perspective plan of the object constructed from the given plan, done in the case of the rectangular card in

exactly as Was Fig. 27.

110. Having constructed the complete perspective plan, every point in the perspective projection of the object will be found vertically above the corresponding point in the perspective plan.

VH, is the vertical trace of the plane on which the perspective projection is supposed to rest. a cally over a in the perspective plan.

is found on VH, verti

P

Pe is a vertical line of

measures for the object, and shows the true height given by the elevation.

To find the height of the apex (k) of the roof, imagine a horizontal line parallel to the line ab to pass through the apex, and to be extended till it intersects the picture plane. A line. drawn through k3, vanishing at ab, will represent the perspective plan of this line, and will intersect VI, in the point m, which is the perspective plan of the point where the horizontal line through the apex intersects the picture plane. The vertical distance nm, laid off from VII, will show the true height of the point k above the ground. P will be found vertically above k”, and on the line through, vanishing at b. The student should find no difficulty in following the construction for the remainder of the figure.

111. Fig. 29 illustrates another example of a similar nature to that in Fig. 28. The student should follow carefully through the construction of each point and line in the perspective plan and in the perspective projection. The problem offers no especial difficulty.

Plate VI. should now be solved.

CURVES.

112. Perspective is essentially a science of straight lines. If curved lines occur in a problem, the simplest way to find their perspective is to refer the curves to straight lines.

If the curve is of simple, regular form, such as a circle or an ellipse, it may be enclosed in a rectangle. The perspective of the

сн

Fig.30

enclosing rectangle may then be found. A curve inscribed within this perspective rectangle will be the perspective of the given curve. Fig. 30 shows a circle inscribed in a square. The points of intersection of the diameters with the sides of the square give the four points of tangency between the square and circle. The sides of the square give the directions of the circle at these points. Additional points on the circle may be established by drawing the diagonals of the square, and through the points m", k", n", and h drawing construction lines parallel to the sides of the square, as indicated in the figure. Fig. 31 shows the square, which is supposed to lie in a horizontal plane, in parallel perspective. One side of the square (a) lies in the picture plane, and will show in its true size. The vanishing point for the sides perpendicular to the picture plane will coincide with SPY (§ 52, note). The measure point for these sides has been found at mab, in accordance with

h

FH a"

principles already explained. ab, is laid off on VH, to the right of the point a", equal to the true length of the side of the square. A measure line through b, vanishing at mab, will determine the position of the point P. PP will be parallel to adP (§ 54. note).