Theory of Projections 

Projection theory
In engineering, 3-dimensonal objects and structures are represented graphically on a 2-dimensional media. The act of obtaining the image of an object is termed “projection”.  The image obtained by projection is known as a “view”.  A simple projection system is shown in figure 1.
All projection theory are based on two variables:
  •           Line of sight
  •           Plane of projection.
Plane of Projection
A plane of projection (i.e, an image or picture plane) is an imaginary flat plane upon which the image created by the line of sight is projected.  The image is produced by connecting the points where the lines of sight pierce the projection plane. In effect, 3-D object is transformed into a 2-D representation, also called projections. The paper or computer screen on which a drawing is created is a plane of projection.

Figure 1 : A simple Projection system 
Projection Methods
Projection methods are very important techniques in engineering drawing.
Two projection methods used are:
  • Perspective and
  • Parallel 
Figure 2 shows a photograph of a series of building and this view represents a perspective projection on to the camera. The observer is assumed to be stationed at finite distance from the object. The height of the buildings appears to be reducing as we move away from the observer.  In perspective projection, all lines of sight start at a single point and is schematically shown in figure 3. . 

Figure 2. Photographic image of a series of buildings.

Figure 3.  A schematic representation of a Perspective projection

In parallel projection, all lines of sight are parallel and is schematically represented in figure. 4. The observer is assumed to be stationed at infinite distance from the object.



Figure 4.  A schematic representation of a Parallel projection
Parallel vs Perspective Projection
Parallel projection
√ Distance from the observer to the object is infinite projection lines are parallel – object is positioned at infinity.
√ Less realistic but easier to draw.
Perspective projection 
  • Distance from the observer to the object is finite and the object is viewed from a single point – projectors are not parallel.
  • Perspective projections mimic what the human eyes see, however, they are difficult to draw.
Orthographic Projection Orthographic projection is a parallel projection technique in which the plane of projection is perpendicular to the parallel line of sight. Orthographic projection technique can produce either pictorial drawings that show all three dimensions of an object in one view or multi-views that show only two dimensions of an object in a single view. These views are shown in figure 5.
Figure 5.  Orthographic projections of a solid showing isometric, oblique and multi-view drawings.



Transparent viewing box Assume that the object is placed in a transparent box, the faces of which are orthogonal to each other, as shown in figure 6. Here we view the object faces normal to the three planes of the transparent box. Figure 6. The object placed inside a transparent box. When the viewing planes are parallel to these principal planes, we obtain the Orthographic views The picture we obtain when the line of sight is projected on to each plane is called as the respective view of the object. The image obtained on the projection planes , i.e., on the top face, Front Face, and Right side face are respectively the Top View, Front view and Right side view of the object and is shown in figure 7.
Transparent viewing box

Assume that the object is placed in a transparent box, the faces of which are orthogonal to each other, as shown in figure 6.  Here we view the object faces normal to the three planes of the transparent box.



Figure 6. The object placed inside a transparent box.

When the viewing planes are parallel to these principal planes, we obtain the Orthographic views
The picture we obtain when the line of sight is projected on to each plane is called as the respective view of the object. The image obtained on the projection planes , i.e., on the top face, Front Face, and Right side face  are respectively the  Top View, Front view and Right side view of the object and is shown in figure 7.
Multi-view Projection
In an orthographic projection, the object is oriented in such a way that only two of its dimensions are shown. The dimensions obtained are the true dimensions of the object .
Frontal plane of projection
Frontal plane of projection is the plane onto which the Front View (FV) of the multi-view drawing is projected.
Figure 8 illustrates the method of obtaining the Front view of an object. Front view of an object shows the width and height dimensions.

Figure 8 illustrates the method of obtaining the Front view of an object.
Horizontal plane of projection
Horizontal plane of projection is the plane onto which the Top View of the multi-view drawing is projected and is shownin  Figure 9. The Top view of an object shows the width and depth dimensions of the object.
Figure 9 illustrates the method of obtaining the Top view of an object.