DRAWING BY ALDREN A. WATSON FOR GULLIVER'S TRAVELS
Illustrated Junior Library
Gr asset & Dunlap, Publishers
HOW TO US
CT I VE
Ernest W. Watson
REINHOLD PUBLISHING CORPORATION
N*u> York
19 55
RKINHOUD PUBLISHING CORPORATION
J*rtt*d i I/JSU4., JLrffrvwry of Con&r+mm Cmtalop Cmrd A^tt-mber 5S-628O
second, pri-nting. 1957
This book is gratefully
dedicated to my wife Eve,
partner in its preparation
contents
INTRODUCTION 9
i MATERIALS AND PROCEDURES 17
ii THE STRUCTURAL APPROACH 25
Hi THE SQUARE AS A UNIT OF MEASURE 31
iv THE PICTURE PLANE 39
v THE CUBE 47
vi FORESHORTENING AND CONVERGENCE 51
vii THE CIRCLE 69
viii THE CONE 89
ix THE HOUSE OF SEVEN VANISHING POINTS 95
x FLOOR TILES 99
xi UP STAIRS AND DOWN 105
xii UP HILL AND DOWN 111
xiii THREE-POINT PERSPECTIVE 115
xiv REFLECTIONS 129
xv SHADOWS 133
xvi FURNITURE 141
xvii UNIVERSAL PERSPECTIVE 147
xviii FIGURES IN PERSPECTIVE 151
xix PROBLEM OF THE BRIDGE TRUSS 157
INDEX 158
introduction
awing by the author
an advertisement
Eldorado Pencils.
WHAT IS CREATIVE PERSPECTIVE?
The answer will be found in the work of top contemporary illustra-
tors whose work is reproduced and analyzed in this book. As their
pictures are studied, it will be seen that they are more dramatic and
more convincing because the artists took broad liberties with textbook
rules, often violating the academic methods of scientific perspective.
How to violate perspective (profitably) is fully as important for
a practicing artist as are the rules of perspective, which are quite
simple. When rules are violated and perspective effects are achieved
through the artist's own devices, his methods can be called "creative."
This book has been written for the student who, while in no less
need for thorough knowledge of academic method, ought also to learn
that by using perspective creatively he can bend it to his uses rather
than be limited always to strict conformity.
Another factor which makes this book timely is the very great influ-
ence upon picturemaking-hence on perspectiveof the airplane, the
cinema, and modern photographic concepts. They have introduced new
ways of looking at our familiar world, ways that have made us radically
revise some concepts of perspective appearance.
Then there is "modern art" which defies tradition and projects revo-
lutionary viewpoints into the art of picturemaking, freeing the artist
from slavery to conventions that formerly were considered inviolate.
All of these influences have made the older texts obsolete in part.
Although the creative aspects of perspective are emphasized in this
book, the academic precepts are demonstrated sufficiently to give the
student of freehand perspective what theoretical knowledge he needs
to have of conventional practice having in mind the beginner who first
needs step-by-step introduction to this subject.
10
Fifteenth century woodcut by an
artist who had no knowledge
of scientific perspective.
The facts of perspective, to repeat, are quite simple. They can be
learned readily by anyone of ordinary intelligence. The only difficulty
lies in their effective use by the artist. By effective use I mean some-
thing other than their correct application to picturemaking in a photo-
graphic sense. Such use may not be effective at all. Effective perspec-
tive more often than not is to be had in violation of photographic
reality and the so-called "rules" of mechanical procedure. (Through-
out the book the term photographic reality or photographic appearance
is used to refer to such a transcript of nature and objects as is recorded
by the camera.) Photography comes nearest to being what we see, or
think we see, with the physical eye. In reality, no picture photographic
or otherwise-can duplicate what our eyes see. For one thing, the
camera picture is recorded on a flat plate or film ; the retina of the
human eye is concave.
All pictures, we must recognize, are a compromise with what the
eye actually sees. The assumption in perspective theory is that the
artist's direction of sight does not change in the making of his picture.
As a matter of fact, it is never static; his eye restlessly darts here
and there over the entire area of the scene without being conscious
of doing so. It has to, because the eye can focus only upon a single
point and a very limited one-at one time.
In spite of this inconsistency, we have been taught to predicate our
method upon the erroneous assumption that every picture is in reality
the record of what can be seen without shifting the gaze from point
to point. We establish what is known as the center of vision f and give
the picture t plane a fixed relation to it. There are exceptions to this
procedure, as we shall see.
Some of the greatest art of past centuries-yes, most of it-has been
produced by artists who have been either ignorant of or indifferent to
scientific methods of representation. Long before the early Renais-
sance when modern perspective procedure was first used, painters
were employing a sort of perspective that suited their purposes very
well indeed. Some moderns might even maintain that truly creative
painters were better off without the "tyranny of rules" which, admit-
tedly, has weakened the work of many painters in periods when slavish
adherence to scientific perspective has been regarded as essential to
good picturemaking. Although unaware of the rules of perspective as
taught today, the old fellows knew enough about appearance to make
their pictures sufficiently realistic. The Chinese, the Japanese and all
oriental artists throughout the centuries got along very well without
perspective rules and gave the world much of its greatest art. But, in
recognizing this, we must at the same time remember that before the
11
3
"Abandoned Powerhouse" an oil painting by Julian Levy,
collection of A.L. Simmons.
In this picture the artist, being familiar with scientific
perspective, violated it for the sake of design.
invention of perspective the painter's public was used to these strange
to the modern eye-methods of representation. The entire concept
of picturemaking was quite unlike that of our present era, which
demands the appearance of reality in illustration as people have come
to conceive it in terms of photographic appearance. But even the
concept of photographic reality has recently changed. Modern photo-
graphic practice has accustomed us to the camera distortion of close-
ups and odd angle exposures which not so long ago would have violated
our sense of reality.
And modern art-I am speaking of painting now-f rowns upon nat-
uralism. The modernist actually flouts scientific perspective, goes out
of his way to avoid it. In this philosophy, nature painting is not art
at all and the further the artist gets away from it the better. At any
rate, perspective as used by the modernist is quite different from that
employed by the naturalistic or illustrative painter. The latter uses
perspective to give a realistic appearance of distance of going back
into the picture. The modernist distorts scientific perspective in order
to flatten out the depth effect into two-dimensional pattern. He tries to
keep his painting "on the picture plane" ; that is, on the surface of the
canvas.
Conservative painters continue to employ perspective devices that
give emphasis to photographic appearance. But the best of these con-
servatives are by no means slaves to mechanical rules. They take many
liberties with perspective that to the layman's eye may not be obvious.
What I have just been saying applies particularly to the painter.
The illustrator's problem is entirely different; his function, usually,
is to depict the facts and events of the familiar world with as much
realism as possible. He must make his pictures look natural. Photo-
graphic perspective that is, scientific perspective is indispensable to
his purpose. Yet even the creative illustrator is not a slave to his per-
spective. Although he has to be thoroughly conversant with theory,
in practice he favors design when design is in serious conflict with
perspective. And he has adopted, to a considerable extent, the mod-
ernist's intentional distortion. Such distortions have indeed become
a vogue in contemporary drawing. A large body of present-day illus-
tration, which might be typified by Richard Erdoes' drawing, achieves
a liveliness and design distinction while it ignores perspective rules.
