Sierpinski (<1K)Maths for (Games) Programmers
Section 3 - The Art of Functions

Functions of a Single Variable
    Look Up Tables
          ThinnessErrors     Sparseness Errors
    Bit-Shifting Methods
    Iterative Methods
    Approximation Functions
          Least Squares Polynomials     Minimax Polynomials     Minimax Rational Functions
    Basic Math Functions
          Square Root function     Power Function     Sine and Cosine functions     Arctangent function     Logarithm function     Antilog or Exponential Function     Reciprocal function     Gamma Function
    Dropoff Functions
          ½-symmetrising     Linear     Cubic     Quartic     Squared cosine     Bias     Gain     Slope1     Sinc Function     Dropoff derivatives   
    Random Variables
          Uniform     General     Random Directions

Functions of Several Variables
    Scalar and Vector Fields
          Gradient of a scalar field     Divergence of a vector field     Curl of a vector field     Laplacian of scalar and vector fields     Jacobian Matrix and The Chain Rule     First and Second Derivatives of Composite Functions     Fractal Sum     Fractal Multiply

Recurrance Relations
    Solving Recurrance Relations
          Example - Damped Motion
    Successive Evaluations of Polynomials Via Iteration
          Example - Iteration of Bezier Curves
    Succesive Evaluations Via The Midpoint Algorithm
          Example - Division-Free 2D Line Draw     Example - Division-Free Perspective Texture Mapping
    Inverse Functions Via Iterative Approach
    General Functions Via Iterative Approach
    Circle Drawing Using Simultaneous Recurrance Relations
    Ellipse Drawing Using Circle Iterations

Bezier Curves
          Subdividing Beziers
    Bezier Approximations
          To Cubic     To Circular Arc     To General 1-D Curve     To General N-D Curve

Lattice Blends
    Lattice Blending
          Anisotropic Regular Lattice Blending     Lerped Lattice Blending     0-interferant lattice blending     Bi-Lattice Value Blends     Lattice Value-Gradient Blends     Trigonometric Lattice Blending     Isotropic Lattice Blending
    Triangular Lattice Blending

Noise Functions
    Terminologies and Conventions
          White Noise     Pink Noise     Gray Noise     Brown Noise     Mauve Noise
    Sparse Displacement Noise
    Trigonometric Noise
          Range of Trigonometic Noise     Grad of Trigonometic Noise
    Gradient Noise
          Popular Uses of Perlin Noise     Restricted Vocabulary     Range of Gradient Noise     Grad of Gradient Noise     Grad of Value Noise     VariPly Noise     Directed Noise     Variable Frequency Noise
    Ridged Noised
          EquiRidged Noise     Capped EquiRidged Noise     Ridged Noise     CapRidged Noise     Ripple Noise
    Petal Noise
          Grad of Petal Noise
    Island Noise
          Squared Polar Tiling     Island Tiles
    References/Source Material

Celtic Functions
          Sloss Crossover Tiles     Sloss Border Tiles     Constructing Knots     Functional Form     Coloured Bands
    References/Source Material

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