Matrices: Orientations and Transformations
Vector Triads
General Matrices
Identity Matrix
Transpose
Determinants
Inverse Matrices
Discrete Transformations - Orientations
Rotations
Reflections
4x4 Transformation Matrices
Eulerian Angles
Pan Tilt and Cant
Rotations from Reflections
Quaternions
Kopp Rotations
Multiplication-free dot products of unit vectors
Multiplication-free diffuse lit spherical textures
Multiplication-free bump-mapped spheres
Multiplication-free specular bump-mapped spheres
Continuous Transformations - Motion
Discrete Rotation Rates
Example: "Magic Angles"
Representing 2D and 3D Objects
Points Lines and Planes
Points
Lines
Colinearity of Three Points
Planes
Coplanarity of Four Points
Polygons
Convex Hulls
Spheres Circles and Conics
Fitting a Circle to Three 2D Points
Rings and Disks
Conics and Quadrics
3D Clipping
Rectangular View Cone
Checking Spheres
Checking Projected Spheres
Checking and Clipping Lines
Circular View Cone
Checking Spheres
Point Checking Celestial Points
Clipping to a Sphere
Visibility Checks
Facets of Convex Hull
Arbitrary Camera Orientations
3D Projection
Projective Methodologies
Projected Gradients
Projections of common objects
Projected Lines
Projected Quadrics
Projected Circles
Projected Spheres
Circle fit to projected sphere
Bezier fit to projected sphere
Projected Conic Sections
Projected Bezier Curves
Inverse Projection - Ray Casting
To Plane
Iteration of projected planar boundary in texture space
To Sphere
Texturing
Reconstructed Perspective
Arbitrary Camera Orientations
Rotation and Projection of a Point
Cartesian Coordinates
Spherical Polar Coordiantes
Cylindrical Polar Coordiantes
In summary:
Rotation and Projection of Multiple Points
Image-warp Projections
Illumination
Lit Objects in 3D
Illuminated Quadrics
Illuminated Spheres
