Rule #1 Reads – “When the halves of a symmetrical figure are symmetrical in the plan and the elevation, and when the planes in the elevation are parallel, the true lines may be formed by using either view.”

The best example for Rule #1 is shown in Figure 1A, this would be a common square to round transition where the center of the square would also be the center of the round. The plan view would be a practical choice of the two ways as all you will need is the height of the fitting shown in elevation and one corner of the transition to develop a true length diagram. The elevation method would be another choice, however you would need an additional drawing as you will have to develop and extend the profile of the round Figure 1B separately to develop your true length diagram. Either way you would only need to solve for one section, as this will be similar for all 4 sections of the fitting. Take this one step further and all you really need is one section of the transition as shown in the shaded area of Figure 1B – Look at how easy this can be?

Take a look at Figure 1B as we establish the true length lines from the elevation view. Once the profile is drawn and divided into equal sections, reference these 1 through 4, now draw a line perpendicular to the top plane to each division on the profile establishing points 1, 2", 3" and 4" on the top plane. Create a true length diagram by drawing two lines perpendicular to each other and marking off ½ the distance of the plan A to B as shown A' to B. Using your dividers, transfer the lengths of A1, A2", A3" and A4" to the base of the true length diagram using A' as a center and striking a reference mark to these mentioned lengths as shown along the base by A' to1', 2', 3' and 4'. Perpendicular to each one of these lengths on the base is a line drawn to 2x, 3x and 4x. We get the distance from the profile in the elevation view 2 to 2", 3 to 3" and 4 to 4". If you did this correctly and all is truly symmetrical the true length lines from B to1' and B to 4x will be the same length as well as B to 2x and B to 3x. The other true length lines necessary for the pattern are already shown in true length in the elevation as A to B, being half of the length of the base, but all of what we need to develop the quarter pattern.

Rule #2 Reads – “When the halves are not symmetrical in the plan view and the planes are parallel in the elevation, the plan should be used without the aid of the elevation – this is because only one height is required and if this is known we really have no other use for remainder of the elevation, so it is eliminated all together.”

Not much to say here. a good example of Rule # 2 would be a square or rectangular to round fitting where the round is offset two ways from center as shown in Figure 2. Notice on what we mean on not symmetrical – See the plan drawing in Figure 2, the sides 1 and 2 can not be duplicated by laying out 1 side and using it as a template for the other, so you’re having to develop the true length lines from the plan. The only useful information in Figure 2B would be the height of the fitting and you don’t need to draw an elevation for only this.
 
This rule could apply to a number of transitions including tapered round with an offset as long as the top and bottom round are parallel.

Rule #3 – “When the halves are not symmetrical in the plan view and the planes are not parallel in the elevation, both views are necessary to produce the surface lines. If the heights of the elevation and the base lines of the plan are known, a diagram of triangles can be drawn.”

In Figure 3, we use the drawing from Figure 2 but we added a slant to the base. In Figure 2 (rule 2), we learned that we had no use for the elevation. In Figure 3, rule # 3 we are told we now need both the elevation and the plan to develop the pattern. All this because of one change and that would be that plane 1 and plane 2 are no longer parallel to one another in Figure 3B as they were in Figure 2B.
 
We can see by the drawing in Figure 3A that there are no symmetrical sides in the plan as well as plane 1 and 2 are not parallel to each other in the elevation - Figure 3B. This particular fitting looks a little more complicated because it’s elevated and we need to solve for each true length line individually as we’ll briefly describe in Figure 3C -

Together with the aid of both elevation view and plan view, you’re going to solve for each true length line – to do so you need to establish the height of each line (elevation view) and the base length of each line (plan view) the hypotenuses of the two corresponding lines is the true length of that line. In this particular fitting to establish the height of the true length diagram, we extend two horizontal lines, one from each A and B to the right as shown in the elevation view. To the right of the elevation view referenced as B1, draw a line perpendicular to reference X as the height of the diagrams. With your dividers or trammel points, transfer the distances from plan view A’ to 1’, 2’, 3’ and 4’ to the line extended from A in the elevation view as shown, using A as center and striking reference marks as shown 2”, 3”, 1” and 4”. Connecting these to point X will establish several of the true length lines necessary for this part (side 1) of the transition.  The other lines that must be established are 4 to F from elevation, again the base line is drawn (shown in the elevation) and the true length is established. The plan shows the true length of lines F to A’ and A’ to e. In the plan view, the true length line of 1’ to e can be taken from the elevation (shown as 1 to A), as would be the same reference mark for e.