In a similar manner, the auxiliary line of measures mrnr might have been used to determine the upper and lower edges of the square. This construction has been indicated, and the student should follow it through.
59. It sometimes happens that no line in the object lies in the picture plane. In such a case there is no principal line of measures, and some vertical plane in the object must be extended until it intersects the picture plane, forming by this intersection an auxiliary line of measures. Fig. 21 illustrates such a case. A rectangular block, similar to those shown in Figs. 19 and 20, is situated some distance behind the picture plane, as indicated by the relative positions of HPP and the diagram.
Its perspective projection will evidently be smaller if the vertical edge ae were in the picture plane, as was the case in Figs. 19 and 20, and the perspective of ae will evidently be shorter than the true length of ae. There is, therefore, no the object that can be used for a line of measures. It becomes necessary to extend one of the vertical faces of the block until it intersects the picture plane, and shows by the intersection its true vertical height. Thus, the plane abfe has been extended, as indicated in the diagram, until it intersects the picture plane in the line mn. This intersection is an auxiliary line of measures for the plane abfe, and niPnP shows the true vertical height of this plane.
Either of the other vertical faces of the block, as well as the face able, might have been extended until it intersected the picture plane, and formed by this intersection a line of measures for the block.
The vanishing points for the various systems of lines have been found as in the previous cases.
From 2nP and NJ', the horizontal edges of the face abfe vanish to v". a.' will be found on the upper edge of this face, vertically below the intersection of HPP with the horizontal projection of the visual ray through the point a in the diagram. A vertical line through a.. will represent the perspective of the nearest verti cal edge of the block, and will establish the position of J.
In a similar manner, bP will be found vertically below the intersection of HPP with the horizontal projection of the visual ray through the point b in the diagram. A vertical line through b' will establish fl and complete the perspective of the face abfe. Having found the perspective of this face, the remainder of the block may be determined as in the previous problems.
Instead of being some distance behind the picture plane, the block might have been wholly or partly in front of the picture plane. In any case, find the intersection with the picture plane of some vertical face of the block (produced, if necessary). This intersection will shoW the true vertical height of the block.
At this point the student should solve Plate II.
To find the perspective of a house, the projections of which are given.
The plan, front, and side elevations of the" house are shown in the figure. The side elevation corresponds to the projection on the profile plan, used in the study of projections. This prob lem is a further illustration of the method of revolved plan and of the use of horizontal vanishing points and auxiliary lines of measures. It is very similar to the three previous problems on the rectangular blocks.
The first step in the construction of the perspective projec tion is to make. a diagram (§ 53) which shall show the horizontal projections of all the features that are to appear in the drawing. The diagram should be placed at the top of the sheet, and turned so that the sides of the house make the desired angles with the picture plane. In Fig. 22 the diagram is shown with the long side making an angle of 30° with the picture plane. The roof lines, the chimney, and the positions of all windows, doors, etc., that are to be visible in the perspective projection, will be seen marked on the diagram.
The nearest vertical edge of the house is to lie in the picture plane. This is indicated by drawing HPP through'the corner of the diagram which represents this nearest edge.
VH may be chosen at any convenient distance below HPP.