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Case 1

The development of Case 1 of this problem in which the axes of the prisms intersect at right angles, is shown in Diagram 1. Note that inter-edge lines are required for the development of both solids, their positions being found by projectors drawn from the different views of the drawing to the full view of the end.

Case 2

Case 2 of the problem in which the axes intersect at 45°, is developed in a similar manner. The projections for this are shown on the plate at Fig 1(a). In order to avoid confusion of lines, projectors are sometimes drawn as shown on this plate, that is, only their starting points are indicated, as between the two views of the octagonal prism in this drawing. First, reproduce the projections. Next, develop the stretch outs for the solids on the lines MN and M'N', and draw edge and inter-edge lines through their respective points. The positions of the inter-edge lines are found by projecting the point A in the plan across to the full view, as shown in (d) afterwards locating the points x and y at x' and y' in (d'); then they are projected to the elevation and carried to the development in the usual manner, the resulting figures at (b) and (c) completing the development of the solids.

Question

What I need to know is, should both drawings be drawn in an elevation and plan way? And where exactly is the problem in both cases that should be developed?

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    $\begingroup$ First angle, third angle - whichever is expected or matches what you have been told to do, as this looks like homework. $\endgroup$ – Solar Mike Aug 1 '18 at 11:41
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The problem that needs to be solved and the method you described to solve that problem would be how to cut the octagonal prism along it's circumference in such a way that it would smoothly fit with the kite shaped prism. The plausible, theoretical shape described by the drawing is useless if it cannot be manufactured. This method allows one to mark special points along the circumference of the prism, trace their path, and cut along that path in such a way to generate a smooth surface that will allow the two pieces to be joined with minimal gap. This development before computer aided drafting was critical in making many important cuts with minimal aid. Especially for pipe fitters, which frequently need to be joined pipes together with a "saddle-cut" all the time:

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The idea is to start with flat edge prisms and then improve the technique to circles. However, I found the most complicated of these in real life involve non-prismatic shapes, such as a cone intersecting a pipe at 90 degrees. Other complications involve intersections off-center, as is shown in case 3, where further complications are found that need to be resolved via the drafter to derive a complete solution.

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