Computer Graphics

• Friday, April 16, 2004
• Introduction, applications
• Survey of the rendering pipeline
  
• Geometric transformations: translations, rotations, reflections
• Rotations in space
  
• Monday, April 19, 2004
• Scalings, affine transformations, shearings
• Projections
  
• Invariance of lengths, angles, area, parallel lines, ratios
  
• Homogeneous coordinates: definition, basic construction
  
• Friday, April 23, 2004
• Homogeneous coordinates: intersection of parallel lines, points at infinity affine transformations, projective transformations
• The projective plane: algebraic and geometric definition
  
• Projective Space
  
• Monday, April 26, 2004
• Rasterization:
• The Bresenham line scan algorithm
• Drawing of circles
  
• Friday, April 30, 2004
• Drawing of circles
• Light and Color
  
• Monday, May 3, 2004
• spectral colors
• human color perception
• additive mixing and optical mixing of colors
• Friday, May 7, 2004
• The RGB, HSV and HLS color models
• Monday, May 10, 2004
• Compression of color information; the YIQ model
• subtractive mixing of colors
• Color models CMY and CMYK
  
• Friday, May 14, 2004
• Geometric transformations in the rendering pipeline
• Perspective transformation
  
• Monday, May 17, 2004
• Properties of perspective transformations and projections, vanishing points
• Transformation to device (viewport) coordinates
• Clipping, the Cohen-Sutherland algorithm
• Monday, May 24, 2004
• Properties of perspective transformations; invariance of cross-ratios
• Transformation of plane coordinates
• Visible and invisible surfaces
• Shading of points
  
• Friday, May 28, 2004
• Shading of points: diffuse and specular reflection, ambient light
  
• Shading of areas through interpolation: Gouraud shading, Phong shading
• Normal directions in polyhedral models
  
• Monday, May 31, 2004: Pfingstmontag, no lecture
  
• Friday, June 4, 2004
• Filling of triangles and more general polygons
  
• Linear interpolation in world coordinates
• Monday, June 14, 2004
• Problems with Phong shading and linear inerpolation in screen coordinates
• Hidden-surface removal
  
• Friday, June 17, 2004
• Artifacts associated with Phong shading and linear inerpolation in screen coordinates
• The z-buffer
• Shadows
• Texture mapping, bump mapping
  
• Monday, June 21, 2004
• physics-bases models of reflection from surfaces
• Global illumination: the rendering equation
• Photometric quantities and units of measurement
• Spatial angles
  
• Friday, June 25, 2004
• Global illumination: Radiosity
• Iterative solution of the radiosity equations
  
• Form factors
• Refraction
  
• Monday, June 28, 2004
• Ray-tracing
  
• Friday, July 2, 2004
• Two-way ray tracing
• Illustrations: caustics
  
• Modeling of curves and surfaces
• Different specifications of surfaces, and operations on them
• implicit curves and surfaces
• parametric curves and surfaces
• polygonal curves and surfaces
• Bézier curves: definition, Bernstein polynomials, and their properties
  
• Friday, July 9, 2004
  
• Bézier curves: The subdivision algorithm of de Casteljau
  
• Friday, July 16, 2004
• Rational parametric curves
  
• B-splines, NURBS
  
• Ausblick auf das Praktikum im Wintersemester