87. The front face of the room (aP er), which is dent with the picture plane, may first be established. Each point in the perspective of this front face will be found to lie vertically under the corresponding point in plan, and horizontally in with the corresponding point in elevation. . Thus, ar is vertically under an, and horizontally in line with ay.
All lines in the room which are perpendicular to the picture plane vanish at vad (coincident with SPv).
Drawing visual rays from every point in the diagram, the corresponding points in the perspective projection wrill be verti cally under the points where these visual rays intersect HPP. The construction of the walls of the room should give the student no difficulty.
88. In finding the perspective of the steps, the vertical heights should first be projected by horizontal' construction lines from the .elevation to the line-of measures (aPeP), as indicated by the divisions between eP and m. These divisions can then be carried along the left hand wall of the room by imaginary hori zontal lines vanishing at vad. The perspective of the vertical edge where each step intersects the left hand wall may now be determined from the plan. Thus, the edge s'ep of the first step is vertically below the intersection of HPP with a. visual ray drawn through the point sH in plan, and is between the two hori zontal lines projected from the elevation that show the height of the lower step. The corresponding vertical edge of the second step will be projected from the plan in a similar manner, and will lie between the two horizontal lines projected from the elevation that show the height of the second step, etc.
From sr the line which forms the intersection of the wall with the horizontal surface of the first step will vanish to vad, etc.
From the intersection of the first step with the floor of the room will be a line belonging to the same system as arbr, and will therefore show as a true horizontal line. The Point e may be projected from the diagram by a visual ray, as usual. From e the vertical edge of the step may be drawn till it intersects a horizon tal line through sr, and so on, until the steps that rest against the side wall are determined.
89. The three upper steps in the flight rest against the rear wall. The three upper divisions on the line e'm may be carried along the left hand wall of the room, as indicated, till they inter sect the rear vertical edge of the wall, represented by the line dPItP. From these intersections the lines may be carried along
the rear wall of the room, showing the heights of the three upper steps where they rest against the rear wall.
The three upper divisions on the line ePm, have also been projected across to the line fPbP, and from this line carried by imaginary horizontal lines along the right hand wall of the room to the plane N, across the plane N to the plane 0, and from the plane 0 to the plane M. Thus, for illustration, the upper division, representing the height of the upper step, has been carried from m to c ; from c to g along the right hand face of the wall; from g to j along the plane N ; from j to k on the plane 0, and from le to pP on the plane M.
The point pP is where the line which represents the height of the upper step meets a vertical dropped from the intersection of IIPP with a visual ray through the point pH in the diagram. pP is one corner in the perspective of the upper step, the visible edges of the step being represented by a horizontal line, pP-1c, a line (pPoP) vanishing at rad, and a vertical line drawn from pP between the two horizontal lines on the plane II, which represent the height of the upper step. The point oP is at the intersection of the line drawn through pP, vanishing through rad, with the hori zontal line on the rear wall drawn through the point n, and representing the upper step where it rests against the rear wall.
The remaining steps may be found in a similar manner. The student should have no difficulty in following out the construction, which is all shown on the plate.
90. The position of the point tP on the line rPtP vs%as deter mined by projecting in the usual manner from the diagram. The position of tP might have been found in the following manner: In the figure the line Or is a line of measures (§ 81), and divisions on this line will show in their true Size. Thus, if we imagine a horizontal line to be drawn through tP, parallel to the wall of the room, it will intersect ePfP in the point n. Since ePu is on a line of measures, it will show in its true length. Thus, tP might have been determined by laying off ePn equal to the distance env, taken from the plan, and then drawing through the point u a line van ishing at ea. The intersection of this line with the horizontal line drawn through r" will determine C.