But Erdoes is as thoroughly versed in perspective as anyone could
be ; what is more, he could not have achieved the beauty of this "art-
less" drawing were he not a master of perspective.
The existing conflict between design and perspective in picture-
making may be a new thought to beginners, but the serious art student
"Street Scene in Morocco"
from Column Magazine, by Richard Erdoes.
An exciting drawing by a top
illustrator, in which scientific
perspective has been flouted for the
sake of an amusing design.
soon becomes aware of it. More and more he discovers that the demands
of designthat is, the arrangement of lines and tones needed for
effective composition and for the clear expression of his idea force
him to violate perspective rules ; and his picture actually may be more
convincing when his lines do not conform to photographic reality.
Every one who draws or paints, in whatever manner, ought to be
completely conversant with the laws of scientific perspective. Unless
fortified with this knowledge the artist is ill-equipped either to draw
accurately or to take liberties with the facts of appearance. The great
majority of artists, and all illustrators even those who most often
seem to do without it frequently are called upon to put the facts of
scientific perspective to meticulous use in their work. Without intimate
knowledge of it and great skill in its practice, no one can pose as a
professional illustrator.
In all learning processes there is theory and there is practice. Each
is dependent upon the other : they should go hand-in-hand. The busi-
ness of the author and teacher is to present theory ; practice is up to
the student. In the classroom the instructor can dictate to his students
the kind and extent of practice he considers necessary ; on the pages
of a book he can only advise.
So, I advise the serious student of perspective to spend a great deal
of time putting into practice the procedures demonstrated on these
pages. He will need a lot more than the reading and understanding
of the theory that he will find set forth in this book. He will need
practice, and plenty of it. One acquires skill in drawing only by draw-
ing, drawing, drawing and more drawing.
By way of emphasizing the effectiveness of concentrated practice,
I am tempted to offer my own learning experience during my first six
weeks of art study in The Massachusetts Normal Art School in Boston
(now the Massachusetts School of Art).
The first day of school we were ushered into a large studio, in the
center of which was a disordered pile of wooden grocery boxes of
Advertising drawing by Eric Fraser
for the American Rolex Watch Corporation.
A meticulously accurate drawing was
required for this particular
type of advertising illustration.
assorted shapes and sizes. Chairs and drawing tables -were arranged
in a wide circle around these uninspiring models. We were directed to
draw the boxes. That was our only instruction; we were given no
perspective theory, no hint of any kind of procedure.
We assumed that this exercise was merely a device to keep us occu-
pied during the confusion of the opening day, and we looked forward
expectantly to the morrow when something more exciting would be
forthcoming, perhaps drawing from a living model. Imagine our dis-
may to find the situation unchanged except that the boxes had been
knocked about a bit. We were told to draw them in this new arrange-
ment. The next day it was the same, and the next. Sometimes each
drawing was limited to an hour, sometimes to two hours. A monitor
was chosen to rearrange the boxes at stated intervals.
This went on for six weeks without any theory -whatsoever! We
were told nothing about foreshortening or about convergence of lines ;
"we were merely instructed to draw what we observed. The accuracy of
our observation, I should explain, was checked and corrected by the
instructor who admonished us to use our eyes more expertly. At the
end of six weeks we were finally taught the scientific facts of perspec-
tive appearance.
When, years later, I began teaching perspective at Pratt Institute,
I remembered this grueling and uninspiring six weeks, and I was
critical of the method. I reasoned that it would have been better had
we, at the outset, been given some theory that would have warned us
what to look for as we drew those rectangular forms day after day.
I soon changed my opinion. I discovered that my own students very
readily mastered the theory I was offering them, but still they couldn't
draw. That was because they lacked the very attitude that was forced
upon me by that six weeks' grind which taught me so well how to
use my eyes. I came to the conclusion that theory and practice should
be mixed in the proportion of 1 part theory to 50 parts practice, and
I suggest to the reader that this premise be kept in mind.
Much drawing from objects without dependence upon theory cul-
tivates the habit of three-dimensional thinking. One acquires the feel-
ing of form : the feeling of lines and planes actually receding and not
merely fooling the eye by their direction or shape on the paper. The
professional artist forgets the surface of his paperthe picture plane
as soon as he begins to draw or paint upon it. When he sets down lines
or masses to represent distance he actually thinks and feels distance.
He projects himself right through the paper, figuratively, into a limit-
less beyond.
In drawing the outlines of those boxes as they actually looked in
relation to each other, rather than trying to determine the convergence
of their lines by considering how they ought to look (according to the
vanishing points of perspective theory) we youngsters were getting
just the kind of training needed to develop the sense of "form in space,"
without which no one ever becomes a good draftsman.
I make a good deal of this at the outset because the beginner does not
realize how much practice he needs in drawing from objects. He is
likely, especially when a book is his instructor, to believe that the
theories set forth therein are his salvation. He does not fully appre-
ciate the truth that all theory can do for him is to offer certain mechan-
ical aids to his own observation and his own skills. Certainly he can
do without theory better than he can dispense with practice.
Today the illustrator makes extensive use of photography in his
work. And photographs of just about everything under the sun are
available for his useeven for copying, if he chooses. Does he need
an extensive knowledge of perspective, without which artists in pre-
camera days were helpless?
There are many occasions, it is true, when he can and does literally
copy his subject from photographs ; but the present-day illustrator still
needs as much skill in perspective as ever. Fred Ludekens once made
many illustrations for Hiram Walker whiskey. 'These involved the
drawing of innumerable barrels in all sorts of positions. Ludekens
thought his assistant, with photographs before him, might relieve
him of the tedium and time involved; in the end, Ludekens had to
draw the barrels himself.
As a teacher at Pratt Institute, I asked to have my first perspective
course labeled, Structural Perspective. That was to emphasize the
necessity of developing a structural sense, an engineering sense that
enables an artist to analyze every object, no matter how intricate, in
terms of its simple geometric basis.
The development of this analytical skill is really the most important
task before the student of perspective drawing. No matter how thor-
oughly conversant he may be with the facts of perspective appearance,
he will be quite incompetent without a large degree of this engineering
skill. Many problems that will seem very puzzling to the uninitiated
call for some very keen detective work, even by a mind that is trained
in a mechanical as well as a freehand approach.
6 Preliminary drawing by Albert Dome for his
illustration in color for Collier's.
Note the meticulous drawing of every detail,
demonstrating this master's amazing knowledge and facility as a draftsman.
16
This brings us inevitably to the use of mechanical views the cus-
tomary approach of engineers and architects. These include top, front,
side and sectional aspects of the subject which supply information that
is indispensable for much illustrative drawing. To deal with this con-
structive phase of our work we need to make use of at least elementary
instrumental drawing. And of course there are occasions when the
illustrator has to resort to somewhat involved instrumental strategy.
