied in geodesy and geoinformatics.
- To apply the knowledge in mathematics and physics for the purpose of recognizing, formulating and solving problems in the field of geodesy and geoinformatics,
- To use information technology in solving geodetic and geoinformation tasks.
- To plan the continuation of academic education in the field of geodesy and geoinformatics, or related disciplines, and to develop the lifelong learning attitude.
Learning outcomes expected at the level of the course
- Troubleshoot and draw constructive task of applying the transformation plane / space using dynamic geometry Sketchpad 5:03CRO
- To construct geometric figures by animation using the dynamic geometry sketchpad 5:03
- To solve constructive tasks by iteration method
- The basics of mathematical (geometric) model and apply them
- Ability to formulate problems of geodesy on geometric (mathematical) language as well as their analysis and resolution
- Demonstrate skills geometric reasoning
Course content broken down in detail by weekly class schedule (syllabus)
- A brief history of geometry / Computer geometry (1 hour)
- Transformation of the plane (translation, symmetry, rotation, slide symmetry). (3 hours)
- Solving constructive tasks by methods of plane transformation s. (4 hours)
- Solving constructive tasks using as the locus of points. (4 hours)
- The composition of plane transformations and symmetry groups and their display using the dynamic geometry (4 hours)
- Basic concepts of fractal geometry and structure fractal iteration method using dynamic geometry (2 hours)
- Visualization of projective planes (2 hours)
- Display plane curves 2 and a higher degree with the program dynamic geometry as tool for for drawing (2 hours)
- Animation as the foundation of computer graphics, construction geometric figure animation (2 hours)
- The use of dynamic geometry (2 hours)
- Non-Euclidean geometry (4 hours)
Screening student work
- Class attendance - 0.5 ECTS
- homeworks - 1 ECTS
- Tests - 1.2
- Oral exam - 1.2
- Written exam - 1.1
|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,
|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.
|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.