Parallel projection facts for kids

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.

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.

Images for kids

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".
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 dimetric projection in Chinese art in an illustrated edition of the Romance of the Three Kingdoms, China, c. 15th century CE.
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.