Editing Descriptive geometry (section)

==Heuristics==

There is heuristic value to studying descriptive geometry. It promotes visualization and spatial analytical abilities,  as well as the intuitive ability to recognize the direction of viewing for best presenting a geometric problem for solution. Representative examples:

=== The best direction to view ===
* Two [[skew lines]] (pipes, perhaps) in general positions in order to determine the location of their shortest connector (common perpendicular)
* Two skew lines (pipes) in general positions such that their shortest connector is seen in full scale
* Two skew lines in general positions such the shortest connector parallel to a given plane is seen in full scale (say, to determine the position and the dimension of the shortest connector at a constant distance from a radiating surface)
* A plane surface such that a hole drilled perpendicular is seen in full scale, as if looking through the hole (say, to test for clearances with other drilled holes)
* A plane equidistant from two skew lines in general positions (say, to confirm safe radiation distance?)
* The shortest distance from a point to a plane (say, to locate the most economical position for bracing)
* The line of intersection between two surfaces, including curved surfaces (say, for the most economical sizing of sections?)
* The true size of the angle between two planes

A standard for presenting computer-modeling views analogous to orthographic, sequential projections has not yet been adopted. One candidate for such is presented in the illustrations below. The images in the illustrations were created using three-dimensional, engineering computer graphics.

Three-dimensional computer modeling produces virtual space ''behind the screen'' and may produce any view of a model from any direction within this virtual space. It does so without the need for adjacent orthographic views and therefore may seem to render the circuitous, stepping protocol of descriptive geometry obsolete. However, since descriptive geometry is the science of the legitimate or allowable imaging of three or ''more'' dimensional space, on a flat plane, it is an indispensable study, to enhance computer modeling possibilities.

=== Examples ===

==== Finding the shortest connector line QT between two given skew lines PR and SU ====
[[File:Descriptive geometry lines.svg|thumb|Example of the use of descriptive geometry to find the shortest connector between two skew lines, PR & SU. The red, yellow and green highlights show distances which are the same for projections of point P.]]
Given the X, Y and Z coordinates of P, R, S and U, projections 1 and 2 are drawn to scale on the X-Y and X-Z planes, respectively. Projections 1 and 2 are delineated by hinge line H<sub>1,2</sub>, and aligned such that each point projects perpendicularly across the hinge line (P1:P2, R1:R2, S1:S2, U1:U2).   

To get a true view (length in the projection is equal to length in 3D space) of one of the lines: SU in this example, the projection 3 view is chosen perpendicular to S<sub>2</sub>U<sub>2</sub> by drawing a hinge line H<sub>2,3</sub> parallel to S<sub>2</sub>U<sub>2</sub>. To get an end view of SU, the projection 4 view is chosen is perpendicular to the true view of line S<sub>3</sub>U<sub>3</sub> by drawing a hinge line H<sub>3,4</sub> perpendicular to S<sub>3</sub>U<sub>3</sub>. The perpendicular QT is the true length of the connector and its distance ''d'' gives the shortest distance between PR and SU.

To locate points Q and T on these lines giving this shortest distance, projection 5 is drawn with hinge line H<sub>4,5</sub> perpendicular to QT and parallel to P<sub>4</sub>R<sub>4</sub>, making both P<sub>5</sub>R<sub>5</sub> and S<sub>5</sub>U<sub>5</sub> true views (any projection of an end view is a true view). Projecting the intersection of these lines, Q<sub>5</sub> and T<sub>5</sub> back to projection 1 (magenta lines and labels) allows their coordinates to be read off the X, Y and Z axes.