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Graphical projection is a protocol by which an image of an three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing.
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Overview
The projection is achieved by the use of imaginary "projectors". The projected, mental image becomes the technician’s vision of the desired, finished picture. By following the protocol the technician may produce the envisioned picture on a planar surface such as drawing paper. The protocols provide a uniform imaging procedure among people trained in technical graphics (mechanical drawing, computer aided design, etc.).
There are two types of graphical projection, categories each with its own protocol:
Types of projection
Parallel projection
In parallel projection, the lines of sight from the object to the projection plane are parallel to each other. Within parallel 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. Because pictorial projections innately contain this distortion, in the rote, drawing instrument for pictorials, some liberties may be taken for economy of effort and best effect.
Orthographic projection
The Orthographic projection is derived from the principles of descriptive geometry and is a two-dimensional representation of a three-dimensional object. It is a parallel projection (the lines of projection are parallel both in reality and in the projection plane). It is the projection type of choice for working drawings.
Pictorials
Axonometric projection
Within parallel projection there is an subcategory 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. Parallel projection 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. Parallel projection pictorials rely on the technique of axonometric projection ("to measure along axes").
Isometric projection
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.
Dimetric projection
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.
Trimetric projection
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.
Oblique projection
In oblique projections the parallel projection rays are not perpendicular to the viewing plane as with orthographic projection, but strike the projection plane at an angle other than ninety degrees. In both orthographic and oblique projection, parallel lines in space appear parallel on the projected image. Because of its simplicity, 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. Special types of oblique projections are cavalier projection and cabinet projection.
Perspective projection
Perspective projection is a type of projection where three dimensional objects are not projected along parallel lines, but along lines emerging from a single point. This has the effect that distant objects appear smaller than nearer objects.
It also means that lines which are parallel in nature appear to intersect in the projected image, for example if railways are pictured with perspective projection, they appear to converge towards a single point, called vanishing point. Photographic lenses and the human eye work in the same way, therefore perspective projection looks most realistic[1].
Perspective projection is usually categorized into one-point, two-point and three-point perspective, depending on the orientation of the projection plane towards the axes of the depicted object[2].
See also
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- Curvilinear perspective
- Engineering drawing
- Descriptive geometry
- Map projection
- Plans (drawings)
- Technical drawing
References
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This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (March 2009) |
- ^ D. Hearn, & M. Baker (1997). Computer Graphics, C Version. Englewood Cliffs: Prentice Hall], chapter 9
- ^ James Foley (1997). Computer Graphics. Boston: Addison-Wesley. ISBN 0201848406], chapter 6
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