Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Computer Graphics

    A tantárgy neve magyarul / Name of the subject in Hungarian: Számítógépes grafika

    Last updated: 2024. február 23.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics     		Computer Graphics
    Course ID Semester Assessment Credit Tantárgyfélév
    VIIIAB12 4 3/0/1/v 5  
    3. Course coordinator and department Dr. Szirmay-Kalos László,
    Web page of the course https://cg.iit.bme.hu/portal/en/cgbme
    4. Instructors Dr. Balázs Csébfalvi, Department of Control Engineering and Information Technology
    5. Required knowledge The C++ programming language, Event-driven programming, Introduction to computational theory (vector operations, linear algebra), Analysis (derivation of one- and two-variable vector functions), Physics (center of gravity, dynamics, geometric optics).
    6. Pre-requisites
    Kötelező:
    (NEM
    (TárgyTeljesítve_Képzésen("BMEVIIIAB07") ) )

    ÉS

    ((EgyenCsoportTagja("INFO - 2022 - MINTATANTERV HALLGATÓI") ÉS
    (TárgyTeljesítve("BMEVISZAA06") VAGY
    TárgyTeljesítve("BMEVISZAA03") VAGY
    TárgyTeljesítve("BMEVISZAA00") )

    ÉS
    TárgyTeljesítve("BMEVIIIAA03"))

    VAGY

    ((EgyenCsoportTagja("2014_tanterv_hallgatoi_info") VAGY
    EgyenCsoportTagja("5NAA8_2022 előtti tanterv")) ÉS
    (TárgyTeljesítve("BMEVIIIAA03")
    VAGY
    TárgyTeljesítve("BMEVIIIAA00"))) )

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

    7. Objectives, learning outcomes and obtained knowledge The subject presents the algorithms for the production and processing of image information, introducing students to the development of interactive graphics applications and the programming of graphics hardware.
    8. Synopsis

    1. Analytic geometry overview and review. Construction of geometries, the main characteristics of various important geometries. Analytical geometry of Euclidean space: point, vector, coordinate systems. Meaning and implementation of vector operations in C++. Combination of points: parametric equations of a segment, line and circle. Distance: plane, sphere implicit equation. Algebras: vector, matrix, complex number, Clifford algebra.

    2. Geometric modeling. Classic curves: implicit, parametric and explicit forms. Freeform curves with a combination of points. Lagrangian interpolation. Hermite interpolation to two points. Bezier approximation. Catmull-Rom spline. Parametric surfaces. Surface with extraction and rotation. Catmull-Clark split curve and surface.

    3. Geometric transformations: Elementary transformations and their matrix formalism. Homogeneous coordinates. Projective geometry (ideal point, relation between Cartesian and homogeneous coordinates). Homogeneous linear transformations and their properties. Shift, scale, rotate (Rodriguez formula).

    4.  2D image synthesis: Vectorization of curves. Dividing polygons into triangles. Modeling transformation. View transformation. Cutting sections and areas. Section drawing. Area filling.

    5.  GLUT/OpenGL 3 and 4/GLSL: Syntax, connection with the windowing system. Open window, register event handler functions. Vertex array object and vertex buffer object. The GPU pipeline for 2D graphics. GLSL shaders. Implementation of "Hello triangle" in OpenGL/GLSL environment.

    6.  Basic optical model of 3D image synthesis: Beam density. BRDF. Optically smooth materials, law of reflection and refraction of geometrical optics, Fresnel equations. Wrinkled surfaces, diffuse and shimmering surface. Direction and point light source. Concept of colors, color matching.

    7.  Ray tracing: Solving the visibility problem, normal vector of surfaces, shadow calculation. Recursive ray tracing: reflection and refraction.

    8.  Incremental 3D image synthesis. Tessellation of surfaces. Modeling transformation. View transformation in the case of perspective projection. Cutting in homogeneous coordinates. Masking problem in screen coordinate system, z-buffer algorithm. Gouraud and Phong shading. Texture mapping. 3D graphics application of OpenGL and graphics hardware. Texture rendering, filtering. GPU programming.

     9. Computer games: Construction of virtual reality systems and games. The avatar. Game engine. Posters, particle systems. The physics of games. Field modeling. Movement of characters.

    9. Method of instruction The subject is application-oriented, i.e. the program-level implementation of the theory and algorithms presented in the lectures is also discussed, which the students themselves practice during the laboratory classes. As an implementation environment, we use the C++ language, the version of the OpenGL library (over version 3.3), and the GLSL shader language.
    10. Assessment The mid-term test and the final exam contribute to the final mark with 25% and 75%, respectively. In the mid-term test, at least 40% of the points need to be gathered to make it successful. A successful mid-term test is necessary to sit for a final exam in the examination term.
    11. Recaps An unsuccessful mid-term test can be retaken once.
    12. Consultations Group consultation upon request.
    14. Required learning hours and assignment
    Kontakt óra56
    Félévközi készülés órákra20
    Felkészülés zárthelyire34
    Házi feladat elkészítése 
    Kijelölt írásos tananyag elsajátítása 
    Vizsgafelkészülés40
    Összesen150
    15. Syllabus prepared by Dr. László Szirmay-Kalos, full professor