FPF:FPFVA034 Comp. geometry and graphic II - Course Information

FPFVA034 Computational geometry and computer graphics II

Extent and Intensity

0/1/0. 5 credit(s). Type of Completion: z (credit).

Teacher(s)

doc. RNDr. Luděk Cienciala, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Luděk Cienciala, Ph.D.
Faculty of Philosophy and Science in Opava

Prerequisites

Computational geometry and computer graphics I

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

Content of the course is a computer graphics in 3D, basic algorithms, basic of geometry used in computer graphics

Learning outcomes

- 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.

Syllabus

• 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

Literature

recommended literature
• 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

Language of instruction

English

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

Teacher's information

- 70% attendance in classes
- active participation in discussions
- critical essay of 2-3 pages debating a chosen text

• Enrolment Statistics (Winter 2021, recent)
  
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