Fig. 19 shows a rectangular block resting upon the ground plane in plan and elevation. The perspective of each point has been found by Rule E. Connecting these points by straight lines, the perspective of the block is determined. Since the object lies some distance behind the picture plane, as seen by comparing the plane with HPP, the perspective is smaller than the object. Any line which lies in the picture plane will show its true length in the perspective view, and is called a measure line. It can be drawn at once to scale and used to determine the dimensions of other parts of the object which do not lie in the picture plane and consequently appear larger or smaller than their real dimen sions, according to whether they are in front of or behind it. Any vertical plane if extended will intersect the picture plane in a ver tical line. The intersection will be a measure line on which true vertical dimensions may be scaled. Thus, in fig. 19, the left ver tical face of the block can be extended forward until it intersects the picture plane in a measure line on which the distance avm will show the true height of the block. The right vertical face if extended will also give a measure line, on which lizin shows the true height.
Fig. 20 illustrates the fundamental method of constructing a perspective from which all other methods are derived. A plan and elevation are given on the left, an end view on the right. HPP determines the picture plane in horizontal projection, VH determines the plane of the horizon in vertical projection. VH1 determines the plane of the ground on which the object is to rest. The ob server's eye, SP, is given in vertical and horizontal projections. The resulting perspective is to show the house with the vertical corner ae lying in the picture plane, and with the face aefb mak ing an angle of 45° with it. This position is indicated by the diagram, which is a plan of the house revolved about a vertical axis until the side aefb makes the specified angle of 45° with HPP, and placed with the corner ae touching HPP in accordance with the specification. The point a will thus lie both in the picture plane and on the plane of the ground. Its perspective must be at a!' on
and directly under the point a in the diagram. As the front corner lies in the picture plane it will be a measure line and its true height taken from the elevation can be laid off directly from aP, determining eP as indicated. Next, by Rules D and E establish the vanishing point for the system of lines parallel to ab, as follows : the hori zontal projection of the visual ray will pass through SP" parallel to ab in the diagram, and will cross HPP at the point io. Since ab is a horizontal system the vertical pro jection of the visual ray will pass through SP' and coincide with VH. The desired vanishing point must be on VH directly below io, at
Similarly the vanishing point for the hor izontal system parallel to ad will be found on VH at Vad. The upper and lower edges of
the right face run from eP and aP respectively and vanish at Va b. The observer sees the rear edge of the right face projected on the picture plane directly below the point where a visual ray from fb in the diagram crosses HPP. As the perspective of a vertical line upon a vertical picture plane is always a vertical line, the rear edge will be found at bPfP. In a similar way the upper and lower edges of the left face vanish at Vad, and the rear edge of this face is found at dPhP. The rectangular portion of the house is com pleted by lines running from by and fP vanishing at Vad, and from dP and hP vanishing at VGb, establishing by their intersections cP and gP.
To find the roof of the main house, extend the ridge (1k) in the diagram until it intersects HPP in the point 12. Imagine a vertical plane to pass through the ridge. It will intersect the pic ture plane in a vertical line dropped from the point 12. This will be a measure line for the ridge and the true height of the ridge above the ground, 2-1, taken from the elevation, can be laid off on it. A horizontal line through 1 vanishing at Vad must contain the ridge which will be located on this line at kP/fl directly below the points in which visual rays through the extremities of the ridge in the diagram, intersect HPP. From kP, lines to eP and fP respectively, and from ii', lines to hP and gP respectively will complete the roof.
The chimney can be located in a similar manner. Extend the front face through p in the dia gram until it intersects HPP in 13. The plane of this face will inter sect the picture plane in the ver tical line dropped from 13, which will be a measure line for this face. Lay off on this measure line the true height of the top of the chimney 8-7, and the true height of the bottom line of the front face, 8-9. Through 7 and 9 lines vanishing at Vad will con tain the top and bottom edges of the front face which will be located vertically below the points where visual rays from the front face of the chimney in the diagram intersect HPP. The construction of the rest of the chimney is obvious from the drawing.
A measure line for the right vertical face of the porch is found by extending this face in the diagram until it intersects HPP and dropping a vertical 3-4. On this vertical shows the true height front face, 8-9. Through 7 and 9 lines vanishing at Vad will con tain the upper and lower edges of the right hand face. The points rP and ml' can be located by visual rays drawn through r and in on the diagram. 5-6 shows the true height of the ridge of the porch laid off on the measure line for the ridge. A line through 5 vanishing at Vab will contain the ridge. Points s1' and nP on this ridge can be located by visual rays through s and n in the diagram. The construction of the remainder of the porch can be readily understood from the drawing.