Orthographic projection

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Orthographic projection (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where all the projection lines are orthogonal to the projection plane,^[1] resulting in every plane of the scene appearing in affine transformation on the viewing surface. It is further divided into multiview orthographic projections and axonometric projections. A lens providing an orthographic projection is known as an (object-space) telecentric lens.

The term orthographic is also sometimes reserved specifically for depictions of objects where the axis or plane of the object is also parallel with the projection plane,^[1] as in multiview orthographic projections.

Symbols used to define whether a projection is either Third Angle (right) or First Angle (left).

Origin

The orthographic projection has been known since antiquity, with its cartographic uses being well documented. Hipparchus used the projection in the 2nd century B.C. to determine the places of star-rise and star-set. In about 14 B.C., Roman engineer Marcus Vitruvius Pollio used the projection to construct sundials and to compute sun positions.^[2]

Vitruvius also seems to have devised the term orthographic (from the Greek orthos (= “straight”) and graphē (= “drawing”) for the projection. However, the name analemma, which also meant a sundial showing latitude and longitude, was the common name until François d'Aguilon of Antwerp promoted its present name in 1613.^[2]

The earliest surviving maps on the projection appear as woodcut drawings of terrestrial globes of 1509 (anonymous), 1533 and 1551 (Johannes Schöner), and 1524 and 1551 (Apian).^[2]

Multiview orthographic projections

Main article: Multiview orthographic projection

With multiview orthographic projections, up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative to each other according to either of two schemes: first-angle or third-angle projection. In each, the appearances of views may be thought of as being projected onto planes that form a 6-sided box around the object. Although six different sides can be drawn, usually three views of a drawing give enough information to make a 3D object. These views are known as front view, top view and right side view.

Pictorials

Main article: Axonometric projection

Within orthographic projection there is the subcategory known as pictorials. Axonometric pictorials show an image of an object as viewed from a skew direction in order to reveal all three directions (axes) of space in a single picture.^[3] Orthographic pictorial instrument drawings are often used to approximate graphical perspective projections, but there is attendant distortion in the approximation. Because pictorial projections inherently have this distortion, in the instrument drawing of pictorials, great liberties may then be taken for economy of effort and best effect. Orthographic pictorials rely on the technique of axonometric projection ("to measure along axes").

See also

• Graphical projection
• Multiview orthographic projection
• Orthographic projection (cartography)
• Telecentric lens
• Telephoto lens
• Orthographic projection (geometry)

References

1. ^ ^{a b} Maynard, Patric (2005). Drawing distinctions: the varieties of graphic expression. Cornell University Press. pp. 22. ISBN 0801472806. http://books.google.com/?id=4Y_YqOlXoxMC&pg=PA22&lpg=PA22&dq=axonometric+orthographic&q=axonometric%20orthographic. 
2. ^ ^{a b c} Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections pp. 16–18. Chicago and London: The University of Chicago Press. ISBN 0-226-76746-9.
3. ^ Mitchell, William; Malcolm McCullough (1994). Digital design media. John Wiley and Sons. pp. 169. ISBN 0471286664. http://books.google.com/?id=JrZoGgQEhKkC&pg=PA169&dq=axonometric+orthographic#v=onepage&q=axonometric%20orthographic. 

External links

• Normale (orthogonale) Axonometrie in german
• Orthographic Projection Video and mathematics

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Infographics Graphical projections Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Valdemar IV of Denmark Spherical harmonics Look at other dictionaries: Orthographic projection — Orthographic Or tho*graph ic, Orthographical Or tho*graph ic*al, a. [Cf. F. orthographique, L. orthographus, Gr. ?.] 1. Of or pertaining to orthography, or right spelling; also, correct in spelling; as, orthographical rules; the letter was… …   The Collaborative International Dictionary of English orthographic projection — n. a two dimensional pictorial representation of a three dimensional object in which the object is shown separately in two or more accurate, scaled down views, as from the top, front, and side: the views are typically displayed with the top view… …   English World dictionary orthographic projection — noun Date: 1668 1. projection of a single view of an object (as a view of the front) onto a drawing surface in which the lines of projection are perpendicular to the drawing surface 2. the representation of related views of an object as if they… …   New Collegiate Dictionary orthographic projection — a two dimensional graphic representation of an object in which the projecting lines are at right angles to the plane of the projection. Also called orthogonal projection. Cf. isometric (def. 5). [1660 70] * * * ▪ engineering       common method… …   Universalium orthographic projection — ortografinė projekcija statusas T sritis fizika atitikmenys: angl. orthographic projection vok. orthographische Projektion, f rus. ортографическая проекция, f pranc. projection orthographique, f …   Fizikos terminų žodynas Orthographic projection (cartography) — Orthographic projection (equatorial aspect) of eastern hemisphere 30W–150E An orthographic projection is a map projection of cartography. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or… …   Wikipedia Orthographic projection (geometry) — In Euclidean geometry, an orthographic projection is an orthogonal projection. In particular, in 3D it is an affine, parallel projection of an object onto a perpendicular plane. A simple orthographic projection onto the plane z = 0 can be defined …   Wikipedia orthographic projection — noun 1. : projection in which the projecting lines are perpendicular to the plane of projection called also orthogonal projection 2. : a map projection of one half the globe as it would appear to a camera centered on any point desired from an… …   Useful english dictionary orthographic projection — noun Engineering a method of projection in which an object is depicted using parallel lines to project its outline on to a plane …   English new terms dictionary orthographic projection — orthograph′ic projec′tion n. erg a two dimensional graphic representation of an object in which the projecting lines are at right angles to the plane of the projection. Also called orthog′onal projec′tion Compare isometric 4) • Etymology: 1660–70 …   From formal English to slang 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”