- 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