Perspectivity

In geometry and in its applications to drawing, a perspectivity is the formation of an image in a picture plane of a scene viewed from a fixed point.

According to Kirsti Andersen, the first author to describe perspectivity was Leon Alberti in his De Pictura (1435).

[1] In English, Brook Taylor presented his Linear Perspective in 1715, where he explained "Perspective is the Art of drawing on a Plane the Appearances of any Figures, by the Rules of Geometry".

[2] In a second book, New Principles of Linear Perspective (1719), Taylor wrote In projective geometry the points of a line are called a projective range, and the set of lines in a plane on a point is called a pencil.

[4] A special symbol has been used to show that points X and Y are related by a perspectivity;

The dual concept, axial perspectivity, is the correspondence between the lines of two pencils determined by a projective range.

The bijective correspondence between points on two lines in a plane determined by a point of that plane not on either line has higher-dimensional analogues which will also be called perspectivities.

Let Pn−m−1 be an (n − m − 1)-dimensional subspace of Rn with no points in common with either Sm or Tm.

This composition is a bijective map of the points of S2 onto itself which preserves collinear points and is called a perspective collineation (central collineation in more modern terminology).