Graphical projection

Graphical projection is a protocol by which an image of a three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing.The projection is achieved by the use of imaginary "projectors".

There are two types of graphical projection, categories each with its own protocol:

1. perspective projection (Previously Discussed)
2. parallel projection

Isometric Projection 

One Point Perspective

Oblique Projection

Oblique Projection

    

      Parallel projection

In parallel projection, the lines of sight from the object to the projection plane are parallel to each other

A.      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.

 

B.       Pictorials

i.            Axonometric projection      

Within parallel projection there is a 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").

ii.            Isometric projection  

In isometric pictorials, 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.

All isometric drawings are made with the 30-60 triangle, and most of them are done in angular "perspective" where the two sides make an angle of 120 degrees with each other and 30 degrees with the horizontal. In isometrics all sides that are parallel stay parallel and will not vanish to a vanishing point if prolonged. There are neither vanishing points nor foreshortening in isometric drawing. The difference between true perspective and isometric drawing is shown in the diagram 34, where A is the perspective of a block and B is the isometric drawing of it. It is also shown clearly in Figure 35 where C is the perspective and D the isometric drawing of the same thing.

The three vertical edges a, b, and c of the block are called isometric axes, and all lines parallel to these edges are called isometric lines. Measurements can be made on the main isometric axis (b) only, for all other lines are inaccurate because they are not in true perspective.

Isometric drawing

Is made up of a series of parallel vertical lines and parallel 30 degree lines

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It is usually drawn out with the aid of a 30/60 degree set square. Isometric is 30 degrees only

Sometimes Isometric grid paper is used to aid the drawing

NOTE: THERE ARE NO HORIZONTAL LINES

iii.            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.

 

Method of Drawing

 

Oblique projection is a method of drawing objects in 3 dimensions. It is quite a simple technique compared to isometric or even perspective drawing. However, to draw accurately in oblique projection traditional drawing equipment is needed

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The technique for drawing a cube in oblique projection is outlined below, stage by stage. To draw it correctly in oblique projection three main rules must be followed:
1. Draw the front or side view of the object.
2. All measurements drawn backwards are half the original measurement.
3. 45 degrees is the angle for all lines drawn backwards

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A. Draw the front view. Remember to use a T-square and 45 degree set square.

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B. Draw 45 degree lines from each corner of the square. The distance of any lines drawn back at 45 degrees should be halved. For example, a cube may have sides of 100mm but they must be drawn 50mm in length. This should mean that the cube will look more realistic and in proportion

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             C. Draw 45 degree lines from each corner of the square. The distance of any lines drawn back at 45 degrees should be halved. For example, a cube may have sides of 100mm but they must be drawn 50mm in length. This should mean that the cube will look more realistic and in proportion.