Projective geometry is less restrictive than either Euclidean geometry or affine geometry. Hence shape is an invariant of affine geometry. An algebraic variety can be neither affine nor projective. Every real or complex affine or projective space is also a topological space. There are two main kinds of finite plane geometry&colon; affine and projective. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. This is the first isomorphism theorem for affine spaces. Therefore, SIFT descriptors are invariant to minor affine changes. This includes Euclidean spaces, which are affine spaces. The Euclidean group is a subgroup of the group of affine transformations. Sometimes other algebraic sites replace the category of affine schemes. But also all of the etale cohomology groups on affine space are trivial. An important example is the projection parallel to some direction onto an affine subspace. All rigid transformations are examples of affine transformations. Geometry in affine spaces over a finite fields has also been widely studied.