In a similar manner the vanishing point for the roof line, represented in the diagram by by, may be determined. First find, from the given plan and elevation of the object, a revolved plan and elevation of hg, to agree with the position of the line in the diagram. Revolve bH9H in the given plan about the point gu, until it is parallel to bg in the diagram, and occupies the position indicated by the line klign. The corresponding revolved elevation is represented by the red line bive.
and now represent respectively the horizontal and vertical projections of an element of the system to which the roof line, represented by bg in the diagram, belongs. The vanish ing point of this system can be found by Problem III. Through SPH draw a line parallel to b,He (or bg in the diagram), repre senting the horizontal projection of the visual element of the sys and through SPv draw a line parallel to ifigv, representing the vertical projection of their visual element. The visual ele ment, represented by these two projections, pierces the picture plane at giving the perspective of the vanishing point of the roof line, represented in the diagram by the line by.
By a similar process, and are found to represent respectively the horizontal and vertical projections of an element of the system to which belongs the roof line represented in the diagram by the line a. The perspective of the vanishing point of this line has been found at v".
et, vbk, and ear have all been found to lie above VH (§ 51. note).
71. vm, vo, and vkl are found exactly as were ye, vbg, and v"k ; but, as the systems to which they belong vanish down ward, they will lie below VH (§ 51, note).
Thus, flld,H and fvd,v are respectively the horizontal and vertical projections of an element of the system represented fd in the diagram. A line drawn thrthigh SP", parallel to fHd,H (or fd in the diagram), will intersect HPP in the point w. A verti cal line through w will intersect a line through SPIT parallel to below VH.
72. Having found the perspectives of these vanishing points, the perspectives of the vanishing traces of all the planes in the object should be drawn as a test of the accuracy with which the vanishing points have been constructed. The roof planes in the house are lettered with the capital letters M, N, 0, P, etc., on the diagram.
The plane 0 contains the lines af, ad, and fd. Therefore, the
vanishing trace (TO) of the plane must be .a straight line passing through the three vanishing points, v", vaa, and vm (§ 24 d). If all three of these vanishing points do not lie in a straight line, it shows some inaccuracy, either in draughting or in the method used in finding some of the vanishing points. The student should not be content until the of his work is proved by draw ing the vanishing trace of each plane in the object through the vanishing points of all lines that lie in that plane.
The plane M contains the lines fd, ye, and de. The last line belongs to the system ab, and hence its vanishing point is The vanishing trace (TM) of the plane M must pass through vm, vga, and vab.
Similarly, the vanishing trace (TP) of the plane P must pass through vga, vbg, and v". TN must pass through vab, vat, and vbg. TQ must pass through and v". TR must pass through and vaa.
73. The vanishing trace of a vertical plane will always be a vertical line passing through the vanishing points of all lines which lie in the plane. Therefore, the vanishing trace of the vertical planes in the house that vanish towards the left will be represented by a vertical line (TS) passing through vaa.
The vanishing trace of the vertical planes of the house that vanish towards the right will be represented by a vertical line (TT) passing through v". As the vertical plane which forms the face of the porch belongs to this system, and as this plane also contains the lines ltk and id, TT will be found to pass through v" and as well as vab.
74. It will be noticed that the vanishing points for the lines mn and on have not been found. These vanishing points might have been found in a manner exactly similar to that in which the other vanishing points were found, or they may be determined now, directly- from the vanishing traces already drawn, in the following manner: The line mn is seen to be the line of intersection of the two planes N and Q. Therefore (§ 24 e) vm must lie at the inter section of TN and TQ. • For a similar reason, v" must lie at the intersection of TN and TR. TN and TR do not intersect within the limits of the plate, but they are seen to converge as they pass to the left, and, if produced in that direction, would meet at the vanishing point for the line on.