Hier alle technische details van een 3d engine uitgelegd in normale (wel engelse) taalLinear Transformations
A linear transformation can be described as any operation on a vector which can be done with a matrix. Projections, rotations, dilations, skewtheshitoutofavectorations, etc are all linear operations. More formally, a linear transformation is a transformation which is linear, i.e. any transformation which satisfies A(cx+dy) = c(Ax) + d(Ay), where A is a matrix, x and y are vectors, c and d are scalars. Note that one thing that is not possible with a matrix is to translate. Translation requires moving the origin, but any matrix multiplied by a 0 matrix (or vector) will always return 0. It is because of this that 4x4, and not 3x3 matrices are used to transform 3 dimensional vectors (for our purposes, we can call them points, as we are using the matrices to transform the vertices (points) of a triangle).
I recommend taking the time to read the italics and understanding what it means if you really want to understand linear transformations. The definition is extremely powerful; from it comes everything you'll ever need to know about linear transformations, or almost everything.
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