What is the relationship among orthogonal transformation, affine transformation and projection transformation?

Orthogonal transformation: Let V be an N-dimensional Euclidean space and α ∈ end V. If α satisfies (α α, α β) = (α, β) and α, β∈V is arbitrary, then α is called orthogonal transformation.

Affine transformation: let v, v' be a linear space on the number field p, α, α'; M, m' are vectors and subspaces of V and V' respectively, and G is a linear isomorphism from M to M'. Then π α′ gτ-α is called affine transformation from α (α+m) to α (α ′+m ′).

Projective transformation: Let f:V→V → v' be isomorphic in linear space. The isomorphism ρ (f) from ρ (v) to ρ (v') induced by f is called the projective transformation from ρ(v) to ρ(v').