Graphical projection
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Graphical projection in the visual sciences is an imaging procedure the protocols of which preclude the necessity of mathematical calculation.
Graphical projection is a protocol by which an image of an imaginary three-dimensional object is projected onto a plane surface by the use of imaginary "projectors". The projected, mental image becomes the technician’s vision of his desired, finished picture. By following the protocol the technician may produce his invisioned picture on a plane surface, e.g., drawing paper. The protocols provide a uniform imaging procedure among people trained in technical graphics (mechanical drawing, computer aided design images, etc.).
Graphical projection contains three broad categories each with its own protocol: orthographic (for protocol, see orthographic projection) oblique (for protocol see oblique projection), and perspective (for protocol, see perspective projection).
Orthographic projection is derived from the principles of descriptive geometry and may produce an image of a specified, imaginary object as viewed from any direction of space. It is distinguished by parallel projectors from the imaged object and which intersect a plane of projection at right-angles. It is the projection type of choice for working drawings.
Pictorials
Within orthographic projection there is an ancillary category known as pictorials. Pictorials show an image of an object as viewed from a skew direction in order to reveal all three directions (axes) of space in one picture. Orthographic pictorial, rote, instrument drawings are often used to approximate graphical perspective projections, but there is attendant distortion in the approximation. Because Pictorial projections innately contain this distortion, in the rote, instrument drawing of Pictorials, great liberties may then be taken for economy of effort and best effect. Orthographic pictorials rely the technique of axonometric ("to measure along axes") projection.
A characteristic of axonometric projections/drawing is, one axis of space usually displays as vertical.
There are three categories of Pictorials within axonometric projection/drawing: osometric, diametric and trimetric. In isometric pictorials (for protocols see isometric projection), the direction of viewing is such that the three axes of space appear equally foreshortened, of which the displayed angles among them and also the scale of foreshortening are universally known. However in creating a final, isometric instrument drawing, in most cases a full-size scale, i.e., without using a foreshortening factor, is employed to good effect because the resultant distortion is difficult to perceive. In dimetric pictorials (for protocols see dimetric projection), the direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing; the scale of the third direction (vertical) is determined separately. Approximations are common in dimetric drawings. In trimetric pictorials (for protocols see trimetric projection), the direction of viewing is such that all of the three axes of space appear unequally foreshortened. The scale along each of the three axes and the angles among them are determined separately as dictated by the angle of viewing. Approximations in Trimetric drawings are common.
In oblique projections parallel projectors are imagined to emanate from all points of an imaginary object and which strike the projection plane at an angle other than ninety degrees - as opposed to orthographic projectors, which strike the plane of projection at ninety degrees. In orthographic and oblique projection, parallel lines in space appear parallel on the final, projected image. Because of its simplicity oblique Projection (for protocols see oblique projection) is used exclusively for pictorial purposes rather than for formal, working drawings. In an oblique pictorial drawing, the displayed angles among the axes as well as the foreshortening factors (scale) are arbitrary. The distortion created thereby is usually attenuated by aligning one plane of the imaged object to be parallel with the plane of projection thereby creating a true shape, full-size image of the chosen plane. This type of general oblique drawing is called a Cavalier projection. A special case is to draw the receding axis scale as half-size and at an angle of 45-degrees. This is called cabinet projection (for protocols see oblique projection). It is popular in furniture illustrations.
Perspective
Classical, i.e., artificial (see perspective distortion) Perspective Projection is seldom technically regarded as a pictorial. Classical perspective projection is an attempt to reproduce the image beheld by the eye, i.e., to the eye, parallel lines in nature appear to intersect. Perspective projection is distinguished in that projectors from the imaged object are not parallel but concurrent at a single point (station point) and create an image thereby upon a projection plane (picture plane). The picture plane is arbitrarily positioned for convenience. (It should be parenthetically acknowledged that the eye itself produces an inherit distortion of nature. In nature parallel lines never intersect; in the image beheld by the eye parallel lines always intersect - as in the image of receding railroad tracks). Be aware that classical perspective projection, per se, produces an inherent distortion of the (distorted, per parenthetical note above) image beheld by the eye.