Such occasions may be the rendering of a factory interior or the nave
of a cathedral, projects that involve knowledge of instrumental per-
spective that can be found only in books wholly devoted to that subject.
It will of course be understood that no competent illustrator has to
follow the mechanical procedures that are here presented for purposes
of instruction in the solution of many problems. Such, for example, as
those demonstrated in the chapter on Shadows, and in the analysis of
Peter Helck's drawing. But it goes without saying that the procedures
involved are not only thoroughly understood by the illustrators but
that they are actually in operation at least in the subconscious mind.
Just as a skilled musician has long since mastered the elements of
his craft and can concentrate on the purely creative aspect of his art,
so the perspective procedures of a professional artist's work become
very nearly automatic.
There is such a phenomenon as "photographic vision." By this I
mean the gift possessed by a few artists of just naturally knowing how
to draw anything correctly without recourse to the kind of thinking
and analytical study here demonstrated. This however is a rare gift;
it is one that would better not be counted on by the student.
I believe the most valuable contribution of this book will be found
in the study of pictures by prominent illustrators reproduced on the
following pages and accompanied by analytical diagrams that demon-
strate the solutions to many different perspective problems. These
examples reveal the kind of resourcefulness and the graphic strategy
that enter into the illustrators' art.
It is said that Paolo Uccello (1397-1475), the Italian painter, was
largely responsible for perfecting the science of perspective. At any
rate he was hypnotized by it and, according to Vasari, he begrudged
time for sleeping and eating. He neglected his painting seriously and
when his wife remonstrated, he would only reply, "Oh, this delightful
perspective."
Of course I do not anticipate that my book will infect any readers
with that degree of fanaticism, but I do hope that it will help to make
the subject as pleasurable as it has been to me and to innumerable
students. For, when the study of perspective is given the right ap-
proach, it can be as fascinating as crossword puzzles or other games
that challenge the wit and stimulate the intellect.
Ernest W. Watson
January 1955
chapter i lr
MATERIALS AND PROCEDURES
Although we are dealing with freehand perspective in this book,
it will be necessary as explained in the introduction to use some of
the procedures of instrumental perspective in the development of our
experiments. Hence, the student should be supplied with the following
minimum items of equipment.
A drawing board about 16 by 24 inches is recommended. A piece of
illustration board the same size, tacked to one side, will give a pleas-
anter surface on which to work ; and when drawing on tracing paper,
the white illustration board underneath will be especially appreciated.
Drawing paper 16 by 12 inches or thereabouts is recommended for
many drawing exercises. Larger sheets will sometimes be necessary,
as smaller drawings-particularly when instrumental work is involved
will not be so accurate. The smaller the drawing, the greater the
probability of inaccuracy.
A T-square of good quality, and 45 and 30-60 degree triangles-all
of the transparent type-are essential. Two brass-edged rulers, one 24
inches long, a draftsman's compass and a pair of dividers will suffice
as a minimum instrumental outfit.
When making instrumental diagrams, pencils with leads of hard
degree are needed-H or 2H grades. These should be sharpened with a
knife to points much longer than are produced by mechanical sharpen-
ers. The leads should be kept well-pointed during all instrumental
work, in order to avoid inaccuracies that would invalidate the whole
procedure. For free sketching the softer leads will be preferred.
A large pad of tracing paper (about 19 by 24) is indispensable. Get
samples from your dealer and select the most transparent sheet. There
is a wide range of transparency in tracing papers. The student often
will want to lay the transparent sheets over photographs and repro-
ductions of artists' work, in order to analyze them by tracing the con-
verging lines and extending them until they find their vanishing points.
In this way much will be learned, not only of natural appearances as
recorded by the camera but of illustrators' strategy in changing the
rules to meet the needs of special situations. More about this later.
Many times, in making these analyses, it will be found necessary
to fasten several sheets of paper together with scotch tape in order to
secure a large enough area for the location of vanishing points which
may be some distance away from the picture on either side. In this
event, a yardstick may be substituted for the ruler in drawing the con-
verging lines. When the vanishing points are found to be even beyond
19
13
the edges of the drawing table, the drawing can be laid on the floor and
the lines projected by means of strings or threads extending from pins
stuck in the picture, as shown in fig. 7.
In such a case we might assume that the illustrator who made the
original drawing established his far-flung points by the same method.
However, the chances are that once he had established his vanishing
points with strings from two converging lines on each side, he resorted
to the following device to get directions of all other converging lines
without actually carrying them out to the far-flung points.
Extending a very thin wire string is unsuited because it stretches
from pins stuck in at the vanishing points (already located, as in fig. 7)
and attaching the other end to pencil points, arcs are inscribed on the
drawing board as shown in fig. 8. (Good wire, as fine as thread, comes
on spools.)
Templates are then cut with a sharp knife or razor blade, after
having traced the arcs made on the drawing board and transferred
them to thick cardboard. These templates are tacked firmly to the
drawing board so that the arcs of their curved sides coincide with
the arcs drawn by the wire compass demonstrated in fig. 8. Now the
blade of a T-square placed against the curved side of a template (fig.
9) will always radiate from the vanishing point as it is moved along
the arc ; that is, its center line will. All one needs to do is to remove the
bladeby removing the screws and reset it on the stock so that one
edge will be centered on the stock, as seen in fig. 10. Of course the
blade must be set at exact right angles to the stock. By moving the
T-square back and forth along the arcs, the direction of any line in
the perspective drawing can be quickly and accurately drawn.
When a vanishing point is on the drawing board, a pin stuck upright
at the vanishing point (as in fig. 11) will facilitate the drawing of
converging lines. The straightedge can be placed against the pin and
swung at any desired angle.
Fig. 12 demonstrates how strips of heavy cardboard, cut as shown,
can be attached by pins to the vanishing points and used in place of
the straightedge. Note that the pinhole in the strip must be in line with
its drawing edge.
In fig. 13 we see another device for finding correct line directions
when one or both of the vanishing points is beyond the edge of the
drawing board. The right VP (vanishing point) is within range; the
left VP is far out of bounds since the front lines of the cabinet are
nearly horizontal.
We extend the vertical line of the nearest corner (1-3) upward to
the eye-level (4). At any distance beyond the object at the left (the
further the better) we drop a vertical from the eye-level to converg-
ing line (A) whose direction has been determined freehand. This ver-
VP
REILLY
17
18
tical (1A-4A) is shorter than the nearer vertical 1-4, but if it is
divided proportionately into the same divisions as 1-4 we have points
through which converging lines would pass on their way to their
vanishing points far to the left. Thus the top of the cabinet (3) is
half the height of 1-4. On the 1A-4A line we mark off a point (3A)
halfway up that line. Point 2 on the cabinet is one-quarter the height;
on 1A-4A we give 2A its corresponding position. Any number of meas-
urements on 1-4 can be duplicated proportionately on 1A-4A.
