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:
- perspective projection (Previously Discussed)
- parallel projection
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| Isometric Projection |
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| One Point Perspective |
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| Oblique Projection |
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| 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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| click on Image |
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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| click on Image |
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
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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| click on Image |
A. Draw the front view. Remember to use
a T-square and 45 degree set square.
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| click on Image |
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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| click on Image |
