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Course detail
Computer Geometry and Graphics
Course unit code:  FSI1PG  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  1  
Semester:  winter  
Number of ECTS credits:  5  



























Type of course unit:
Lecture:  26 hours, optionally 

Teacher / Lecturer:  Mgr. Jana Hoderová, Ph.D. RNDr. Ludmila Chvalinová, CSc. doc. PaedDr. Dalibor Martišek, Ph.D. Mgr. Jana Procházková, Ph.D. doc. Ing. Pavel Štarha, Ph.D. 
Syllabus:  1. Euclidean space, topologic dimension, curve, surface, solid. Projective space, dividing ratio and cross ratio, projection 2. Basic mappings in plane and space, their analytic representation (rotation, translation, axis and central symmetry, homothety), analytic representation of parallel and central projection). 3. Analytic curves, Point function, tangent and normal of curve, curvature. Analytic surfaces, isolines, tangent plane, normal, normal and Gaussian curvature (basic information) 4. Focus and projective attributes of conics, circle  ellipse affinity, Triangle, stripe and Rytz construction. Curve representation in CAD systems, affine point combination, control points. Beziere curves, Bspline curves and surfaces, NURBS curves. 5. Fundamentals of kinematic plane geometry (motion, fixed and moving centrode, circle arc rectification, rolling motion, cycloid and involute curve  synthetic and analytic construction, animation principle, software modeling) 6. Elementary surfaces and solids (prism, pyramid, cylinder, cone, sphere) twoplane (Monge) Monge projection (MP) and orthogonal axonometry (OA), NURBS surfaces, NURBS representation of elementary curves and surfaces. 7. Slices of solids, the intersection of line and solid, intersection of solids  Monge's projection and axonometry solutions 8. Helix, analytic representation, MP and OA projection. 9. Methods of surface generation in graphic system, Basic generating principles. Developable surfaces (cylindric and conic surface, curve tangent surface, transition surfaces). Undevelopable surfaces (conoid, cranc mechanism surface, oblique transition surface)  analytic representation, computer modeling 10. Rotation surfaces (torus, rotation quadric)  Monge's projection and axonometry,  analytic representation, computer modeling 11. Skrew surfaces, cyclic and linear surfaces,  Monge's projection and axonometry, analytic representation, computer modeling 12. Hausdorff dimension, fractal. Selfsimilarity and selfafinity, random walk method, midpoint method, Lsystems 13. Lighting of elementar solids, lighting models in computer graphics, Ray Tracing, Ray Casting 
seminars in computer labs:  26 hours, compulsory 
Teacher / Lecturer:  Mgr. Jana Hoderová, Ph.D. RNDr. Ludmila Chvalinová, CSc. Ing. František Janošťák Mgr. Jiří Kratochvíl Ing. Jakub Kůdela doc. PaedDr. Dalibor Martišek, Ph.D. Mgr. Jana Procházková, Ph.D. Ing. Adam Rychtář doc. Ing. Pavel Štarha, Ph.D. 
Syllabus:  1. Introduction to the computer graphics  raster and vector image. Image processing, CAD data visualization. Rhinoceros  introduction, view setting, elementary examples and commands. 2. Image and color models. Solids in Rhinoceros (colour, solids operation, rendering) 3. Lines, elementary objects in raster images. Freeform modeling, surfaces, lighting, curves mapping 4. Curves and surfaces in computer graphics  NURBS. General surfaces  boundary curves, revolution surfaces, sweep and offset surfaces. 5. Textures. Preciseform modeling (coordinates, curve modeling) 6. Lighting, visibility. Preciseform modeling (machine components modeling) 7. 2D and 3D transforms, 3D > 2D transforms 8. Animation. Kinematic geometry (cycloid curve, involute) 9. Linear perspective, two center projection, 3D images and films, virtual reality 10. Curves and surfaces, topological and Hausdorff's dimension, fractals and their modeling. 11.  13. Seminar work 