Homography
In projective geometry, a
homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which they are derived. It is a bijection that maps lines to lines, and thus a collineation. In general, there are collineations which are not homographies, but the fundamental theorem of projective geometry asserts that is not so in the case of real projective spaces of dimension at least two. Synonyms include
projectivity,
projective transformation, and
projective collineation. Historically, homographies have been introduced to study perspective and projections in Euclidean geometry, and the term "homography", which, etymologically, roughly means "similar drawing" date from this time. At the end of 19th century, formal definitions of projective spaces were introduced, which differed from extending Euclidean or affine spaces by adding points at infinity. The term "projective transformation" originated in these abstract constructions. These constructions divide into two classes that have been shown to be equivalent.