Descriptive Geometry - General Solutions

General Solutions

General solutions are a class of solutions within descriptive geometry that contain all possible solutions to a problem. The general solution is represented by a single, three-dimensional object, usually a cone, the directions of the elements of which are the desired direction of viewing (projection) for any of an infinite number of solution views.

For example: To find the general solution such that two, unequal length, skew lines in general positions (say, rockets in flight?) appear:

  • Equal length
  • Equal length and parallel
  • Equal length and perpendicular (say, for ideal targeting of at least one)
  • Equal to lengths of a specified ratio
  • others.

In the examples, the general solution for each desired characteristic solution is a cone, each element of which produces one of an infinite number of solution views. When two or more characteristics of, say those listed above, are desired (and for which a solution exists) projecting in the direction of either of the two elements of intersections (one element, if cones are tangent) between the two cones produces the desired solution view. If the cones do not intersect a solution does not exist. The examples below are annotated to show the descriptive geometric principles used in the solutions. TL = True-Length; EV = Edge View.

Figs. 1-3 below demonstrate (1) Descriptive geometry, general solutions and (2) simultaneously, a potential standard for presenting such solutions in orthographic, multiview, layout formats.

The potential standard employs two adjacent, standard, orthographic views (here, Front and Top) with a standard "folding line" between. As there is no subsequent need to 'circuitously step' 90° around the object, in standard, two-step sequences in order to arrive at a solution view (it is possible to go directly to the solution view), this shorter protocol is accounted for in the layout. Where the one step protocol replaces the two-step protocol, "double folding" lines are used. In other words, when one crosses the double lines he is not making a circuitous,90° turn but a non-orthodirectional turn directly to the solution view. As most engineering computer graphics packages automatically generates the six principal views of the glass box model, as well as an isometric view, these views are sometimes added out of heuristic curiosity.


Figure 1: Descriptive geometry - skew lines appearing perpendicular
Figure 2: Descriptive geometry - skew lines appear equal length
Figure 3: Descriptive geometry - skew lines appear in specified length ratio

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