DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.25888#0127
PERSPECTIVE.
Ill
point lines parallel to the sides of the object to intersect the
picture-line. The points of intersection, or vanishing
points, for the sides and edg’es of the plate are, like the sta-
tion-point, beyond the limits of the paper. We have chosen
in this case such a point of view for the picture, and such
a, distance as would throw the station and vanishing
points beyond the limits of the paper advisedly, as these
are conditions of constant occurrence in practice, and it
is right that the learner should at the outset be made
acquainted with the difficulties of the art and the means
of overcoming them. These means in this case may be
two. The first and most ready is to fix slips of lath to the
drawing-board, on which the horizon-line may be extended
to the requisite distance. The other is to draw the con-
verging lines by the centrolinead invented by Mr. Nicol-
son. This instrument, however, is not so applicable to
the drawing of machinery as of architecture, as it requires
frequent alteration to adjust it to the various vanishing
points. We prefer, therefore, the simple plan of fixing
laths to the board, and inserting at each vanishing point
a needle, against which the straight-edge may work as a
centre. We shall now proceed to describe the process in
detail.
Fig. 1 A is a plan of the wall, the iron plate, and the
nuts at the top of the plate. We have already described
the manner of drawing the extreme visual rays, picture-
line, and central plane; these being drawn, we proceed to
draw the visual rays from the various points of the plan.
We then prepare for the perspective representation, as
in Fig. 1 B, by drawing the ground-line of the picture
4 4, the horizon-line 5 5, the latter at such a height as the
eye of the spectator is supposed to be; and the vertical pro-
jection of the central plane 0 0. Now let us trace the
drawing of any point in the plan, as A, to its perspective
representation. From A draw the visual line A a, cutting
the picture-line in a, and produce the line B A to the
picture-line in A'. Transfer the point A' to the ground-
line of the perspective at A', and draw A' A2 indefinitely
at right angles to the ground-line. This line then being
in the plane of the picture, on it is to be set up the origi-
nal height of the objects in the plane B A, measured from
the geometrical drawing. In the same way transfer the
point A to a in the perspective, and draw through it an
indefinite perpendicular to the ground-line. This line is
the indefinite perspective representation of the corner of
the Plate A. The ground-line in the perspective drawing
is assumed at the level of the bottom of the plate, there-
fore from A draw to the left hand vanishing point a line
to represent the perspective of the bottom of the plate, and
its intersection with a A is the perspective of the bottom of
the hither corner. To find the perspective of the top edge
of the plate, from A' on the ground-line set up from the
geometrical drawing the height of the plate in c, and
through c draw to the vanishing point the line c d, which
is the indefinite perspective of the top edge of the plate,
and its hither angle is defined by the perpendicular from a.
To find the further vertical edge of the plate, it is only
necessary from the point B on the plan to draw the visual
ray B b, and to transfer its distance from the central plane
o O b to the ground-line in the perspective at b, and from
this to draw the perpendicular to B, produced to intersect
the perspectives of the top and bottom edges. The heights
of the perspectives of the horizontal parts of the rim of
the plate are also set up on the line A' A2, and the vertical
parts are obtained by drawing visual rays. The perspec-
tive of the return or thickness of the hither edge of the
plate is obtained by drawing from the upper and lower
corners, lines to the right hand vanishing point, and de-
fining their extent by drawing the visual ray E e, and
transferring the distance O e to the perspective ground-
line in e.
The perspective of all the other objects in the ground-
plane, such as the nuts, it will be seen, are obtained first
by drawing visual rays from the points of the objects;
transferring the points in which these intersect the picture-
line to the perspective ground-line; from these, drawing
indefinite perpendiculars, and then obtaining their heights
by producing the plane of the object, such as that of the
face of the nuts F /, to the picture-line, and transferring
the point of intersection / to the ground-line, and drawing
a perpendicular on which the heights are to be set up.
The perspective of the curve in the plate is found thus:—
The absolute depth of the curve is shown in the ground-
plan at A g. The small drawing 1 c shows the vertical
elevation, and from this the height of the points of inter-
section of the curve with the wall is obtained at h h, and
set up on the plane of the wall produced to meet the pic-
ture, while the height of the point g of the curve is set
up on the plane of g g, produced to intersect the picture.
The remainder of the drawing will elucidate itself.
Plate 68, fig. 2 A (Perspective Lesson, Part Second).
To the ground plan we now add the circles representing
the horizontal bevel-wheel, and the profiles of the vertical
bevel-wheels. To find the perspectives of circles, as we
already know, we have to draw the perspectives of their
circumscribing squares. Each circle is accordingly found
in this drawing, by first drawing the square within which
it is inscribed, an operation which must be familiar to the
student who has attended to the elementary part of the
treatise, and need not therefore be described. The bevel-
gear being frustrums of cones, the perspectives of the lines
of their teeth will, like the same lines in the geometrical
drawing, converge to a point where the apices of the cones
meet. This point is found in the perspective, by drawing-
through the centre of the horizontal wheel (the point
where the diagonals of the square intersect each other) a
vertical line intersecting at ft a line drawn through the
centres of the vertical wheels to the left hand vanishing
point. The ellipses, which are the perspectives of the
circles, should be drawn by the simple mode shown and
described, ante pp. 105, 106.
