FPFVA034 Computational geometry and computer graphics II

Filozoficko-přírodovědecká fakulta v Opavě
léto 2021
Rozsah
0/1/0. 5 kr. Ukončení: z.
Vyučující
doc. RNDr. Luděk Cienciala, Ph.D. (cvičící)
Garance
doc. RNDr. Luděk Cienciala, Ph.D.
Filozoficko-přírodovědecká fakulta v Opavě
Předpoklady
Computational geometry and computer graphics I
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
předmět má 22 mateřských oborů, zobrazit
Cíle předmětu
Content of the course is a computer graphics in 3D, basic algorithms, basic of geometry used in computer graphics
Výstupy z učení
- Student will get acquaint with the typical problems of computational geometry and computer graphics in 3D.
- Student will understand the existing solutions and their applications in computer graphics in 3D.
- Student will get deeper knowledge of mathematics.
- Student will learn the principles of geometric algebra including its application in graphics and vision related tasks.
- Student will practice programming, problem solving and defence of a small project.
Osnova
  • 1. Surfaces and curves - introduction and properties, interpolation and aproximation surchaces
    - Parametric surfaces, surface continuity - Parametric and geometric continuity, properties of surfaces
    - Interpolation surfaces
    - Aproximation surfaces: Hermit bicubic surface, twelve vector surface, sixteen vector surface
    - Surfaces connecting two curves
    - Surfaces set by border - bilinear Coons surface, bicubic surface, general bicubic surface
    2. Bézier surface, B -spline surface, NURBS surface
    - Bézier surface, properties
    - Bézier bicubic surfaces
    - Transformation of Bézier bicubic surfaces into triangle net
    - B -spline surfaces, properties
    - Bicubic B -Spline surfaces (Coons patch)
    - NURBS surfaces, properties
    3. Sweeping, skinning,
    - Sweeping - translational, rotational and general sweeping
    - Skinning
    4. Implicit surfaces, Subdivision surfaces.
    - Implicit surfaces, implicit surface modelling, potential function, implicit surface displaying
    - Subdivision surfaces, splitting schemes, face -split, vertex -split, aproximation, interpolation, properties of splitting schemes, splitting scheme Doo -Sabin and Catmull -Clark
    5. Solid representation and modelling
    - Representation and modelling of solids, triangle mesh, triangle strip, triangle fan, decreasing the number of triangles, decimation of triangle meshes
    - Boundary representation (B -rep), manifolds, nonmanifolds, wire -frame model, polyhedra representation, winged edge representation, point representation
    6. Constructive solid geometry, modelling by deformation, volume solid representation.
    - Constructive solid geometry, CSG tree
    - Modelling by deformation, global and local deformation, Barr deformations, model elementary deformations, deformation by rescaling, tapering, twisting bending
    - Free -form deformation
    - Volume representation and multidimensional data. Cell, voxel, 6 -connected, 18 -connected, 26 -connected, surface finding, A set of contours in parallel cuts, surface reconstruction by sheathing of contours, transformation of isosurfaces into triangle meshes: algorithms Marching cubes, Marching tetrahedrons and Dividing cubes
    7. Procedural Modelling, fractal geometry, particles systems.
    - Procedural modelling, fractals, L systems, turtle graphics
    - Fractal geometry, self -similarity, fractal dimension, multifractals, linear deterministic fractals, non -linear deterministic fractals, non -deterministic fractals, random fractals
    - Random midpoint displacements, random faults method
    - Diffusionlimitd aggregation - DLA
    - Particle systems
    8. Projection, parallel projection, central projection, viewing frustum, viewing transformations.
    - Projection
    - Parallel projection: ortographics, oblique
    - Axonometric projection: isometric, dimetric, trimetric
    - Oblique projection: cabinet, cavalier
    - Central projection
    - Unified projection
    - Viewing volume
    9. Light, lighting models, shading.
    - Radiometry terms
    - Radiance
    - Bidirectional Reflectance Distribution Function, properties
    - Local Illumination model
    - Reflection, Differential reflection, Specular reflection
    - Refraction
    - Glossy reflection
    - Phong Illumination model
    - Light source, point light, Directional light, Area light, Spot light, general luminaires, sky
    - Shading: flat, Gouraud and Phong shading.
    10. Visibility.
    - Line algorithms - Roberts algorithm, Appel algorithm, Weiler - Atherton algorithm,
    - Raster algorithms -z -buffer, Painter's algorithm, Warnock subdivision algorithm
    11. Shadows.
    - Shadows, hard shadow, penumbra
    - Projection methods
    - Shadow volume
    - Shadow depth map
    12. Textures
    - Classification of textures
    - Texture mapping
    - Inverse mapping
    - Inverse mappping of cylindrical surfa
Literatura
    doporučená literatura
  • Klawonn, F. Introduction to Computer Graphics: Using Java 2D and 3D. Springer, 2012. ISBN 9781447127321. info
  • Sarfraz, M. Interactive Curve Modeling: With Applications to Computer Graphics, Vision and Image Processing. Springer, 2010. ISBN 9781849966634. info
  • Mark de Berg a kol. Computational Geometry: Algorithms and Applications. Springer, 2008. ISBN 9783540779735. info
  • Agoston, K., M. Computer Graphics and Geometric Modelling: Implementation & Algorithms. Springer, 2005. ISBN 9781852338183. info
  • Egerton, P. A., Hall, W. S. Computer Graphics - Mathematical first steps. Pearson Education, 1999. info
  • ŽÁRA, J., BENEŠ, B., FENKEL, P. Moderní počítačová grafika. Brno Computer Press, 1998. ISBN 80-7226-049-9. info
  • Hudec, J. Algoritmy počítačové grafiky. Praha, ČVUT, 1997. info
  • Granát, L., Selechovský, H. Počítačová grafika. Praha, ČVUT, 1995. info
  • Drs, L., Ježek, F., Novák, J. Počítačová grafika. Praha, ČVUT, 1995. info
  • Sobota, B. Počítačová grafika a jazyk C. České Budějovice, KOOP, 1995. info
  • Žára, J., Sochor, J. Algoritmy počítačové grafiky. ČVUT Praha, 1993. info
  • Skála, V. Světlo, barvy a barevné systémy v počítačové grafice. Praha, ČVUT, 1993. info
  • Drdla, J. Metody modelování křivek a ploch v počítačové geometrii. Olomouc, UP, 1992. info
  • Slavík, P. Metody zpracování grafické informace. Praha, ČVUT, 1992. info
  • Poláček, J., Ježek, G., Kopincová, E. Počítačová grafika. Praha, 1991. info
  • Heinz-Otto Leitgen, Peter H. Richter. The Beauty of Fractals. Springer, 1986. ISBN 9783540158516. info
  • Drs, L. Plochy ve výpočetní technice. Praha, ČVUT, 1984. info
Vyučovací jazyk
Angličtina
Informace učitele
- 70% attendance in classes
- active participation in discussions
- critical essay of 2-3 pages debating a chosen text
Další komentáře
Studijní materiály
Předmět je dovoleno ukončit i mimo zkouškové období.
Předmět je zařazen také v obdobích léto 2019, zima 2019, léto 2020, zima 2020, zima 2021, léto 2022, zima 2022, léto 2023, zima 2023, léto 2024.