A camera and a projection machine are indispensable tools in the
contemporary illustrator's equipment. Still more indispensable is such
an inventive faculty as Frank J. Reilly brings to the solution of many
of his illustration problems, of which the subject of this demonstra-
tion is an examplea picture of a marshalling yard, which Reilly
painted for a Pennsylvania Railroad advertisement.
The picture illustrated the catch line, "An aircraft carrier goes by
rail, before it goes to sea." It dramatized the part the railroads play
in transporting material for the building and outfitting of a "flattop."
It was specified that a certain number of freight cars should appear
in the picture not as simple a result to achieve as one would imagine,
says Reilly.
After futile experiments with pencil sketches in an effort to include
the required number of cars, Reilly went to the lumber yard and
brought back to his studio an armful of wood strips approximately
one inch square in section. Upon these he marked off car lengths, care-
fully proportioning the lengths to the widths in order that his models
would be in correct scale. Then he laid the strips on the floor in parallel
rows to represent freight trains in a marshalling yard (fig. 15).
Reilly mounted a stepladder with his camera, and counted the num-
ber of "cars" that appeared upon the ground glass within a vertical
mask that he had carefully cut to the proportion of the advertisement.
Experimenting with the distance of his camera from the models, he
soon discovered the position from which to take a photograph that
would include exactly the specified number of cars, and allow for a
few locomotives and some empty track.
He pasted the 3% x 4% -inch print that resulted from this process
upon a large sheet of paper, tacked to his drawing board, and-
projecting the converging lines of the print located the three vanish-
ing points. The photo print was so small that all three points fell
within the area of the drawing board (fig. 16).
From each vanishing point he then swung an arc on the paper, near
the edge of the photographic print, as illustrated (fig. 16) .
The next step was to enlarge the picture to the size of the intended
painting. He did this in the following way. He made a photograph
of the photo print also the paper with the arcs upon which the print
was mounted; and, from the film, projected all onto the surface of
16
14
.VP 1
20
Advertising painting
for the
Pennsylvania Railroad
by Frank J. Reilly.
19
his paper (fig. 17). He then traced the main lines of the car models
on the projected enlargement with his pencil, tracing the arcs as well.
On the enlarged drawing (thumbtacked to a large drawing table) ,
templates cut of thick cardboard were tacked, their curved edges
identical with the arcs of the projected enlargement (fig. 18). The
T-square, traveling along the curved arcs of the templates as shown,
served for all converging lines, many of which, in addition to those
of the photographic print, were needed for the detailed drawing.
Note, however, the necessity of resetting the blade of the T-square
so that one edge of it bisects the stock and becomes what otherwise
would be the center line of the blade.
The lower vanishing point (fig. 19) is located in a vertical that
passes through the vertical lines of the picture-quite near its left
edge. Study the chapter on three-point perspective in connection with
this, pages 114-127.
The advisability-indeed the necessity-of drawing from models
cannot be overemphasized. For flat models (21 to 28) use a heavy card-
board that will not warp. The heavy cardboard will not do for three-
dimensional models that have to be scored, folded and assembled. For
these, select a reasonably heavy bristol board that is rigid enough not
to buckle and warp, yet is easy to work. A little experimenting with
papers will reveal the most suitable one.
If the flat, geometric models are used constantly by the student the
correct drawing of these basic forms will soon become second nature.
Take the triangle, for example. This figure, as demonstrated on later
pages, can be drawn quite easily by semi-mechanical procedure ; but
mechanical means can often be dispensed with by the student who
with sufficient practice has acquired an authentic visual concept
through practice drawing from the model (fig. 24) . It is safe to say
that one who makes 50 careful drawings from this model, turned in
22
21
22
23
24
all possible angles and placed at different heights in relation to the
eye, will have acquired a knowledge of this figure's appearance that
will serve him well in years to come.
The same can be said for models 25, 26 and 27 ; especially fig. 26. The
reason for this will be apparent later on when it will be seen how
important it is to know how to relate correctly the right angle (ABC)
to the circle seen in perspective (an ellipse).
The illustrator often has the problem of drawing several circular
objects that are lying on the ground. A splendid exercise as training
for this kind of assignment is drawing from dinner plates or phono-
graph records arranged on the table or floor. For some drawings use
plates of the same size, for others select plates of different sizes.
If drawing these models seems to be tedious .exercisecomparable
perhaps to the pianist's five-finger exercises the student who really
wants to learn how to draw will attack them eagerly since they assure
greater facility and authority in all subsequent work for the rest of
his life.
A four-inch model of a cube is easily made from stiff paper (see
diagram on next page) . After the flat pattern has been cut out a razor
blade and brass-edged ruler will do this best the parts marked for
folding should be scored. Scoring can be done with a letter-opener or
similar instrument. Fold so that the scoring is on the outside of the
model. Transparent scotch tape is ideal for securing free edges. Before
folding, inscribe a circle on at least one side and blacken it with india
ink. It is not necessary to make a paper model of a cylinder though
that is relatively simplebecause cylindrical cans and boxes of all
shapes and sizes are available in the kitchen.
The cone can be easily constructed as indicated on the next page.
After the base has been trimmed level (at right angles to the altitude)
a circular piece of heavy cardboard can be fitted to it and secured with
scotch tape.
Fig. 31 illustrates a model that is very important; a rectangle
preferably a square attached to a cylinder. This is another model
that ought to be drawn many, many times, turning it in all positions.
The importance of practice with the model will be evident in numerous
problems encountered in this book.
Sometimes special models like that pictured in fig. 33 are of great
help. The aim of such models is a geometric analysis of the object
rather than its facsimile. An analytical model is one which represents
the simplest geometric forms from which the object can be developed.
Oftentimes the most successful model is one which least resembles the
object, thus model 33 gives no hint whatever of the object for which
it was made the wagon wheels (fig. 36).
Another word about tracing paper. Illustrators make extensive use
of it. They often correct a first drawing on a sheet of overlaid tracing
paper. A third or fourth correction is frequently made in this way.
The final drawing is then transferred to illustration board for ren-
dering in any required medium.
*4
34
30
Good transfers can be made by blackening the back of the tracing
paper with a 6B pencil and rubbing the tone smooth with the fingers
or a wad of tissue paper. Carbon paper is not practical because the
carbon line is hard to erase. A sharply pointed hard lead is used to go
over the lines of the drawing in making the transfer. If such a transfer
is carefully made, with sufficient pressure, transferred lines will be
so black and definite that it may not be necessary to go over them with
pencil or ink in order to strengthen them. Albert Dome paints colored
inks, which are transparent, right on top of such a tracing without
touching the transferred lines. In the reproduction they appear to
have been made with india ink. Another advantage of working on
tracing paper is the possibility of studying the drawing in reverse.
Errors are often detected and corrected in this way. Studying the
drawing in a mirror gives the same result, although without the same
ease of correction.
It goes without saying that those who draw a great deal from
objects, indoors and out, will make the most progress. A certain
amount of drawing from photographs is recommended too. These will
involve subjects presenting structural problems that otherwise may
not be brought to one's attention. But, it must be realized, photographs
are often distorted impressions, quite unlike the images the same
scenes would produce upon the retina of the human eye. Thus all pho-
tographs should be questioned in the light of what is demonstrated on
the following pages, as well as from one's own observation of things
seen and experienced. Comparisons of photographic effects with illus-
trators' drawings will prove interesting.
