Parallel projection

The transformation P is the orthogonal projection onto the line m.

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P² = P. Projections map the whole vector space to a subspace and leave the points in that subspace unchanged.^[1]

Parallel Projection Media

Parallel projection terminology and notations. The two blue parallel line segments to the right remain parallel when projected onto the image plane to the left.
Two parallel projections of a cube. In an orthographic projection (at left), the projection lines are perpendicular to the image plane (pink). In an oblique projection (at right), the projection lines are at a skew angle to the image plane.
A parallel projection corresponds to a perspective projection with a hypothetical viewpoint; i.e. one where the camera lies an infinite distance away from the object and has an infinite focal length, or "zoom".
Various projections and how they are produced
Comparison of several types of graphical projection. The presence of one or more 90° principal angles is usually a good indication that the perspective is oblique.
Optical-grinding engine model (1822), drawn in 30° isometric perspective
Example of a dimetric perspective drawing from a US Patent (1874)
Example of a trimetric projection showing the shape of the Bank of China Tower in Hong Kong.
Detail of the original version of Along the River During the Qingming Festival attributed to Zhang Zeduan (1085–1145). Note that the picture switches back and forth between axonometric and perspective projection in different parts of the image, and is thus inconsistent.

N. Dunford and J.T. Schwartz, Linear Operators, Part I: General Theory, Interscience, 1958.
Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics, 2000. ISBN 978-0-89871-454-8.