The heights of the tops and bottoms of the windows can be taken directly from the end view and laid off on aPeP which is the measure line for the right hand face of the main house. Hori zontal lines through these heights will establish the top and bot tom lines of the windows. The vertical sides can be located ver tically below where visual rays from the windows in the diagram cross HPP. In this way the entire perspective can be completed. Vanishing Points of Oblique Lines.--The vanishing points for the inclined lines in the roof ek, kf, lg, lh, etc., are not ab solutely necessary for the construction of the perspective. The method of determining them, however, should be understood as in some problems the vanishing points of oblique lines form an important part of the solution. The construction for their de termination is shown on fig. 20.
First consider ek. A line drawn through the station point parallel to ek will establish the vanishing point by its intersection with the picture plane (Rule D). The horizontal projection of such a line will pass through SP" parallel to ek in diagram, and will cross HPP at 14. The vanishing point will be vertically in line with 14 and on the vertical projection of the line through SP' parallel to ek (Rule E). But since the diagram containing ek has been revolved from the original position of the given plan, no vertical projection is given which corresponds to the revolved direction of ek. The line ek must therefore be revolved back into its original direction, i.e., parallel to in the given plan, in order that the given vertical projection evkv may be used to establish its vanishing point. As the vanishing point must lie in the vertical through 14, the vanishing point will not be disturbed if the vertical line through 14 is used as the axis about which the revolution takes place. During the revolution, the horizontal projection of any point in the line, as SP", will describe a circle with the point 14 as its centre. The vertical projection, SPv, of the same point in the line, will move in a horizontal path along VH, and at any instant during the revolution will be found directly under SP". The revolution will be continued until the horizontal projection of the line is parallel to ehkh in the given plane. The line will now be in its original direction, SPh will have moved to will have moved to and the given elevation evkv can be drawn through determining by its intersection with the vertical through 14, the desired vanishing point Vek. Since the
line ek slopes upward as it recedes, Vek is found to be above VH (Rule A).
In a similar manner the vanishing point for lg can be found. The line through SPh parallel to lg coincides with the one parallel to ek. This is swung back about a vertical axis through 14 until parallel to lhg", in which position it will coincide with the line parallel to ehkh, and SPh will have revolved to will be on VH directly below and a line parallel to the given eleva tion logy, drawn through will, by its intersection with the vertical through 14, determine Pg. Since the line lg slopes down ward as it recedes, its vanishing point is found below the horizon (Rule A).
To find the vanishing point for rs draw a line parallel to rs, in the diagram, through SPh, crossing HPP at i 1. Vrs will be found somewhere on a vertical through I z. Swing the line about a ver tical axis through II until parallel with rhsh in the given plan. SPh will revolve to SP2h and will be found on VH vertically in line Through draw a line parallel to rvsv in the given elevation which will determine by its intersection with the vertical through II, the vanishing point rs. This will be found above VH as rs vanishes upward. A similar series of steps will determine the vanishing point for st at Vst below the horizon.