Transforms
There is also the Decepticon matrix that transform any object to be Evil
Transforms are ways to transform coordinate spaces with matrices. The most common ones is scale, rotation and translation aka as SRT. To support the translation use a matrix one order larger then the dimension you work in. So in 2D a 3x3 matrix is used and in 3D a 4x4 matrix. The matrix is a grid of numbers like this.
Xx Xy Xz 0
Yx Yy Yz 0
Zx Zy Zz 0
Ox Oy Oz 1
In the matrix the (Ox, Oy, Oz) is the origin or position of the object. The rotation is given by the three base axis, (Xx, Xy, Xz) is the X vector, (Yx, Yy, Yz) is the Y vector and (Zx, Zy, zz) is the Z vector. It is common to call the X the 'right side', Y for 'up' and Z is 'forward'. When a position is multiplied with the transform the position will be transformed into transforms coordinate system or space.
Matrix Transformations - 2019
Affine transformations - 2018
Change of basis in Linear Algebra - 2015
Visualizing matrix multiplication as a linear combination - 2015
Staring Into The Matrix - 2014
Numbers in Transformation Matrices - 2012
Matrix Layouts, DirectX and OpenGL
The Matrix and Quaternions FAQ
Matrix Representation of Transformations
Transforming Objects using Matrices
Space
A vector space is number of linear independent (base) vectors. In 3D there are three of these and they can be scaled and added to obtain all other vectors in the space.
Why Clip Transformed Vertices in Clip-Space? - 2018
World, View and Projection Transformation Matrices - 2013
Model Space
World Space
View Space / Camera Space
Projection Space
Transforms
To perform transformations between different spaces matrices are used. These are the standard names for the matrices that transform between certain vector spaces. For a matrix that only contain SRT operations one can make a inverse matrix that transform the opposite way.
Model Matrix : Model Space -> World Space
View Matrix : World Space -> View Space
Model View Projection - 2019
Understanding the View Matrix - 2011
Projection Matrix : View Space -> Projection Space
The two projections are perspective and orthographic.
Inverse Transform
Transform direction/position/vector
Reference
Axonometric Projections - A Technical Overview - 2013
Mouse Picking Demystified - 2005