Syllabus for 15-462, Computer Graphics, Spring 2007

Topics that you should expect to learn this semester. Topics will be taught in approximately but not exactly in order.

1. Introduction
   • Administrative matters
   • What is Computer Graphics?
2. The 3D Graphics Pipeline
   • Graphics Programming and OpenGL
   • Event-driven Programming
3. Transformations:
   • Homogeneous vector and matrix notation
   • 2D/3D Transformations
   • Chaining transformations
   • Nonlinear transformations (free form deformation)
4. Modeling Hierarchies
   • What hierarchies are and why we use them
   • Matrix stack primitives
   • Hierarchy Algorithms
   • Modeling examples
   • Getting the right "control knobs"
   • Hierarchies w/nonlinear transformations
   • Interface and implementation issues
5. 3D Viewing and Projection:
   • Perspective projection
   • Viewing and view volumes
   • Clipping
6. Geometric Modeling
   • Polygons and polygon meshes
   • Spline curves: Natural, Hermite, Bezier, etc.
   • Recursive subdivision, forward differencing
   • Bicubic surfaces
   • Solid primitives, sweeps, B-reps
   • Implicit surfaces, quadrics, blobs
   • Booleans, CSG,
   • Fractals
7. Animation:
   • Traditional cel animation
   • Keyframes: state space points and trajectories
   • Inbetweening: linear interpolation,
   • interpolating splines, slow in and out, etc.
   • Procedural animation
   • Inverse Kinematics
   • Dynamics and Control
   • Interface and implementation issues.
8. Rendering
   • Line and polygon scan conversion
   • Painter's algorithm
   • Z-buffer algorithm
   • Light and Color
   • Illumination and reflection
   • Gouraud & Phong shading
   • Texture Mapping
9. Ray tracing
   • Ray-surface intersection testing
   • Ray casting
   • Shadows and Transparency
   • Recursive ray tracing
   • Spatial data structures for optimization
10. Image Algorithms and 2D Special Effects
    • Flood fill, dithering
    • Point processing (contrast enhancement, compositing)
    • Filtering