projection

—projectional /preuh jek"sheuh nl/, adj.

/preuh jek"sheuhn/, n.

1. a projecting or protruding part.

2. the state or fact of jutting out or protruding.

3. a causing to jut or protrude.

4. the act, process, or result of projecting.

5. Cartog. a systematic construction of lines drawn on a plane surface representative of and corresponding to the meridians and parallels of the curved surface of the earth or celestial sphere.

6. Photog.

a. the act of reproducing on a surface, by optical means, a remote image on a film, slide, etc.

b. an image so reproduced.

7. the act of visualizing and regarding an idea or the like as an objective reality.

8. something that is so visualized and regarded.

9. calculation of some future thing: They fell short of their projection for the rate of growth.

10. the act of communicating distinctly and forcefully to an audience.

11. Psychol.

a. the tendency to ascribe to another person feelings, thoughts, or attitudes present in oneself, or to regard external reality as embodying such feelings, thoughts, etc., in some way.

b. Psychoanal. such an ascription relieving the ego of a sense of guilt or other intolerable feeling.

12. the act of planning or scheming.

13. Alchemy. the casting of the powder of philosophers' stone upon metal in fusion, to transmute it into gold or silver.

[1470-80; < L projection- (s. of projectio) a throwing forward. See PROJECT, -ION]

Syn. 1. jut, overhang, protrusion. 9. prediction.

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▪ cartography

      in cartography, systematic representation on a flat surface of features of a curved surface, as that of the Earth. Such a representation presents an obvious problem but one that did not disturb ancient or medieval cartographers. Only when the voyages of exploration stimulated production of maps showing entire oceans, hemispheres, and the whole Earth did the question of projection come to the fore. Mercator produced the simplest and, for its purposes, the best solution by in effect converting the spherical Earth into a cylinder with the open ends at the poles; this cylinder was then opened to form a plane surface. East–west and north–south directions could be represented with fidelity, and the distortions in size became gross only near the polar regions (rendering Greenland, for example, disproportionately large). The Mercator projection is still widely used, especially when north–south dimensions are of chief importance. Many other projections are used, for example, the conic projection, drawn from a point directly above the North or South Pole. All projections involve some degree of distortion, and those showing the entire Earth involve a large degree.

▪ geometry

 in geometry, a correspondence between the points of a figure and a surface (or line). In plane projections, a series of points on one plane may be projected onto a second plane by choosing any focal point, or origin, and constructing lines from that origin that pass through the points on the first plane and impinge upon the second (see illustration—>). This type of mapping is called a central projection. The figures made to correspond by the projection are said to be in perspective, and the image is called a projection of the original figure. If the rays are parallel instead, the projection is likewise called “parallel”; if, in addition, the rays are perpendicular to the plane upon which the original figure is projected, the projection is called “orthogonal.” If the two planes are parallel, then the configurations of points will be identical; otherwise this will not be true.

      A second common type of projection is called stereographic projection. It refers to the projection of points from a sphere to a plane. This may be accomplished most simply by choosing a plane through the centre of the sphere and projecting the points on its surface along normals, or perpendicular lines, to that plane. In general, however, projection is possible regardless of the attitude of the plane. Mathematically, it is said that the points on the sphere are mapped onto the plane; if a one-to-one correspondence of points exists, then the map is called conformal.

       projective geometry (q.v.) is the discipline concerned with projections and the properties of projective configurations.

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