It is suggested that the student make a file of pictorial scrap illus-
trating the points covered in the various chapters. For example, when
working in the cylinder chapter, collect as many pictures of cylindrical
objects as possible. Analyze them on tracing paper overlays. This is
equivalent to enlarging the scope of the book and extending the oppor-
tunity it offers for study. Some may prefer to paste such scrap in a
loose-leaf notebook, along with analytical studies of the pictures.
The making of such picture collections will do more than anything
else to make one "perspective conscious," to cause one always to be
on the lookout for interesting applications of the principles being
studied, to observe and understand, not merely to see.
chapter ii
It will help the drawing student if he thinks of himself as a builder
or a structural engineer. While he does not handle wood, steel, or con-
crete, with his pencil he does construct on paper the forms created by
these materials. The more he can develop his engineering sense, the
surer and speedier will be the growth of his power as an illustrator.
Illustrative skill involves considerably more than the training of
the eye and hand to see and record the correct appearance of things
observed, essential as that is. There are those who can make reasonably
good drawings of things they are looking at, but who are lost when
they try to construct objects "out of their heads/' They have a photo-
graphic eye, but they lack imagination.
Imagination, as it relates to our problem, is the faculty of compre-
hending the structural basis of all objects. It is the ability to analyze
objects no matter how complicated or cluttered with detail in terms
of the simplest geometric forms to which they are related : the cube,
the sphere, the cylinder and the cone. It is the ability to see around and
through objects. The illustrator must possess an x-ray vision ; for him
there can be no invisible lines. Like the engineer he deals with plans
and elevations ; like the mechanical draftsman he develops the habit
of dealing with mechanical views top view, side view, front view,
and sectional view. These views give him information needed to clarify
his problem. This structural sense is his very first need ; without it,
knowledge of perspective principles will not amount to much.
I used to send my students out with their rulers and notebooks to
get structural facts of such objects as letter-boxes, furniture, the
concrete mixer at work on the street, a wheelbarrow, the newsdealer's
booth on the corner. They came back, not with perspective sketches of
these things but with top views, front views and side views, together
with their measurements. From this data they made perspective draw-
ings in the classroom.
Such exercises are a means of developing one's imagination and
an engineering sense. They constitute the structural approach. The
student will do well to follow this prescription for basic training. This
kind of study of simple objects such as those mentioned will provide
the right habit of approach to all problems, no matter how complicated
they might seem to be.
TO? VIEW
40
37
"Safety Poster."
39
Let us see how this structural approach applies to a few specific
problems. Take the elementary problem of a ladder leaning against
a building.
In the City Safety Council poster the painter is warned to set the
ladder at a safe angle. The artist, in drawing it, needs to "watch the
angle" in a different way. He has to visualize the ladder as one side
of a triangular prism pushed against the wall. Otherwise his drawing
is guesswork. There is no other way for him to test his drawing.
In fig. 38 we see the triangular prism correctly drawn, its base line
AB parallel with the sill line CD and converging with it to the right
vanishing point. (See Chaps. IV and VI for instruction on convergence
of parallel lines.) Hence we know that the foot of the ladder rests
where it should on the ground. In fig. 39 the error is obvious ; the ladder
rests in an impossible position, since AB is not parallel with CD as it
should be.
The engineering approach has to be applied to the drawing of as
simple an object as a mallet. The top and side views in fig. 40 tell us
that the handle is at right angles to the cylindrical head, and that we
find point B on a line extending from A into the cylinder's axis (D).
Getting the direction of the handle is the first step in the perspective
view. This is best done by drawing imaginary line AC, which is directly
under the handle on the ground. It is much easier to find point A by
this indirect approach. Line AC must, of course, be at right angles to
the cylinder's axis. There is no mechanical means of establishing this
46
47
A drawing by Thomas Rowlandson.
angle; it is a matter of freehand judgment. Whether the correct line
is the one shown in fig. 41 or whether one of the dotted lines is more
accurate is something that can be known only through the artist's
experience. It involves the ability to draw a right angle in any position
in relationship to the cylinder in certain positions. (See fig. 31, page
24.) The acquisition of this ability is of first importance to the student.
Once line AC has been established, the rest is mechanical procedure.
We have to cut a section, as it were, through the cylinder at its center
(fig. 42) in order to find point B.
The analysis and procedure in the hinged box cover (fig. 43) is one
that is applied to many situations, of which the open door (fig. 44) is
perhaps the most common.
The trained artist always looks for a simple geometric basis for
every object he draws. Thus the scotch-tape holder (fig. 45) obviously
is a combination of two cylinders with a cylindrical hole in the larger
one.
The proper way to draw the coach is shown in the analytical diagram
in fig. 46 ; a large cylinder for the rear wheels and a smaller one for
the front ones. It is natural and helpful to sketch an ellipse as a guide
for the drawing of the curved body line, although only an arc of the
ellipse is involved. Thomas Rowlandson, an 18th century English
artist, drew the accompanying coach. It is strange that an illustrator
who was such a perceptive observer and delineator of life and charac-
ter should have completely failed in the drawing of the wheels of his
coach.
ts
52
48
B 49
8 51
FRONT VIEW
56
More Than 8,900 Advertisers Use T. &
To "Stffaw Their Advertising Program"
SIDE VIEW
57
The drawing in this advertisement
for Thomas Register
was made by illustrator W. N. Hudson.
HUDSON
Many times the solution of a problem is facilitated by imagining
that the object is carved out of, or contained within, geometrical solids.
The lawn sweeper (fig. 48) might be analyzed in this manner. Study-
ing its side view (fig. 49) we discover that the handle, extended to
the ground (A) forms a triangle ABC. If, then, we draw in perspective
a triangular prism (50) of correct proportion, we have a basic geo-
metric form which, if accurately drawn, solves our problem.
In order to draw that triangle in correct proportion we have to have
some way of measuring it. In the next chapter it will be seen that we
measure things in perspective by means of the square. Now we see in
fig. 51 that the rectangle (ABCD), which encloses the triangular
form, is wider than it is high. Fig. 51 demonstrates that it is one square
(AEGD) and one quarter in width. If, then, we construct a square
(AEGD) in perspective (fig. 52) and add a quarter square to it we
shall have a rectangle of correct proportion within which our triangle
is inscribed. The important thing here is to estimate properly the
square, a simple matter for one who, through much practice in drawing
squares, has acquired this facility.
In fig. 53 we draw the wheels, noting, by referring to fig. 49, that
they are of such size and in such position on the handle AC, that they
just touch a vertical at A. The completion of the drawing from this
point on is merely a matter of detail.
Now consider illustrator W. N. Hudson's problem when he was
asked to make the drawing of scales for the Thomas Register adver-
tisement. For this subject he did not have a model from which to draw ;
probably all he had to go on was a rough layout made by the art direc-
tor to indicate what was wanted or perhaps just a verbal suggestion.
