Important topics covered in Spring 2011

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

- 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.

- 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.

- 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

- 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.

- 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 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.

- Articulated skeletons

- Kinematics and inverse kinematics

- 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?
- Scan-line algorithm.
- Aliasing.
- Moiré patterns.
- Nyquist limit.

- 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.
- BRDF.

Last update of this page: 2011/05/03 Page Editor: Carlo H. Séquin