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
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
Prewarping
PolarNoise
Uping
Island Noise
Squared Polar Tiling     Island Tiles
References/Source Material

Celtic Functions
Knotwork
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: www.iancgbell.clara.net/maths or www.bigfoot.com/~iancgbell/maths
18 Nov 2006.