# Figure Plane Projection Problem

Figure 13 (on the following page) shows the solution, which was derived at by the following:

Step 1. Identify the lines that define plane 1-2, 2-4, 4-3, and 3-1.

Step 2. Project the individual points 1, 2, 3, and 4 into the right side view.

Step 3. Draw in, with object lines, the lines that define the plane.

The lines drawn in step 3 define the right side view of plane 1-2-3-4.

In line theory we found that the end view of a line was a double-point. A similar situation appears in the plane theory, which is explained by the following axiom:

The end view of a plane is a line (really several lines directly behind each other).

This may be verified by holding a sheet of paper horizontal to the ground and rotating it until you are looking directly at one edge. Although it is a plane, the sheet appears as a line.

h. Curves. So far, we have considered only straight lines. Point, line, and plane projection theory may be extended to include curved lines if we consider the following axioms:

To a draftsman, a curved line is a visible line connecting three or more points which form a smooth, nonlinear line.

To a draftsman, the accuracy of a curve is a function of the number of points used to define the curve.

To draw a perfectly accurate curve would require an infinite number of points. To do this is not only impossible, it is also impractical. Most curves may be very closely approximated by a finite number of points, and it is up to the draftsman to determine what level of accuracy is required and how many points he needs to achieve this level. Circles and perfect arcs are exceptions to the axioms because they may be drawn with perfect accuracy using a compass.

Figure 14 is an example of the curved line projection problem, while figure 15 (on the following page) offers the solution to this problem.