0.5

1 cm

PERSPECTIVE.

97

lines on it, a representation of the object, as seen by the

spectator, will be obtained. The transparent plane re-

presents the picture, and the problem in perspective, is as

we have said, to make a section of the pyramid or cone

of rays as the case may be, by a plane, curved, or other

surface. The figure illustrates the mode of doing this.

(Fig. 188.)

A horizontal projection of the visual rays is made, that is

to say, from the plane or horizontal projection of the

point required to be found in perspective, a line is drawn

to the position of the spectator, as A a C, and another line

from its vertical projection to the eye of the spectator, as

A a' 0. At the points of intersection of the first set of

lines with the horizontal projection of the picture, a per-

pendicular a a' is drawn, and the intersection of this with

the corresponding line from the vertical projection, gives

the point a' required.

A much better idea of the mode of operation will be

obtained from the following figures, in which the process

described is repeated geometrically.

Let O and o' (Fig. 189) be the projection of the eye,

E F e f those of the picture, and ABG, ab cdg, those of

a pyramid with quadrangular base.

Now, if from the eye a line is drawn to the points A a

of the object, we shall have for the projections of that

line, the lines AO ,a o'. The points a a, where these pro-

jections cut the projections of the picture, are evidently

the projections of the points in which the visual rays meet

the picture, and all that is required is to find the position

of that point on the picture itself. Conceive E' F' to be

the elevation of the face of the picture. To its base E' D

transfer the distances a" b", b' g", g c", c cT, and from the

points draw indefinite lines perpendicular to E' D. On

this line set up at a from the base E' D, the

height E a', in the vertical projection of the

picture, and ar will be the perspective of the

point required. Proceed in the same manner

with all the other points.

As on the problem of finding the perspec-

tive of any point the whole science of perspec-

tive rests, the student should make himself

thoroughly master of it, and although he may

not be able to perceive the direct utility of

what immediately follows, he is recommended

to study it with care and attention, so as to

understand the principles. The application

of these will be developed by and by, and

methods of abridging the labour will be

pointed out; the student will also be enabled

to devise others for himself.

In addition to the vertical and horizontal planes with

which we are familiar in the operations of projection,

several ausiliary planes are employed in perspective, and

particularly the four following :—

1. The horizontal plane A B, (Fig. 190), on which the

spectator and the objects viewed

are supposed to stand; this is

therefore generally termed the

ground ‘plane or geometrical

plane.

2. The plane C R, which has

been considered as a transparent

plane placed in front of the

spectator, on which the objects

are delineated. It is called the

plane of projection or the plane

of the picture. The intersec-

tion C D of the first and second

planes is called the line of pro-

jection, the ground line, or base

of the picture.

3. The plane E F passing horizontally through the eye

of the spectator, and cutting the plane of the picture at

97

lines on it, a representation of the object, as seen by the

spectator, will be obtained. The transparent plane re-

presents the picture, and the problem in perspective, is as

we have said, to make a section of the pyramid or cone

of rays as the case may be, by a plane, curved, or other

surface. The figure illustrates the mode of doing this.

(Fig. 188.)

A horizontal projection of the visual rays is made, that is

to say, from the plane or horizontal projection of the

point required to be found in perspective, a line is drawn

to the position of the spectator, as A a C, and another line

from its vertical projection to the eye of the spectator, as

A a' 0. At the points of intersection of the first set of

lines with the horizontal projection of the picture, a per-

pendicular a a' is drawn, and the intersection of this with

the corresponding line from the vertical projection, gives

the point a' required.

A much better idea of the mode of operation will be

obtained from the following figures, in which the process

described is repeated geometrically.

Let O and o' (Fig. 189) be the projection of the eye,

E F e f those of the picture, and ABG, ab cdg, those of

a pyramid with quadrangular base.

Now, if from the eye a line is drawn to the points A a

of the object, we shall have for the projections of that

line, the lines AO ,a o'. The points a a, where these pro-

jections cut the projections of the picture, are evidently

the projections of the points in which the visual rays meet

the picture, and all that is required is to find the position

of that point on the picture itself. Conceive E' F' to be

the elevation of the face of the picture. To its base E' D

transfer the distances a" b", b' g", g c", c cT, and from the

points draw indefinite lines perpendicular to E' D. On

this line set up at a from the base E' D, the

height E a', in the vertical projection of the

picture, and ar will be the perspective of the

point required. Proceed in the same manner

with all the other points.

As on the problem of finding the perspec-

tive of any point the whole science of perspec-

tive rests, the student should make himself

thoroughly master of it, and although he may

not be able to perceive the direct utility of

what immediately follows, he is recommended

to study it with care and attention, so as to

understand the principles. The application

of these will be developed by and by, and

methods of abridging the labour will be

pointed out; the student will also be enabled

to devise others for himself.

In addition to the vertical and horizontal planes with

which we are familiar in the operations of projection,

several ausiliary planes are employed in perspective, and

particularly the four following :—

1. The horizontal plane A B, (Fig. 190), on which the

spectator and the objects viewed

are supposed to stand; this is

therefore generally termed the

ground ‘plane or geometrical

plane.

2. The plane C R, which has

been considered as a transparent

plane placed in front of the

spectator, on which the objects

are delineated. It is called the

plane of projection or the plane

of the picture. The intersec-

tion C D of the first and second

planes is called the line of pro-

jection, the ground line, or base

of the picture.

3. The plane E F passing horizontally through the eye

of the spectator, and cutting the plane of the picture at