Perspective projection
Perspective projection is as shown in Figure 2.2. Perspective projection is reality in that everything we see in the world is in perspective such that the objects always have vanishing points. Perspective projection is thus the true view of any object. Hence, we use expressions like 'putting something in perspective'! Projectors radiate from a station point (i.e. the eye) past the object and onto the 2D picture plane. The station point is the viewing point. Although there is only one station point, there are three vanishing points. A good example of a vanishing point is railway lines that appear to meet in the distance. One knows in reality that they never really meet, it is just the perspective of one's viewing point. Although there are three vanishing points, perspective drawings can be simplified such that only two or indeed one vanishing point is used. The drawing in Figure 2.2 shows only two vanishing points.
Vanishing point
Figure 2.2 Perspective projection
Station point
Vanishing point
Figure 2.2 Perspective projection
Had the block shown been very tall, there would have been a need to have three vanishing points.
Although perspective projection represents reality, it produces complications with respect to the construction of a drawing in that nothing is square and care needs to be taken when constructing such drawings to ensure they are correct. There are numerous books that give details of the methods to be employed to construct perspective drawings. However, for conventional engineering drawing, drawing in perspective is an unnecessary complication and is usually ignored. Thus, perspective projection is very rarely used to draw engineering objects. The problem in perspective projection is due to the single station point that produces radiating projectors. Life is made much simpler when the station point is an infinite distance from the object so that the projectors are parallel. This is a situation for all the axonometric and orthographic projection methods considered below.
2.2 Axonometric projection
Axonometric projection is shown in Figure 2.3. This is the same as perspective projection except that the projectors are parallel. This means that there are no vanishing points. In axonometric projection, the object can be placed at any orientation with respect to the viewer. For convenience, axonometric projection can be divided into three classes depending on the orientation of the object. These are trimetric, dimetric and isometric projections (see Figure 2.4).
Trimetric projection is by far the most common in that the object is placed at any position with respect to the viewer such that the angles a and P are unequal and the foreshortening in each of the three axes is unequal. The three sides of the cube are of different lengths. This is shown in the lefthand drawing in Figure 2.4. The 'tri' in trimetric means three. In dimetric projection, the angles a and P are the same as shown in the middle drawing in Figure 2.4. This results in equal foreshortening of the two horizontal axes. The third vertical axis is foreshortened to a different amount. The 'di' in dimetric means there are two 'sets' of axes. The particular class of axonometric projection in which all the three axes are foreshortened to an equal amount is called isometric projection. In this case the foreshortening is the same as seen in the righthand drawing in Figure 2.4. In this case, the angles a and p are the same and equal to 30°. The foreshortening of each of the three aj;es is identical. The term 'iso' in isometric projection means similar. Isometric projection is the most convenient of the three types of axonometric projection because of the convenience of using 30° angles and equal foreshortening. Isometric projection will be considered in detail in the following section.
Note: anband ABMCMD
Note: ab and AB=ACMD
Trimetric Projection
Di metric Projection
Isometric Projection
Note: anband ABMCMD
Note: ab and AB=ACMD
Trimetric Projection
Di metric Projection
Isometric Projection
Figure 2.4 The three types of axonometricprojections
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