So he had to build the scales ; that is, build them with his pencil.
In the first place, he had to design the scales much as an industrial
designer would do. This necessarily involved thinking about the object
in terms of "views," in order to establish the facts of its construction
in top, front and side view sketches (see figs. 55-57) . Probably he made
several such trial sketches, varying the proportions of the box, and
varying the size, the height and the position of the pans in relation
to the box. Doubtless he tried out these various designs in perspective
sketches before finally deciding on the one to use.
so
60
59
61
From the first, he would have automatically analyzed the problem
as a box set down between two cylinders (fig. 58).
Next, he would sketch the plan of the object in perspective as in
fig. 59-two circles with a rectangle between. Working from plans in
this way is common perspective practice. This is an important step
and it involves expert knowledge of what these geometric figures would
actually look like in perspective. A beginner attempting this would
do well to test his drawing by reference to models. (Two cardboard
disks or dinner plates and a rectangle of cardboard will serve nicely. )
Next (fig. 60), the box is drawn in correct proportion to the design
decided upon, and a vertical plane ( ABCD) is passed through its center
to establish the height of the two cylinders whose top circular planes
will be drawn as ellipses on the diameters, XY. The arms connecting
the pans with the box will be drawn in this vertical plane.
All that remains now is to draw the top ellipses of the cylinders.
It is not to be supposed that any professional illustrator would care-
fully go through steps similar to those outlined in this chapter for
simple objects which he could draw almost automatically. But the
kind of thinking here demonstrated applied to more complicated situa-
tions is indeed common professional practice.
chapter iii
THE SQUARE AS A UNIT OF MEASURE
An object must be measured before it can be represented accurately
in a drawing. This is as true in freehand sketching as in instrumental
drawing-. In instrumental work the exact dimensions must be known,
the lengths of all lines in feet and inches being required before the
draftsman can make his drawing either full size or to scale.
The artist making a freehand drawing must measure the object just
as carefully, but in an entirely different manner. He does not ask to
know the height, in feet and inches, of the building he chooses to
sketch ; nor is its exact width important to him. But he must know
the relative lengths of these lines the proportion of one to the other.
Proportion is, therefore, his principal concern in the analysis of his
subject. He must have some infallible method of measuring proportion.
The study of proportion has not been included in books on per-
spective, but it is so inseparably related to perspective in practice that,
logically, it should be a part of any program of drawing instruction.
The student is frequently seen holding his pencil at arm's length
and squinting his eyes as he moves his thumb along it in an effort to
measure the lengths of lines. The amateur feels confident in the efficacy
of this device. If the proportion of his drawing is criticized he is likely
to say, "It must be right ; I measured it." This method of measurement
is dangerous because it convinces the beginner he is right when he
is probably quite wrong. Pencil measurements are unreliable. An inch,
measured off on the pencil, represents an eight-foot window sill across
the street. To measure exactly is almost impossible: the hand is
unsteady ; it unconsciously moves closer to the eye at times ; the body
moves forward or back-ward slightly ; the pencil may not be at right
angles to the direction of sight. Any one of these imperfect conditions
can account for serious errors when % inch on the pencil represents
a foot of the line measured. In my classes, pencil measurements have
always been taboo.
How then shall the object be measured? In the first place there must
be a unit of measure. All scientific measurements are based upon some
logical unit of measure. For the purposes of the artist in measuring
proportion, the obvious unit of measure is the square. We can say,
truthfully, that the square is the only possible unit of measure, whether
or not the object is foreshortened.
68
64
65
Draw in outline a 2-inch square in india ink on a small piece of
window glass or transparent plastic. Hold this measuring glass up
and, closing one eye, look through the square at the building across
the street.* By moving the glass nearer or farther away, the size of
the square will conveniently appear larger or smaller and so will serve
as a measure for large or small areas. Remember that we are measur-
ing areas, not lines.
If you were thus studying the proportion of the gate (fig. 62), you
would find your square exactly fitting the gateway. The square would
enclose the chest of drawers (fig. 63). The outlines of the mantel
(fig. 64) would not fit in your square, but you will note that the fire-
place itself is a square. In making your sketch of the mantel you would,
therefore, start your layout with the square opening, it being a simple
matter to relate the other dimensions to it when the square is indi-
cated on the paper. Similarly in fig. 65, you would find a square at
once, and readily observe that the balance of the ornamental iron
screen above takes up one-half of a square.
Imagine now that you are in the garden about to sketch the garden-
house (fig. 66). You find that the square exactly encloses the entire
structure, except for the chimney and steps. And you note that the
eaves' line falls halfway down the square. The rectangular portion of
the ell does not quite fill the square-the dotted line in fig. 68 indicates
the top of the square but its window opening just fills your square
measure, as do the ends of the entrance steps (fig. 69).
SQUARE
66
67
68
The drawings on page* $2 through 35 were
made by the author in a aerie* of advertising drawings
for Eldorado Pencils. Courtesy Joseph Dixon Crucible Co.
38
*I have in my possession a square reducing glass, across the face of which are
engraved lines that cross each other at right angles, forming a series of smaller
squares. When viewing objects through this glass they are automatically measured
in terms othe square. The glass is of French manufacture and so far as I know
is unobtainable in this country.
Now measure the ballroom window (fig. 70). The shade is con-
veniently pulled halfway, making the measurement a simple matter.
Next let us study the Italian subject (fig. 72) . As you move the glass
about, letting the square play over the structure, the only square you
discover is the entrance portico. This square is too small to help much
in finding the proportion of the building. But, if by now you have be-
come "square conscious," you will quickly discover that the right-hand
line of the tower projected down through the building makes a square
(A, fig. 73) which gives you the right start. Your measuring glass
will certainly pick up the partly enclosed space 8, which helps decided-
ly in sketching the tower. Play your square over the tower itself. Note
that the top of the central window conveniently cuts off a square (fig.
73A) . You readily estimate that the remainder is about one-third of a
square.
It is always desirable to make the first measurement include as
much of the area of the subject as possible. The garden-house (fig. 66)
was entirely enclosed within our first square. The Italian subject
(fig. 72) did not suggest an enclosing rectangle because of its broken
contour. The square A was deemed a more practical measure as a
basis for the sketch.
70
71
8 !
78
74
76
The first glance at Coutances Cathedral (fig. 75) reveals the large
square X. The upper portion of the building is not so readily meas-
ured, but, having the correct proportion of the lower part, it is easy
to measure the tower masses. You can hardly fail to pick up square A,
as your measuring glass moves over the facade. This is a very useful
measurement. The structural lines of the tower practically cut the
large square X into three equal vertical spaces, and B is close to being
a square.
The square measurement units that were used to make illustrations
78, 81, 83 and 85 are shown in the drawings accompanying them.
The employment of the square in determining proper proportions
will be found especially useful in memory drawing. If in memorizing
an object to be drawn later we carry in mind a geometric framework
based upon a reliable unit of measure, we can have greater assurance
that our drawing will be a faithful illustration.
