It is seldom that any complicated curve, except occasionally a spiral,
needs to be drawn in perspective; but the student will do well to
practice for some time any fantastic shapes which he can find drawn on
flat surfaces, as on wall-papers, carpets, etc., in order to accustom
himself to the strange and great changes which perspective causes in
them.
[Illustration: Fig. 63.]
The curves most required in architectural drawing, after the circle,
are those of pointed arches; in which, however, all that will be
generally needed is to fix the apex, and two points in the sides. Thus
if we have to draw a range of pointed arches, such as _APB_, Fig. 63.,
draw the measured arch to its sight-magnitude first neatly in a
rectangle, _ABCD_; then draw the diagonals _AD_ and _BC_; where they
cut the curve draw a horizontal line (as at the level _E_ in the
figure), and carry it along the range to the vanishing-point, fixing
the points where the arches cut their diagonals all along. If the arch
is cusped, a line should be drawn, at _F_ to mark the height of the
cusps, and verticals raised at _G_ and _H_, to determine the interval
between them. Any other points may be similarly determined, but these
will usually be enough. Figure 63. shows the perspective construction
of a square niche of good Veronese Gothic, with an uncusped arch of
similar size and curve beyond.
[Illustration: Fig. 64.]
In Fig. 64. the more distant arch only is lettered, as the
construction of the nearest explains itself more clearly to the eye
without letters. The more distant arch shows the general construction
for all arches seen underneath, as of bridges, cathedral aisles, etc.
The rectangle _ABCD_ is first drawn to contain the outside arch; then
the depth of the arch, _Aa_, is determined by the measuring-line, and
the rectangle, _abcd_, drawn for the inner arch.
_Aa_, _Bb_, etc., go to one vanishing-point; _AB_, _ab_, etc., to the
opposite one.
In the nearer arch another narrow rectangle is drawn to determine the
cusp. The parts which would actually come into sight are slightly
shaded.