A line can appear in numerous ways depending on the relative position of the viewer.
If the viewer chooses a position such that his line of sight is parallel to the line, the line will appear as a single point in space. In that case,the line is perpendiclar to the plane it is projected onto; it will appearas a single point.
If the line is viewed such that the lines of sight are perpendicular to the given line, the line will appear in its true length (TL). In that case the line is parallel to the plane onto which it is projected. Remember that the observer must be assumed to be an infinite distance from the projection plane such that the lines of sight are parallel to each other.
If the line is viewed such that it makes an angle other than 90 deg with the projection plane, it will appear foreshortened. It will be a distorted view of the line and the length of the line in that view will be shorter than its true length, but larger than a point.
Lines in space can be classified according to their relationship to the principle projection planes. We will define three different types of lines.
A normal line is a line in space that is parallel to two of the principle planes and perpendicular to the third. Therefore, given three principle views (H, F, P), the line must appear TL in two of the views. In the remaining view it will appear as a point.
An inclined line is a line in space that is parallel to one of the three principle views. It is neither parallel nor perpendicular to the other two views. The line will appear TL in one view since it is parallel to one of the projection planes. It will appear foreshortened in the remaining two views.
An oblique line is a line in space that is neither parallel nor perpendicular to any of the principle planes. It will appear foreshortened in all principle views.
When creating engineering drawings, it is often neccessary to show features in a view where they appear true size so they can be dimensioned. The objectis normally positioned such that the major surfaces and features are either parallel or perpendicular to the principle planes. Views are selected so that most of the features will be visible in the three principle views.The front, top, and side views are most commonly drawn.
Many objects are quite complex, and the three principle views may not best present the geometry of the part. Certain features may not appear true sizeand shape in those views, or may be hidden. In this case one or more auxiliaryviews are drawn.
Imagine an object in a fixed position. As an observer, you are free to movearound the object. The number of possible views is infinite. You can look at the object so that certain features appear visible and also true size and shape.
AUXILIARY VIEWS OF LINES
As previously discussed, a line in space can appear as a point, as a foreshortened line, or in its true length, depending upon its relationship with the projection plane. Using auxiliary views, it is possible to show any line in space in a view where it appears true length or as a single point. These views are often neccessary to adequately dimension drawings or solve problems.
Given an oblique line, it will not appear in true length in the principle views. The line is inclined to all of the principle planes. If a true length view of the line is desired, it will have to be projected onto an auxiliary projection plane. In order for the line to appear true length, the auxiliary projection plane choosen must be parallel to the line. There are an infinite number of projection planes parallel to the line in space. [EXAMPLE]
A fold line or reference line is drawn parallel to the line in any given view. The line is projected onto that auxiliary projection plane and willappear true length (TL). The lines of projection are perpendicular to the fold line, and therefore parallel to each other. The transfer distances for each end point are measured from the fold line.
Auxiliary views can also be used to show the point view of a line. As we will show later, drawing the point view of a line can be useful in solving geometric problems. It is important to realize that you must have a true length view of a line before you can project to find the point view. Given a line in space, it is simple to see what view you must have in order to see it as a point. Your line of sight must be parallel to the line. The projection plane you must project upon in order to see the point view of the line must be perpendiclar to the view where the line appears as true length. There are only two possible views where this can occur.