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## What do projective transformations preserve?

A projective transformation preserves **incidence**. points and three concurrent lines are mapped to three concurrent lines. The latter might involve the case that the point of intersection is mapped to a point at infinity. Because of the incidence preservation, projective transformations are also called collineations.

## What is meant by Euclidean space?

Euclidean space, In geometry, **a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply**; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.

## What is fundamental theorem of projective geometry?

The fundamental theorem of projective geometry says that **an abstract automorphism of the set of lines in Kn which preserves “incidence relations” must have a simple algebraic form**.

## How is projective geometry used in art?

Projective geometry is a field of mathematics which deals which **the relationship between the mappings and projections of real life three dimensional objects** on to a two dimensional plane or paper. … This branch of geometry has been vastly used in painting, drawings and other art forms for hundreds of years.

## Is translation a projective transformation?

Although a translation is a non-**linear transformation** in a 2-D or 3-D Euclidean space described by Cartesian coordinates (i.e. it can’t be combined with other transformations while preserving commutativity and other properties), it becomes, in a 3-D or 4-D projective space described by homogeneous coordinates, a simple …