The Theory and Practice of Perspective Part 28

CLII

SUN BEHIND THE PICTURE, SHADOWS THROWN ON A WALL

As here we change the conditions we must also change our procedure. An upright wall now becomes the plane of shade, therefore as the principle of shadows must always remain the same we have to change the relative positions of the luminary and the foot thereof.

At _S_ (point of sight) raise vertical _SF_, making it equal to _fL_.

_F_ becomes the foot of the luminary, whilst the luminary itself still remains at _L_.

[Ill.u.s.tration: Fig. 273.]

We have but to turn this page half round and look at it from the right, and we shall see that _SF_ becomes as it were the horizontal line. The luminary _L_ is at the right side of point _S_ instead of the left, and the foot thereof is, as before, the trace of the luminary, as it is just underneath it. We shall also see that by proceeding as in previous figures we obtain the same results on the wall as we did on the horizontal plane. Fig. B being on the horizontal plane is treated as already shown. The steps have their shadows partly on the wall and partly on the horizontal plane, so that the shadows on the wall are outlined from _F_ and those on the ground from _f_. Note shadow of roof _A_, and how the line drawn from _F_ through _A_ is met by the line drawn from the luminary _L_, at the point _P_, and how the lower line of the shadow is directed to point of sight _S_.

[Ill.u.s.tration: Fig. 274.]

Fig. 274 is a larger drawing of the steps, &c., in further ill.u.s.tration of the above.

CLIII

SUN BEHIND THE PICTURE THROWING SHADOW ON AN INCLINED PLANE

[Ill.u.s.tration: Fig. 275.]

The vanis.h.i.+ng point of the shadows on an inclined plane is on a vertical dropped from the luminary to a point (_F_) on a level with the vanis.h.i.+ng point (_P_) of that inclined plane. Thus _P_ is the vanis.h.i.+ng point of the inclined plane _K_. Draw horizontal _PF_ to meet _fL_ (the line drawn from the luminary to the horizon). Then _F_ will be the vanis.h.i.+ng point of the shadows on the inclined plane. To find the shadow of _M_ draw lines from _F_ through the base _eg_ to _cd_. From luminary _L_ draw lines through _ab_, also to _cd_, where they will meet those drawn from _F_. Draw _CD_, which determines the length of the shadow _egcd_.

CLIV

THE SUN IN FRONT OF THE PICTURE

[Ill.u.s.tration: Fig. 276.]

When the sun is in front of the picture we have exactly the opposite effect to that we have just been studying. The shadows, instead of coming towards us, are retreating from us, and the objects throwing them are in full light, consequently we have to reverse our treatment. Let us suppose the sun to be placed above the horizon at _L_, on the right of the picture and behind the spectator (Fig. 276). If we transport the length _Lf_ to the opposite side and draw the vertical downwards from the horizon, as at _FL_, we can then suppose point _L_ to be exactly opposite the sun, and if we make that the vanis.h.i.+ng point for the sun's rays we shall find that we obtain precisely the same result. As in Fig.

277, if we wish to find the length of _C_, which we may suppose to be the shadow of _P_, we can either draw a line from _A_ through _O_ to _B_, or from _B_ through _O_ to _A_, for the result is the same. And as we cannot make use of a point that is behind us and out of the picture, we have to resort to this very ingenious device.

[Ill.u.s.tration: Fig. 277.]

In Fig. 276 we draw lines L1, L2, L3 from the luminary to the top of the object to meet those drawn from the foot _F_, namely F1, F2, F3, in the same way as in the figures we have already drawn.

[Ill.u.s.tration: Fig. 278.]

Fig. 278 gives further ill.u.s.tration of this problem.

CLV

THE SHADOW OF AN INCLINED PLANE

The two portions of this inclined plane which cast the shadow are first the side _fbd_, and second the farther end _abcd_. The points we have to find are the shadows of _a_ and _b_. From luminary _L_ draw _La_, _Lb_, and from _F_, the foot, draw _Fc_, _Fd_. The intersection of these lines will be at _ab_. If we join _fb_ and _db_ we have the shadow of the side _fbd_, and if we join _ca_ and _ab_ we have the shadow of _abcd_, which together form that of the figure.

[Ill.u.s.tration: Fig. 279.]

CLVI

SHADOW ON A ROOF OR INCLINED PLANE

To draw the shadow of the figure _M_ on the inclined plane _K_ (or a chimney on a roof). First find the vanis.h.i.+ng point _P_ of the inclined plane and draw horizontal _PF_ to meet vertical raised from _L_, the luminary. Then _F_ will be the vanis.h.i.+ng point of the shadow. From _L_ draw L1, L2, L3 to top of figure _M_, and from the base of _M_ draw 1F, 2F, 3F to _F_, the vanis.h.i.+ng point of the shadow. The intersections of these lines at 1, 2, 3 on _K_ will determine the length and form of the shadow.

[Ill.u.s.tration: Fig. 280.]

CLVII

TO FIND THE SHADOW OF A PROJECTION OR BALCONY ON A WALL

To find the shadow of the object _K_ on the wall _W_, drop verticals _OO_ till they meet the base line _BB_ of the wall. Then from the point of sight _S_ draw lines through _OO_, also drop verticals _Dd_, _Cc_, to meet these lines in _dc_; draw _cF_ and _dF_ to foot of luminary. From the points _xx_ where these lines cut the base _B_ raise perpendiculars _xa_, _xb_. From _D_, _A_, and _B_ draw lines to the luminary _L_. These lines or rays intersecting the verticals raised from _xx_ at _ab_ will give the respective points of the shadow.

[Ill.u.s.tration: Fig. 281.]

The shadow of the eave of a roof can be obtained in the same way. Take any point thereon, mark its trace on the ground, and then proceed as above.

CLVIII

SHADOW ON A RETREATING WALL, SUN IN FRONT