Plate 69, figs. 3 A and 3 B (Perspective Lesson, Part
Third). We now add the teeth of the wheels. Their
divisions may be found in two ways, and both are here
exemplified. It is quite a matter of indifference which
we use, and the draughtsman suits his own conveni-
Ill
point lines parallel to the sides of the object to intersect the
picture-line. The points of intersection, or vanishing
points, for the sides and edg’es of the plate are, like the sta-
tion-point, beyond the limits of the paper. We have chosen
in this case such a point of view for the picture, and such
a, distance as would throw the station and vanishing
points beyond the limits of the paper advisedly, as these
are conditions of constant occurrence in practice, and it
is right that the learner should at the outset be made
acquainted with the difficulties of the art and the means
of overcoming them. These means in this case may be
two. The first and most ready is to fix slips of lath to the
drawing-board, on which the horizon-line may be extended
to the requisite distance. The other is to draw the con-
verging lines by the centrolinead invented by Mr. Nicol-
son. This instrument, however, is not so applicable to
the drawing of machinery as of architecture, as it requires
frequent alteration to adjust it to the various vanishing
points. We prefer, therefore, the simple plan of fixing
laths to the board, and inserting at each vanishing point
a needle, against which the straight-edge may work as a
centre. We shall now proceed to describe the process in
detail.
Fig. 1 A is a plan of the wall, the iron plate, and the
nuts at the top of the plate. We have already described
the manner of drawing the extreme visual rays, picture-
line, and central plane; these being drawn, we proceed to
draw the visual rays from the various points of the plan.
We then prepare for the perspective representation, as
in Fig. 1 B, by drawing the ground-line of the picture
4 4, the horizon-line 5 5, the latter at such a height as the
eye of the spectator is supposed to be; and the vertical pro-
jection of the central plane 0 0. Now let us trace the
drawing of any point in the plan, as A, to its perspective
representation. From A draw the visual line A a, cutting
the picture-line in a, and produce the line B A to the
picture-line in A'. Transfer the point A' to the ground-
line of the perspective at A', and draw A' A2 indefinitely
at right angles to the ground-line. This line then being
in the plane of the picture, on it is to be set up the origi-
nal height of the objects in the plane B A, measured from
the geometrical drawing. In the same way transfer the
point A to a in the perspective, and draw through it an
indefinite perpendicular to the ground-line. This line is
the indefinite perspective representation of the corner of
the Plate A. The ground-line in the perspective drawing
is assumed at the level of the bottom of the plate, there-
fore from A draw to the left hand vanishing point a line
to represent the perspective of the bottom of the plate, and
its intersection with a A is the perspective of the bottom of
the hither corner. To find the perspective of the top edge
of the plate, from A' on the ground-line set up from the
geometrical drawing the height of the plate in c, and
through c draw to the vanishing point the line c d, which
is the indefinite perspective of the top edge of the plate,
and its hither angle is defined by the perpendicular from a.
To find the further vertical edge of the plate, it is only
necessary from the point B on the plan to draw the visual
ray B b, and to transfer its distance from the central plane
o O b to the ground-line in the perspective at b, and from
this to draw the perpendicular to B, produced to intersect
the perspectives of the top and bottom edges. The heights
of the perspectives of the horizontal parts of the rim of
the plate are also set up on the line A' A2, and the vertical
parts are obtained by drawing visual rays. The perspec-
tive of the return or thickness of the hither edge of the
plate is obtained by drawing from the upper and lower
corners, lines to the right hand vanishing point, and de-
fining their extent by drawing the visual ray E e, and
transferring the distance O e to the perspective ground-
line in e.
The perspective of all the other objects in the ground-
plane, such as the nuts, it will be seen, are obtained first
by drawing visual rays from the points of the objects;
transferring the points in which these intersect the picture-
line to the perspective ground-line; from these, drawing
indefinite perpendiculars, and then obtaining their heights
by producing the plane of the object, such as that of the
face of the nuts F /, to the picture-line, and transferring
the point of intersection / to the ground-line, and drawing
a perpendicular on which the heights are to be set up.
The perspective of the curve in the plate is found thus:—
The absolute depth of the curve is shown in the ground-
plan at A g. The small drawing 1 c shows the vertical
elevation, and from this the height of the points of inter-
section of the curve with the wall is obtained at h h, and
set up on the plane of the wall produced to meet the pic-
ture, while the height of the point g of the curve is set
up on the plane of g g, produced to intersect the picture.
The remainder of the drawing will elucidate itself.
Plate 68, fig. 2 A (Perspective Lesson, Part Second).
To the ground plan we now add the circles representing
the horizontal bevel-wheel, and the profiles of the vertical
bevel-wheels. To find the perspectives of circles, as we
already know, we have to draw the perspectives of their
circumscribing squares. Each circle is accordingly found
in this drawing, by first drawing the square within which
it is inscribed, an operation which must be familiar to the
student who has attended to the elementary part of the
treatise, and need not therefore be described. The bevel-
gear being frustrums of cones, the perspectives of the lines
of their teeth will, like the same lines in the geometrical
drawing, converge to a point where the apices of the cones
meet. This point is found in the perspective, by drawing-
through the centre of the horizontal wheel (the point
where the diagonals of the square intersect each other) a
vertical line intersecting at ft a line drawn through the
centres of the vertical wheels to the left hand vanishing
point. The ellipses, which are the perspectives of the
circles, should be drawn by the simple mode shown and
described, ante pp. 105, 106.
Plate 69, figs. 3 A and 3 B (Perspective Lesson, Part
Third). We now add the teeth of the wheels. Their
divisions may be found in two ways, and both are here
exemplified. It is quite a matter of indifference which
we use, and the draughtsman suits his own conveni-