41. Suppose it is desired to determine from Fig. 10 how far the station point lies in front of the picture plane. This is a horizontal distance, and therefore will be shown by the distance between the horizontal projection of the station point and the horizontal projection of the picture plane, or, in other words, by the distance between SPH and HPP. • 42. The point a is a. certain distance above or below the plane of the horizon. This is a vertical distance, and will be shown by the distance between the vertical projection of the point a and the vertical projection of the plane of the horizon ; in other words, by the distance between av and VH. It will be seen that in Fig. 10 the point a lies below the plane of the horizon.
43. If it be desired to find how far in front or behind the picture plane the point a lies, this is a horizontal distance, and will be shown by the distance between the horizontal projection of the picture plane and horizontal projection of the point a, that is, by the distance between IIPP and an. In Fig. 10 the point a lies behind the picture plane.
44. The distance between the plane of the ground and the plane of the horizon is a vertical distance, and will be shown by the distance between the vertical projection of the plane of the horizon and the vertical projection of the plane of the ground ; i.e., the distance between VH and VII,. The distance between the observer's eye and the plane of the ground is also a vertical dis tance, and will be shown by the distance between SPV'and but as SPv must always be found in VII, the distance of the observer's eye above the plane of the ground will always be shown by the distance between VH and VH,..
45. To find the perspective of the point a, Fig. 10, draw the visual ray through the point, and find where this visual ray pierces the picture plane (§ 24/). The horizontal projection of the visual ray is shown by the line RH drawn through the horizontal projection SPH of the observer's eye and the -horizontal pro jection au of the point a. The vertical projection of the visual ray is shown by the line IV drawn through the vertical projec tion SPv of the observer's eye and the vertical projection. av of .the point a. This visual ray pierces the picture plane at the point e" on ltv vertically in line with the point where KH crosses HP? (§§ 35 and 36). is the perspective of the point a.
To find where any line, represented by its horizon tal and vertical projections, pierces the picture plane, is one of the most used and most important problems in perspective projec tion. The point where any line pierces the picture plane will always be found on the vertical projection of the line, vertically above or below the point where the horizontal projection of the line crosses HPP (§§ 35 and 36).
46. In order to avoid confusion between the vertical, hori zontal, and perspective projections of the points and lines in the drawing, it becomes-necessary to adopt some systematic method of lettering the different points and lines. The following method
will be found convenient, and has been adopted in these notes.
If the student will letter each point or line as it is found, in accordance VIr'ith this notation, he will be able to read his drawings at a glance, and any desired projection of a point or line may be recognized instantly.
The picture plane (or vertical coordinate) is indicated by the capital letters PP.
The plane of the horizon (or horizontal coordinate) is indi cated by the capital letter H.
A point in space is indicated by a small letter.
The same small letter with an index v, it, dr indicates its vertical, horizontal, or perspective projection, respectively.
A line in space is indicated by a capital letter, usually one of the first letters in the alphabet..
The same capital letter with an index or indicates its vertical, horizontal, or perspective projection, respectively.
All lines which belong to the same system may be designated by the same letter,' the different lines being distinguished by the subordinate 2, etc., placed after the letter.
The trace of a plane upon the picture plane is indicated by a capital letter (usually one of the last letters in the alphabet) with a capital V placed before it.
The same letter preceded by a capital H indicates the trace of the plane upon the horizontal coordinate.
The perspective of the vanishing trace of a system of planes is indicated by a capital letter preceded by a capital T.
The perspective of the vanishing point of a system of lines is indicated by a small v with an index corresponding to the letter of the lines which belong to the system.
PP = vertical coordinate, or picture plane. • Hpp = horizontal trace of the vertical coordinate, or picture plane.
H =horizontal coordinate, or plane of the horizon.
VH =vertical trace of the horizontal coordinate, or plane of the horizon.
=plane of the ground.
VH, = vertical trace of the plane of the ground.
a = point in space.
av =vertical projection of the point..
e=horiaintal. projection of the point.
=perspective projection of the point.
Arline in space.
Av = vertical projection of the line.
AP=perspective projection of the line. • VS=trace of the plane S upon PP (vertical trace). IIS =trace of the plane S upon H (horizontal trace). TS =perspective of the vanishing trace of the plane S. (See Note 1 below.) vA =perspective of the vanishing point of a system of lines, the elements of which are lettered A3, A4, OW. (See Note 2 below.) A plane in space may also be deSignated by the letters of any two lines which lie in it. Thus, the plane AB would be a plane determined by the two lines A and B. TAB would indicate the perspective of the vanishing trace of the plane. A straight line may be designated by the letters of any two points which lie in it. Thus, the dine ab would be a straight line determined by the two points a and b. v" would cate the perspective of the vanishing point of the line. It is times convenient to use this notation in place of the general one.