Computer Graphics (FSI-SPG)

Academic year 2023/2024
Supervisor: doc. Ing. Pavel Štarha, 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 in creating geometrical models of real systems.
Learning outcomes and competences:

Students will learn how to practically use the knowledge acquired in the theory and computer-oriented courses, supplement it with knowledge of technical curves and surfaces and the ability to display real figures and technical data in various ways. They will deepen their ability to algorithmise technical problems.
Prerequisites:

Descriptive geometry, Basic course of algenra, programming techniques
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 geometric shapes, visibility and shading algorithm, texture mapping.
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 under the condition of a semester project elaboration.
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. Raster graphics, vector graphics, perception of electromagnetic waves, color spaces
2. Vector space, affine space, Euclidean space, projective space, projective space model, basic operations in the Euclidean space
3. Basic operations in the projective space, composition of mappings in plane (rotation around the center, symmetry along the line)
4. Kinematic curves: derivation of parametric equations, visualization
5. Kinematic curves: kinematic motion animation
6. Parallel and central projection, map in projective space
7. Spatial curves, helix in central and parallel projection
8. Analytic curves, isocurves, tangent plane, normal, normal curvature, Gaussian curvature
9. Surfaces generation, cylindrical, surfaces of revolution, helicoids
10. Surface visualization algorithm
11. Rendering pipeline: lighting, shading and visibility
12. 3D visualization, modeling of stereoscopic observation
13. Solution of term papers

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  
B-MAI-P full-time study --- no specialisation -- GCr 3 Compulsory 1 2 W