81
S.MARIA
DELIA SALUTE
first 9 /art re
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desir&bte as a-
first'
77
WELLS CATHEDRAL
78
79
The student will find that after studying proportion for some time
with the measuring glass, he has acquired an accurate concept of the
square and, dispensing with it, will discover that he has become
''square conscious" and possessed with an infallible method of meas-
uring proportion.
We have used architectural subjects only in these demonstrations
but of course the procedure applies to all objects equally well, and
the student is advised to practice measurements on all the common
things that surround him in the home and on the street. Pictures in
magazines make excellent practice material. They can best be analyzed
by laying tracing paper over them.
Thus far we have used the square only to measure objects seen in
front view, or elevation, where no foreshortening is involved. Can this
unit of measure be applied to subjects seen in perspective, like the little
country church (fig. 86) ? It can.
83
86
87
This sketch shows the measuring glass being held at right angles to
the direction of sight, resisting the tendency to turn it in the direction
of the plane being measured. This of course is not a true measurement
of the front of the building which is considerably wider than its height
at the eaves : it merely tells us what the width of the f a$ade on our
sketch paper should be in relation to its height.
But fig. 87, where our square encloses nearly the entire structure
(by bringing the glass closer to the eye), gives us a measurement we
would do well to make at the beginning. Whenever we can enclose
the whole object within the square, we have a convenient means of
placing the drawing on the paper and blocking-out the main lines.
Figs. 88 and 89 indicate still other measurements that are quite
obvious.
Now as we have said, this procedure, although it is an aid in making
our sketch, tells us nothing about the actual measurements of the sub-
ject itself. For that reason its usefulness is limited.
Suppose, for example, our task were to draw the church not from
observation but from specific measurements : width 30 feet, depth 40
feet, height at the eaves 20 feet (fig. 90) .
The long side is a rectangle twice as long as its height, or two
squares. The width of the front is half as much again as its height, or
a square and one half. How are we to measure these dimensions in
perspective, on foreshortened surfaces?
The architectural renderer lays out his perspective drawing instru-
mentally and projects actual measurements ; the illustrator's measure-
ments have to be estimations, but if he knows what a foreshortened
square looks like he will come very close to exactness in his freehand
sketch.
The first step, then, in measuring the front of the church after the
directions of the converging lines has been indicated (fig. 91) is to
establish the estimated width (X) of a square (fig. 92) whose height
is fixed at the corner of the building. How accurate is this figure? Is it
a square?
90
91
88
89
Now it is easier, even for the practiced eye, to judge the foreshort-
ened square when it is visualized as the face of a cube. So let us indi-
cate the other visible face of the cube on the long side of the building
(fig. 93) . This face must be wider-in our sketch-than the other be-
cause, as the steeper convergence of the front lines indicate, the front
plane is turned away from us at a greater angle and all horizontal
measurements on it therefore are more foreshortened ; hence, on the
right side, less foreshortened and wider.
Even the beginner, who, before, might have been undecided about
the X rectangle (supposed to represent a square) now sees at once
that fig. 93 is far too wide to represent a cube and that X, consequently,
cannot be a square. Fig. 94 certainly looks more like it and this cube
will serve in establishing the widths of both front and side walls of
the church. The church's dimensions can now be determined geomet-
rically as shown at fig. 94.
Two distinct methods of measuring with the square have been dem-
onstrated. One employs the square on an imaginary transparent plane
(an actual piece of glass for the beginner) at right angles to the
direction of sight; the other dispenses with the glass and uses the
square in perspective. Which is better?
Each method has its value, but since the experienced illustrator
always thinks of what he is drawing as three-dimensional, he usually
makes his measurements in perspective. He never thinks of the flat
surface of the paper upon which he is working ; he is always project-
ing his image through the paper, as it were. To rely to any extent upon
the methods demonstrated in figs. 86, 87, 88 and 89 is, for him, a rather
artificial method ; it contradicts his whole attitude of three-dimensional
thinking. That is not to say that he never resorts to it by way of check-
ing against his perspective measurements. Chances are that most illus-
trators do just that.
The student is advised to use both methods simultaneously. Until
he has had much practice in drawing cubes and has learned unmistaka-
bly what a cube looks like under all conditions, he will experience much
difficulty in perspective measurements.
chapter iv
THE PICTURE PLANE
Almost everyone, as a child, has demonstrated the function of the
picture plane by tracing upon the windowpane, with wax crayons, the
outlines of the house across the street. In his tracing, the child thus
achieved a reasonably correct, if crude, perspective representation of
the structure, provided the position of the eye was not changed during
the drawing.
And so the picture plane can best be conceived as a sheet of glass
through which the artist observes his subject and, in imagination,
traces its outlines ; the lines actually being drawn on a sheet of paper
which thus takes the place of the transparent glass.
It should be said at the outset that for anyone who has much apti-
tude for drawing, the concept of the picture plane is wholly unneces-
sary in practice. It would not have been introduced into this book were
it not useful now and then in demonstrating certain phenomena and
various procedures otherwise difficult to explain. The person who
draws naturally does not even think of a flat plane. To him the paper
upon which he draws is not a flat surface : it is space. When he sets
down lines to represent distance, his pencil pushes those lines right
through the paper-twenty feet or half a mile. The retreating line
reaching toward the horizon may be only three inches long on the
paper, but to the artist it feels just as long as the street or the railroad
track or whatever he may be drawing.
Hosts of artists have never given the picture plane a thought, and
even children in their first drawings are able to think of the drawing
paper as space rather than a flat surface.
So it seems very unwise to put too much stress upon the concept
of the picture plane in teaching freehand perspective, although it is
absolutely essential in instrumental perspective. An illustrator called
upon to make drawings of buildings or other structures that demand
accuracy of measurement must resort to the same kind of instrumen-
tal procedure that is employed by the architectural and engineering
Tenderer. The student of freehand perspective who intends to become
a professional artist will do well to consult a good text on instrumental
perspective. Here, we can only indicate in the simplest diagrams the
basic principles in instrumental procedure.
When we do think of the picture plane it is important to remember
that it should be imagined at right angles to the central direction of
sight, and that its position should not change in any given picture.
9 6 That is the basic rule but there are exceptions to it, as we shall see.
97 The whole theory of scientific perspective is predicated upon the
assumption that the direction of sight, hence the position of the picture j
plane, remains constant in the picture. The theory is consistent with
photography, which records a wide-angle scene upon an immovable
picture plane-the camera's plate or film.
But the human eye sees things quite differently. Its direction of
sight is constantly shifting; it has to, because our eyes can focus only
upon a single point at one time. As I write, I look down from my
studio at the florist's window on the street corner. I am very conscious
of shifting my gaze in trying to distinguish the various items in the
window within the space of seven or eight feet. Automobiles not thirty
feet from the store window, just around the corner on each intersect-
ing street, are mere blurs. All that I can tell about them without per-
ceptibly changing my direction of sight is their color and their general
type truck or passenger car.
