The Graphic Language

When you first learned to read our written language, you progressed through it in a logical order. You learned the alphabet, then learned simple words. You could not learn the simple words until you knew the letters which formed them. Later, more complex words were added to your vocabulary and the process conintinued.

The same concept can be applied to learning the graphics language. The graphic language can be broken down to an "alphabet" of points, lines, and planes. Solid objects are made up of these features: points representing corners, lines representing edges, and planes representing surfaces.

Engineers are required to design, revise, analyze, and/or construct complex parts or systems. These parts or systems, are conceived or exist in a three-dimensional medium. Until the evolution of 3D solid modeling, it was difficult to define these parts accurately in three-dimensional space. To display these objects on a two-dimensional medium such as a sheet of paper, usually the designer creates a projection of the part.

Projections are drawn by viewing an object with an imaginary transparent plane placed between the observer and the object. The image of the object is projected onto that imaginary plane, defined as the plane of projection. A two-dimensional representation, or view, of the object is the result.

Orthographic Projections - Definition

Many different type of projections are used in the presentation of technical drawings. Our attention will be focused on a specific type known as orthographic projection. Orthographic projection is the representation most commonly used by engineers. Orthogonal views provide a means for describing the exact size and shape of an object.

The simplest feature you can display graphically is a point in space. To demonstrate the concept of orthographic projection, we will begin by showing the projection of a single point in space.

The system of orthographic projection is classified according to the relationship formed by between the observer, the projection plane, and an object. [FIGURE 3-1] Notice that the line of sight (also referred to as the projection line) is perpendicular to the projection plane. This relationship must exist for the projection to be an orthographic projection. The image of point O is projected onto the projection plane and a two-dimensional view of the point can be drawn.

To completely define an object, at least two orthographic views are required. Depending on the complexity of the part, three or more views are required. To keep the example simple, and demonstrate the theory involved, we will continue to consider a single point in space, and show three orthographically projected views.

The Glass Box Theory

The glass box theory is commonly used as a visual aid in defining orthographic projection. Imagine a box with transparent sides that contains point O. The six planes that make up the box are defined as the principal projection planes. The point is assumed to have a fixed position inside the box. [FIGURE 3-2] Projections of the point are made onto three of the surfaces that make up the box: the top or "H" (horizontal) plane, the front or "F" (frontal) plane, and the right side or "P" (profile) plane. The observer has a different position for each of the three views so that the line of sight is perpendicular to the plane onto which the projection is being made.

These three views must be presented so a logical relationship is maintained. The projection planes are simply unfolded so they are on the same plane, i.e. so they can be drawn on a two-dimensional medium such as paper. To maintain the relationships between views, the projection planes cannot be separated, only unfolded about the edges created by the intersection of the planes.

The actual planes that make up the glass box are usually not shown as a part of the completed drawing. These planes are imaginary planes introduced to convey the theory. Foldlines are often included in the drawing and will be shown in the examples as phantom lines (line dash dash line). The foldlines, also called reference lines, are actually the lines where the planes that make up the imaginary box intersect.

The position of the point can be defined by three dimensions.

The point is positioned at a specific height within the box. The top of the box is labeled "H" to identify it as the "horizontal plane," and a dimension Dh is indicated. This distance locates the point horizontally in space and is defined as the distance from the horizontal plane (Dh). You can also consider it to be the distance from the top of the box to the point.

The point also has a fixed depth within the box. The front of the box is labeled "F" to identify it as the frontal plane. A dimension Df is shown to locate the position of the point with respect to the frontal plane. Point O is positioned a fixed distance (Df) behind the frontal plane.

Finally, the point must also be located with respect to one of the sides of the box, a dimension of width. The right side of the box is labeled "P" to identify it as the profile plane. A dimension Dp is shown to locate the point . Point O is located a fixed distance Dp to the left of the right profile plane.

