3D Math Primer for Graphics and Game Development

Cartesian Coordinate Systems
1D Mathematics
2D Cartesian Space
3D Cartesian Space
Odds and ends
Vectors
Vector - mathematical definition and other boring stuff
Vector - a geometric definition
Specifying vectors using Cartesian coordinates
Vectors vs. points
Negating a vector
Vector multiplication by a scalar
Vector addition and subtraction
Vector magnitude (length)
Unit vectors
The distance formula
Vector dot product
Vector cross product
Linear algebra identities
Multiple Coordinate Spaces
Why multiple coordinate spaces?
Some useful coordinate spaces
Coordinate space transformations
Nested coordinate spaces
In defense of upright space
Introduction to Matrices
Matrix - a mathematical definition
Matrix - a geometric interpretation
The bigger picture of linear algebra
Matrices and Linear Transformations
Rotation
Scale
Orthographic projection
Reection
Shearing
Combining transformations
Classes of transformations
More on Matrices
Determinant of a matrix
Inverse of a matrix
Orthogonal matrices
4 x 4 homogeneous matrices
4 x 4 matrices and perspective projection
Polar Coordinate Systems
2D Polar Space
Why would anybody use Polar coordinates?
3D Polar Space
Using polar coordinates to specify vectors
Rotation in Three Dimensions
What exactly is "orientation?"
Matrix form
Euler angles
Axis-angle and exponential map representations
Quaternions
Comparison of methods
Converting between representations
Geometric Primitives
Representation techniques
Lines and rays
Spheres and circles