CS 184: Foundations of Computer Graphics
Important topics covered in Spring 2009

Computer Graphics Hardware and Its Abstract View:

• Display devices: calligraphic, raster.
• Frame buffer organization, color map.

Modeling and Object Representations:

• CSG, Brep, Voxels,
• Winged-edge data structure
  
• Procedural object generation, e.g., sweep operations;
• Instantiations and scene hierarchy.
• Scene-description files SCD_09.
  
• Abstractions, level of details.
• Degrees of freedom.
• Procedural object generation.
• Sweeps.

Transformations, Matrix Operations;

• Rigid-body transformations and affine transformations,;
• Change of coordinate systems;
• Window-to-Viewport transformation.
• Homogeneous coordinates: purpose, implementation.
• Perspective warp into canonical view volume;
• Perspective projection versus parallel projection;
• Oblique projections, generalized camera models.
  
• Master-, world-, image-, NDC-, screen-coordinate systems; transformations between them.
• Efficient and logical ordering of the various functions in the viewing pipeline.

Visibility and Clipping:

• Use of bounding boxes.
• View frustum culling;
• Sutherland-Hodgman polygon clipping.
• Interpolation.
  
• Front- and Back-plane clipping.
• Backface elimination; face normals: formula by Martin Newell .
• Painter's algorithm.
  
• Z-buffer algorithm for hidden feature elimination, scan-line implementation

Illumination Models and Lights:

• Surface models, idealized and real:
• Lambert surfaces, ideal mirrors, Phong lighting model;
• Diffuse-, mirror-, and (Phong)specular- reflection;  metal vs. plastic.
• The various types of lights: ambient, directional, point, spot.
  
• Area light sources.

Rendering:

• The classical rendering pipeline.
  
• Principles of  ray-casting.
• Principles of  ray-tracing.
• Accelerating data structures.
  
• Reflection and refraction.
  
• Principles of  radiosity-based rendering.
• Principles of  photon mapping
• Distribution Ray Tracing
  
• Gouraud shading, Phong shading, and their limitations
• Surface decorations: texture mapping; bump mapping, displacement mapping, environment mapping.
• Image-based rendering.
• Light-field rendering.
  

Splines:

• Parameterized polynomial curves; in particular, cubics.
• Differential geometry of space curves. Frenet frame, curvature, torsion.
  
• Approximating splines, versus interpolating splines.
• Bézier curve segments, and methods to assemble them.
• G0, G1, G2, C1, C2, continuity, and conditions for achieving them.
• Sketching curve segments from points; finding the point for some value t = [0,1]
• DeCasteljeau algorithm for the construction and subdivision of Bézier curves.
• Concept of approximating complicated curves with many (cubic) spline segments.
• Cubic B-spline, how to make smooth closed curves.
• Bicubic Bézier patches. B-spline surfaces.
  
• Catmull-Clark subdivision surfaces.

Systems Modeling:

• Articulated skeletons
  
• Kinematics and inverse kinematics
• Spring-mass systems
• Physics-based simulation
• Basic ways to solve the ODEs, their strength and weaknesses
  

Rasterization, Sampling, Anti-Aliasing:

• Inside/outside determination by parity or winding-number.
• Pixel sampling,
• How to represent points, lines, and areas on a raster device.
• Which polygons owns a pixel when the sampling point falls on the boundary?
• Scan-line algorithm.
• Texture mapping.

Color, Materials Properties:

• 2D color wheels, additive and subtractive mixing.
• 3D spaces: RGB, HSV, HLS.
• Physicist's view: continuous spectrum.
• Perceptual colors, metamers, color matching.
• 3 Grassmann Laws, CIE diagram.
• Identifying and marking colors in these spaces.
• Metamers, color mixing, additive and subtractive.
• Transparency and the effects of color filters.
• Translucency; participating media.
• BRDF.

See also Shirley Chapters: 1, 2.1-2.4, 3, 4.4, 5, 6, 7, 8.2, 10, 11, 12, 13.1-13.3, 15.