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: 2023. február 26.

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

    BSc Computer Engineering
    Course ID Semester Assessment Credit Tantárgyfélév
    VIIIAB07   3/0/0/f 3  
    3. Course coordinator and department Dr. Szirmay-Kalos László,
    Web page of the course http://cg.iit.bme.hu/portal/szamitogepes-grafika
    4. Instructors Dr. László Szirmay-Kalos, full professor
    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:
    (TargyEredmeny( "BMEVIIIAA00" , "jegy" , _ ) >= 2
    VAGY
    TárgyEredmény( "BMEVIIIAA03" , "jegy" , _ ) >= 2
    VAGY
    (TargyEredmeny( "BMEVIIIA114" , "jegy" , _ ) >= 2
    ÉS
    TargyEredmeny( "BMEVIIIA115" , "jegy" , _ ) >= 2) )


    ÉS NEM ( TárgyEredmény( "BMEVIIIA316" , "jegy" , _ ) >= 2
    VAGY
    TárgyEredmény("BMEVIIIA316", "FELVETEL", AktualisFelev()) > 0
    VAGY
    TárgyEredmény( "BMEVIIIAB03" , "jegy" , _ ) >= 2
    VAGY
    TárgyEredmény("BMEVIIIAB03", "FELVETEL", AktualisFelev()) > 0)

    ÉS (Training.Code=("5N-A8") VAGY Training.Code=("5NAA8"))

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

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

    Ajánlott:
    Completion of the "Introduction to the theory of computation 2" course

    AND

    Obtaining a signature of the "Basics of Programming 3" couse
    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 equation of a segment, line and circle. Distance: plane, sphere implicit equation. Algebras: vector, matrix, complex number, Clifford.

    2. Geometric modeling. Classic curves: implicit, parametric and explicit form. 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. Body modeling, Euler theorem, polygon modeling with Euler operators.

    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). A rollover problem.

    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. Release of the first homework assignment.

    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. Issuance of the second homework assignment.

    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. Software architecture of 3D graphic systems. GPGPU, CUDA. Third home release.

    9.  Computer animation. Definition of motion. Real movement. Key-frame animation. Mechanical foundations for point bodies. Discrete time simulation. Collision detection and collision response. Character animation. Inverse kinematics.

    10. 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.

    11. Fractal geometry. Limits of Euclidean geometry. Hausdorff dimension for self-similar and non-self-similar objects. Chaotic dynamic systems, pseudo-random number generator. Attractor of simple formations, stability. Attractor production by iteration. Handling multivalued mappings with random walk. IFS.
    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 their homework. 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
    Three mandatory mini homework tasks  during the semester for 2, 3, and 4 points respectively, and a 30-point midterm at the end of the semesterand. A maximum of 3-point optional homework project can be also completed. Reward questions realted to the mini homework are included in the midterm, for which a maximum of 2 points can be given each, then the points received for the kisházi and the points received for the reward questions are considered as a three-dimensional vector, its scalar product is formed, and then the result is added to the midterm points (i.e. whoever complete it as accurately as possible, and you will receive maximum points for all three reward questions, and you will receive a bonus of 18 points on the ZH). The optional homework project must be agreed with the person in charge by the 12th week and must be presented during the replacement week. The optional homework project points are also doubled (max. 6 points) and added to the midterm result.

    The condition for obtaining the credit is the collection of at least 3 points for and the completion of at least 12 points for the ZH including the points given for the reward questions and the large house points, as well as  answering 70% of the Moodle quiz questions by the given deadline (the 70% are wrong answers are also included).
    11. Recaps None of the homeworks can be retaken. An unsuccessful maidterm can be retaken once.
    12. Consultations We provide online and, upon request, group consultation for the prearation of the homework assignments.
    13. References, textbooks and resources László Szirmay-Kalos, György Antal, Ferenc Csonka: Three-dimensional graphics animation and game development, ComputerBooks, 2005. also available in electronic form from the website
    14. Required learning hours and assignment
    Contact hour 42
    Mid-semester preparation for classes 9
    Preparation for confined spaces 12
    Completing homework 27
    Mastering designated written course material 0
    Exam preparation 0
    Total 90

     

    15. Syllabus prepared by Dr. László Szirmay-Kalos, full professor