Course detail

Computer Graphics

FSI-SPGAcad. year: 2024/2025

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.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. Ing. Pavel Štarha, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Descriptive geometry, Basic course of algenra, programming techniques

Rules for evaluation and completion of the course

Graded course-unit credit is awarded under the condition of a semester project elaboration.


Missed lessons may be compensated for via a written test.

Aims

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.


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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Foley, van Dam: Computer Graphics, , 0
Martišek, D.: Matematické principy grafických systémů, Littera, Brno 2002

Recommended reading

Martišek, D.: Matematické principy grafických systémů, Littera, Brno 2002

Type of course unit

 

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Štarha, Ph.D.

Syllabus

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.