Note that the point could have been located with respect to the other three planes that make up the box as well. A distance from the bottom of the box could have been given instead of Dh, for example. It is more standard however to measure from the top to locate the point. It is also preferred that the point be located from the front as opposed to the back plane. Just as the bottom or rear views of a part are not commonly presented, the bottom and rear reference planes are usually not used to locate points. Left and right side views of objects are common, so when locating the point from the profile plane, both the left side and right side are commonly used. The subscripts Dpr and Dpl are often used to indicate whether the point is located with respect to the right or left projection plane.

The Df, Dp, and Dh distances are always measured from the foldlines (or reference lines).

In [FIGURE 3-3], the orthographic projection of a single point is shown. The position of the observer is schematically shown to be at a measurable distance from the projection plane. To orthographically project the image of any geometric feature larger than a point, the observer must be considered to be an infinite distance from the projection plane. With that assumption, the lines of sight will be parallel to each other. [FIGURE 3-4] We will expand on our example to show the orthographic projection of a line in space.

Missing View Projection

To reinforce the theory of orthographic projection, most of the initial problems will be 'missing view' problems. You will be given two of the three principal views and asked to construct a missing view. You should realize that two views must be known in order to construct additional views. A single orthographic view only contains two dimensions. All three dimenions must be known or the entity is undefined.

Consider the front view of a single point is given. You know the height of the point (Dh) and the postion of the point with respect to one of the profile planes (Dp). But there is nothing to indicate how far the point is behind the frontal plane (Df). That depth (Df) must be given in order to define the position of the point. If the top view was given, Df would be known. Only then could you draw the missing side (profile) view.

To actually construct that side view, first realize that Dh is known. The height of the point in the side view will be the same as it is in the given front view. Simply project height across on a horizontal construction line. Next, realize that Df is also known. The point is a certain fixed distance behind the frontal plane. You can see that distance (it is given) in the top view. The distance that the point is behind the frontal plane (Df) is the same whether you view the point from the top or from the side. Transfer that distance from the top view to the side view (always remembering to measure from the foldline). You will then complete the missing view and solve the problem.

Lines and Surfaces

A line is defined by two points in space. It can appear in numerous ways depending on the relative position of the viewer.

If the viewer chooses a position such that his or her line of sight is parallel to the line, the line will appear as a single point in space. In that case, the line is perpendicular to the plane onto which it is projected.

If the line is viewed with the lines of sight perpendicular to the the given line, the line will appear true length (TL). In that case the line is parallel to the plane onto which it is projected. Remember that one must assume that the observer is an infinite distance from the projection plane so 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 principal projection planes. We will define three different types of lines.

A normal line is a line in space which is parallel to two of the principal planes and perpendicular to the third. Therefore, given three principal 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 principal views. It is neither parallel or 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 which is neither parallel nor perpendicular to any of the principal planes. It will appear foreshortened in all principle views.

To complete our graphics alphabet, we must include plane surfaces. A plane can be defined in space several different ways. Three non-colinear points (points which are not contained on a single line), define a plane surface. Any line and a point not on that line similarly define a plane suface. A plane can also be defined by two parallel lines or two intersecting lines.

A plane surface can be of any particular shape, i.e. the suface on a object. It can also be assumed to continue indefinitely in all directions. For the following discussion, assume a simple plane defined by three points in space. The points are connected to form a plane surface in the shape of a triangle. You can use one of the drawing triangles from your kit as a visual aid.

Just as a line can appear differently depending upon the position of the observer, so to can a plane surface. Consider the surface with a fixed triangular shape.

If the observer views the surface such that the lines of sight are parallel to the plane, he or she will see the plane as a single line. Considering an orthographic projection of the plane in that view, the plane will be perpendicular to the projection plane. This is said to be the line view of the plane. There are an infinite number of positions in which this view can be seen.

If the observer views the surface such that the lines of sight are perpendicular to the plane, he or she will see the plane in its true size and shape. This will hold true if the plane surface is projected onto a projection plane parallel to it. In order for a fixed plane in space to be viewed true size (TS), there are only two positions where the observer could be located; 180 deg appart.

There are an infinite number of views where the surface will appear foreshortened. The plane will appear foreshortened in any view where the surface is neither parallel nor perpendicular to the projection plane.