75. Having found vs", v", vbk, and vtd, TN could have been drawn through v" and vbk; and TO could have been drawn through v" and vfd. As of is the intersection of the two planes N and 0, v" could have been found at the intersection of TN and TO without actually constructing this vanishing point.
Similarly, vg° could have been determined by the intersec tion of TM and TP.
By an examination of the plate, the student will notice that the vanishing point for each line in the object is formed at the intersection of the vanishing traces of the two planes of which the line forms the intersection. Thus, the line ad forms the inter section between the plane 0 and the left hand vertical face of the house. v" is found at the intersection of TO and TS.
The line fg, which forms the ridge of the roof, is the inter section of the planes M and N. The vanishing point for fg is v"", and TM and TN will be found to intersect at v"". v"k is found at the intersection of TQ and TT, v" is found at the inter section of TR and TT, etc.
It will be noticed also that the two lines Zak and ld lie in the same vertical plane, and make the same angle with the horizontal, one vanishing upward, and one vanishing downwal. Since both lines lie in the same vertical plane, both of their vanishing points will be found in the vertical line which represents the vanishing trace of that plane. Also, since both lines angles with
the horizontal, the vanishing point of the line vanishing upward will be found as far above VH as the vanishing point of the line vanishing downward is below VH.
In a similar way, the line bg vanishes upward, and the line fd vanishes downward; each making the same angle with the horizontal (as shown by the given plan and elevation). These two lines do. not lie in the same plane, but may be said to lie in two imaginary vertical planes which are parallel to one another. Their vanishing points will be seen to lie in the same vertical line, vbk being as far above VH as v" is below it.
As a general statement, it may be said that if two lines lie in the same or parallel vertical planes, and make equal angles with the horizontal, one vanishing upward and the other van ishing downward, the vanishing points for both lines will be found vertically in line with one another, one as far above VH as the other is below it.
This principle is often of use in constructing the vanishing point diagram. Tlius, having found via could have been determined immediately by making it lie in a vertical line with and as far below VH as is above it.