CS 184: Foundations of Computer Graphics
Important topics covered in Spring 2011
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.
Transformations, Matrix Operations;
Rigid-body transformations and affine transformations,;
Change of coordinate systems;
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
Efficient and logical ordering of the various functions in the viewing
Visibility and Clipping:
- Use of bounding boxes.
- View frustum culling;
- Sutherland-Hodgman polygon clipping.
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.
- The various types of lights: ambient, directional, point, spot.
- Area light sources.
- 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.
- 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
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.
- Articulated skeletons
- Kinematics and inverse kinematics
Rasterization, Sampling, Anti-Aliasing:
Inside/outside determination by parity or winding-number.
- Pixel sampling.
- Texture mapping.
- How to represent points, lines, and areas on a raster device.
- Which polygons owns a pixel when the sampling point falls on the boundary?
- Moiré patterns.
- Nyquist limit.
Color, Materials Properties:
- Color wheels, additive and subtractive mixing.
3D color 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.
- Transparency and the effects of color filters.
- Translucency; participating media.
Last update of this page: 2011/05/03
Page Editor: Carlo H. Séquin