13. It may be behind or in front of the vertical plane, or it may lie partly behind and partly in front of the vertical plane or partly above and partly below the horizontal plane.
Any point in space may have three different but related pro jections, a plan or horizontal projection, an elevation or vertical projection, and a conical or perspective projection. This is illus trated in fig. 14 where two points in space a and b are shown, each with its vertical, its horizontal and its conical projection. The horizontal pro jection is indicated by an index the vertical projection by an index v, and the perspec tive projection by an index p. The point a is shown behind the picture plane and above the horizon plane. The point b is shown in front of the picture plane and below the horizon plane. The conical projection or perspective is always on the vertical or picture plane.
Fig. 15 shows the planes of projection with the ground plane indicated by its intersection with the picture plane. The point a is shown in space behind the picture plane and below the horizon plane, with its horizontal projection (ah) and its ver tical projection (av). The station point is represented by its two orthographic pro jections just as every point in space. Since it always lies in the horizon plane its hori zontal projection, SP", must always coin cide with the point itself. Its vertical pro jection will be directly in front of SP", on the picture plane as SPY. SPY must always lie in the line VH which represents the vertical projection of the horizon plane.
Just as a point in space has a hori zontal projection and a vertical projec tion, so the visual ray which passes from the point a to the observer's eye has two projections, one on each plane. Its projection is seen on the horizon plane passing through ah and SP". Its vertical projection is seen on the picture plane passing through av and SPv. The visual ray pierces the pic ture plane at aP which is the perspective of the point a (Rule C).
Rule E. The intersection of a visual ray with the picture plane must always lie upon the vertical projection of the visual ray, and must be directly in line with the point where the horizontal pro jection of the visual ray crosses the horizontal projection (HPP) of the picture plane.
In practice both the picture plane and the horizon plane must be represented on one sheet of paper. One can imagine the picture plane to be revolved about its intersection with the horizon plane in the direction indicated by the arrows SI and fig. 15, until the two planes lie coincident as shown in fig. 16. In this position the group of projections on the picture plane will overlap the group on the horizon plane. To avoid the resulting confusion the two planes can be pulled apart as shown in fig. 17. Af ter these move ments of the planes the horizon plane will still contain all of the horizontal projections, which will remain undisturbed in all aspects of their relations to one another.
HPP is the horizontal projec tion of the picture plane and is the reference line for all horizontal projections. Similarly the picture plane will contain all of the verti cal projections. VH is the ver tical projection of the horizon plane, and is the reference line for all vertical projections. rep resents the intersection of the ground plane with the picture plane. The distance between VH and shows the height of the observer's eye above the plane on which the object rests.
The two groups of projections are usually represented as in fig.
18. The only relation between the two groups is that the two corresponding orthographic projections of any point as ah and av, or SPh and SPv, must always be vertically in line with one another. Horizontal projections show distances back and front. Vertical projections show distances up and down.
Distances are never measured between a horizontal and a vertical projection.
The relation of ah to HPP shows the point a to be behind the picture plane. The re lation of ay to VH shows it to be below the plane of the horizon. The two projections of the visual ray through the point a are shown (Rh and Rv). By Rule E, the point p can be determined.