A third plane perpendicular to both coordinate planes, and hence to the ground line, is called a profile plane. This plane is vertical in position, and may be used as a plane of projection. A projection on the profile plane is called a profile view, or end view, or sometimes edge view, and is often required in machine or other drawing when the plan and elevation do not sufficiently give the shape and dimensions.

Fig. 106. Projections of a Line on Horizontal, Vertical, and Profile Planes.

Fig. 107. Three Projections of a Rectangular Prism.

A projection on this plane is found in the same way as on the V plane, i. e., by perpendiculars drawn from points on the object.

Since, however, the profile plane is perpendicular to the ground line, it will be seen from the front and top simply as a straight line; in order that the size and shape of the profile view may be shown, the profile plane is revolved into V using its intersection with the vertical plane as the axis.

Given the line A B, Fig. 106, by its two projections Av Bv and Ah Bh, and given also the profile plane. Now by projecting the line on the profile by perpendiculars, the points Atv Btv and B1hA1h are found. Revolving the profile plane like a door on its hinges, all points in the plane will move in horizontal circles, so the horizontal projections A1h and B1h will move in arcs of circles with 0 as center to the ground line, and the vertical projections B1v and A1v will move in lines parallel to the ground line to positions directly above the revolved points in the ground line, giving the profile view of the line Ap Bp. Heights, it will be seen, are the same in profile view as in elevation. By referring to the rectangular prism, Fig. 107, it is seen that the elevation gives vertical dimensions and those parallel to V, while the end view shows vertical dimensions and those perpendicular to V. The profile view of any object may be found as shown for the line A B, Fig. 106, by taking one point at a time.