Sierpinski (<1K)Maths for (Games) Programmers
Section 2 - Matrix Methods

Vectors and Coordinate Systems
    Coordinate Systems in Two Dimensions
          Cartesian Coordinates     Polar Coordinates
    Coordinate Systems in Three Dimensions
             Cylindrical polar coordinates     Spherical polar coordinates     Scaled Cartesian coordinates     Added square Cartesian Coordinates
    Vector Operations
          Dot Product     Cross Product     Geometric Product     Other Vector Products     Curvature and Tortion
    Polar Function
          Derivatives     Euclidean Length     Approximations to Eulidean Length     Calculating the Polar Angle     Grad of distance functions

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
    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

    Lit Objects in 3D
          Illuminated Quadrics     Illuminated Spheres

Convex Hull Algorithm

Primal Simplex Algorithm
    The Basic Algorithm
    Application to 3D Convex Hulls
          Generating the Vertices of a Convex Hull

Glossary   Contents   Author
Copyright (c) Ian C G Bell 1998
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18 Nov 2006.