• Rastering
• Affine transformations and perspective projections
• Curves and splines
• Surfaces
• Wavelets
• Rendering of 3D objects

• Midpoint subdivision, quadrant and octant DDD, Multi-step DDA
• Rastering of circles (Bresenham algoritm), filled polygons and thick lines
• Antialiasing, supersampling, postfiltering, prefiltering
• Affine 3D rotations, scaling operations, reflections, translations
• Perspective projection, viewport, 2D and 3D clipping
• CAGD, data points, control points, parameter representation, tangent line, osculating circle
• Base matrix, blending functions, barycentric combination
• Linear, Lagrange and Hermite interpolation, extended Neville algoritm
• Blossom notation, multi-linearity, Bézier curve, convex hull property
• Segmentation and raising of degree, continuity of Bézier splines
• Bézier representation of Lagrange of Hermite interpolated curves
• Polynomial B-splines, knot vector, virtual and real knots, nodal points
• Bézier representation of B-splines
• Knot insertion, uniform and open-uniform B-splines
• Cox and de Boor algoritm, rationale B-splines (NURBS)
• Construction ov circles
• 1D-wavelets, analysis or decomposition, synthesis or reconstruction
• Multi-resolution analysis, Haar wavelet transformation and spline wavelets
• Tensor product surfaces
• Bézier patches, NURBS patches, Coons and Gordon surfaces
• 2D-wavelets and tensor product wavelets
• Removal of invisible surfaces: z-Buffer, list-priority, scanline, ray casting and area subdivision algoritms
• Diffuse and mirroring reflection, ambient light, local and global reflection models
• Ray tracing and radiosity
• Gouraud and Phong shading

• Algoritms for rastering of basic objects
• Antialiasing methods
• Calculation of affine transformations and of perspective projections
• Survey of CAGD techniques
• Applying discrete wavelet transformations in computer graphics
• Methods for removal of invisible surfaces
• Applying effects of light and shadow, illuminating and reflection models

• Ability to apply general scientific insights (numerical methods) to scientific problems (rendering of 3D objects) (AWC2)
• Ability to analyse engineering problems in a scientific way, and to solve them (ATC2)
• Ability to use research methods and techiques to solve engineering problems (ATC4)
• Ability to implement and apply basic algorithms and data structures (SC8)
• Ability to obtain knowledge and insight in present-day scientific research in computer science (SC10)

Further reading:

• Farin, Gerald, Curves and Surfaces for CAGD, Morgan Kaufmann, 2002
• Goldman, Ron, Pyramid Algorithms, Morgan Kaufmann, 2003
• Prautzsch, Hartmut, Boehm, Wolfgang en Paluszny, Marco, Bézier and B-Spline Techniques, Springer, 2002
• Salomon, David, Computer Graphics and Geometric Modeling, Springer, 1999
• Stollnitz, Eric J., Derose, Tony D. en Salesin, David H., Wavelets for Computer Graphics, Morgan Kaufmann, 1996