FPF:FPFVA034 Computational geometry and com - Informace o předmětu

FPFVA034 Computational geometry and computer graphics II

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

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