Computer Graphics (FSI-SPG)

Academic year 2018/2019
Supervisor: doc. PaedDr. Dalibor Martišek, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
Students will apply the knowledge acquired in mathematical analysis, algebra, geometry and previous courses dealing with computers. Theoretical knowledge will be practically applied when building geometrical models of real systems.
Learning outcomes and competences:
Students will apply the knowledge acquired in theoretical and computer courses. This knowledge will be extended by technical curves and surfaces and real objects, as well as ability to demonstrate technical data in different ways. Students will improve the quality of algorithm construction and Delphi environment knowledge.
Prerequisites:
Descriptive geometry, Basic course of algenra, programming techniques and their implementation in Borland Delphi
Course contents:
This course is lectured in winter semester in the second year of mathematical engineering study. It introduces basic principles of algorithms of computer graphics. Lectures provide a theoretical basis of computer graphics - euclidean space graphical data and colour spaces, projective space, transforms, basic properties and construkctions of curves and surfaces, realistic representation of spatial figures, hide and shading algorithm, textures.
Teaching methods and criteria:
The course is taught through exercises which are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Graded course-unit credit is awarded on condition of having worked out assigned graphic program constructed in Borland DELPHI environment, and semester work – building of a greater graphic program.
Controlled participation in lessons:
Missed lessons may be compensated for via a written test.
Type of course unit:
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Computer-assisted exercise 1. Euclidean space. Topologic dimension, curve, surface, solid. Projective space, dividing ratio, cross ratio. Raster graphics. Pixel, colour spaces, RGB cube.

2. 2-D transforms, analytic representation and composition.

3. Analytic curves, algorothms their construction construction. Point function, tangent and normal of curve, curvature. Affine combination, control points, Beziere curves, B-spline curves, NURBS curves.

4. Motion, analytic representation, software modelling. Animation principles.

5. Analytic representation of parallel and orthogonal projection, elementary solids modelling. Analytic surfaces, isolines, tangent plane, normal, normal and Gaussian curvature

6. Basic method of surface modelling, NURBS surfaces.

7. Lighting of elementar solids, lighting models in computer graphics, shading and rendering

8. Lighting models, ray tracing, ray casting.

9. Hausdorff dimension and its measure, fractal. Self-similarity and self-afinity. Random walk method.

10. Statistical self-similarity, midpoint moving method.

11. L-systems

12. 13. Semestral work

Presence in the seminar is obligatory.
Literature - fundamental:
1. Foley, van Dam: Computer Graphics, , 0
3. Martišek, D.: Matematické principy grafických systémů, Littera, Brno 2002
Literature - recommended:
1. Martišek, D.: Matematické principy grafických systémů, Littera, Brno 2002
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3A-P full-time study B-MAI Mathematical Engineering -- GCr 3 Compulsory 1 2 W