Editing Descriptive geometry (section)

==== 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.