Thus we see that an immovable picture plane violates the whole
process of seeing. Yet, considering the inconsistency, it serves remark-
ably well provided the artist understands its inconsistency under
certain conditions and knows how to compensate. The skillful artist
is always taking liberties with scientific perspective, violating its rules
for reasons of design or for a more truthful impression.
The diagrams in this chapter demonstrate the basic procedure of
the instrumental method. In fig. 97 we look down upon the picture
plane. Think of it as a large sheet of glass standing vertically on the
ground. Seen from above its top edge would appear as a thin line*
The gray rectangular form represents the plan or foundation of a
building. It touches the picture plane at B. This is not necessary ; it
might be placed at a considerable distance behind the picture plane,
but it is given this position here for a special reason that will appear
later.
The "station point" represents the eye of the observer. It may be
any distance from the picture plane according to the effect desired in
98 the perspective rendering.
From the station point, lines are drawn to the picture plane parallel
with the sides of the building, lines AB and BC. This means, of course,
that the angle at the station point (shaded) is a right angle. These
lines from station point to picture plane locate the two vanishing
points and, as seen in our diagram, they are projected down for the
perspective drawing in figs. 98 and 99.
It will be evident that the placing of the station point controls the
perspective effect. The nearer it is, the more "violent" the perspective.
To avoid this and to get a more normal effect, the distance of the
station point from picture plane can be increased. This automatically
extends the vanishing points further to right and left because the
99 station point angle (shaded) is always a right angle.
Jf **** / Mod*m Art, Atao York.
101
The station point also can be located laterally wherever desired. Its
position taken here is purely arbitrary ; it might have been any dis-
tance to right or left. Try moving the station point both laterally and
more distant from the picture plane and see what happens. What does
happen when the station point is close to the picture plane is seen in
fig. 102, and in fig. 100 where we get violent and distorted images. The
near corner of the rectangle in perspective (fig. 102) is a very acute
angle, an effect never seen in normal vision. Experiment with a rec-
tangle on the floor. It will be found that the near corner is always an
obtuse angle ; it can never be seen as an acute angle as in fig. 102.
Therefore it is usually advisable to locate the station point far
enough away from the picture plane to avoid such distortion. That, as
we have stated, will throw the vanishing points further to the right
and the left, widen angle X (fig. 102) and give a normal appearance.
There are times, to be sure, when the artiat deliberately employs dis-
tortion for a good purpose, as in the Curare drawing on page 122.
Indeed this is very commonly done.
Everyone who has used a camera is aware of what happens when
the picture in taken close to the object, as was the case in photograph-
ing the Museum of Modern Art (fig. 101) . The result of a close camera
range like this is the same as that achieved in drawing when the
station point is near the picture plane. Although it is an "unnatural"
effect, we have become so accustomed to such photographic exaggera-
tions that they are more readily accepted than formerly. If the camera
had been at a great enough distance to give a more "normal" perspec-
tive to the museum building, the picture would have failed to show
sufficient detail. The fact that but a little of the right side shows in
the photograph is a compensating factor. Had it been standing alone,
as in fig. 100, the distortion would have been more noticeable.
Having established our station point and vanishing points (in fig.
97), lines are drawn from the station point to the several corners of
the plan (A, B, C, D, E, G and H in fig. 97). Think of these lines as
beams of light that connect the eye with the object. Where the beams
cut through the picture plane we have points a, &, c, d, e, g and h that,
projected down to the perspective drawing in fig. 98, establish the
correct relative dimensions of the plan in perspective. To fix our van-
ishing points in fig. 98, we have dropped verticals from the vanishing
points already established in plan (fig. 97) until they meet the eye-
level. The eye-level can be placed higher or lower than shown in fig. 98,
according to the vantage point from which we wish to view the subject.
102
Now in practice one would erect the building directly upon the per-
spective plan (blacked-in) in fig. 98, and develop the entire drawing
there. To simplify the procedure and avoid the confusion of a compli-
cated drawing we make a separate diagram (fig. 99). The a, 6, c, d, e,
g, h points have been projected down to this diagram from fig. 97.
The height of the building and its smaller element (C, G, E, H in
the plan) are indicated in the side elevation. Projecting horizontals
from it to the perspective drawing we have points X and Y on the
nearest vertical XB. These are the only measurements needed. When
point Y is projected back to VP 2 on the horizon, it indicates the height
of the small element.
As previously stated, the building touches the picture plane (point B)
for a special reason. Had it been set back from the picture plane we
could not have projected the vertical heights from the elevation (fig.
99) -which is drawn on the picture plane-to the building's near cor-
ner. In that case it would have been necessary to project either line AB
or line CB in fig. 97 forward until it touched the picture plane, giving
us a vertical line on the picture plane upon which we could measure
heights. We could then project our measurements from the side eleva-
tion to that vertical line and project them back toward vanishing
points, as we have done at Y (in fig. 99), to find the height of the
small element. All vertical measurements have to be taken on the pic-
ture plane and projected back into the distance on the foreshortened
planes.
Until relatively recent times the picture plane was invariably con-
sidered a vertical plane ; no one thought of tilting it to look up or down
at objects. But, of course, we do that constantly in viewing things that
surround us. And, when we do, we see objects in 3-point perspective.
There is convergence not only in their horizontal lines; the vertical
lines converge as well-upward or downward as the case may be. A
photograph taken with a tilted camera produces effects of 3-point
perspective with which we are all familiar. This aspect is demon-
strated in a later chapter, therefore we shall not discuss it at this point.
Now let us come back to the reference of a child making a perspec-
tive drawing on the windowpane of a house across the street. He
would have learned, had it been pointed out, that any set of the build-
ing's lines which recede into the distance would, if continued, meet
at a point. That point would be found to be on the exact level of the
observer's eye on the window glass.
Hence the perspective fact, all horizontal, parallel receding lines
converge and meet at a point on the eye-level, or at the horizon-which
is the same thing.
FAWCETT This is demonstrated in illustrator Robert Fawcett's drawing of
the housewife standing at the old kitchen range (105). In that draw-
ing there are four sets of parallel lines, hence there are four different
vanishing points (VP 4 lies outside the ptoge). The long lines of the
stove, the lines of the wall against which the stove is placed and the
short edges of the table (against the back wall) are all parallel to
each other ; therefore they converge to the same vanishing point ( VP 1 )
on the eye-level at the right. The short lines of the stove, the other
wall and the long lines of the table constitute another set of parallel
lines ; they converge to VP 2 , on the eye-level at the left.
The serving table, just behind the figure, is turned at an angle to
the lines just mentioned. As demonstrated, its long parallel lines con-
verge to VP 8 and its short ones to VP 4 . If this table were moved to
the position indicated by the dotted rectangle, its vanishing points
would have still different locations on the eye-level.
In this drawing the eye-level happens to pass through the eye of
the cook. That is merely because the illustrator assumed that he was
standing in the room as he drew and that his height was the same as
that of the woman. Had he assumed a sitting position the drawing
would have been as shown below. The horizon line would have dropped
to his lower eye-level.
104
Tki drawing for an advertitement for Child*
wan wade by illuttrator Robert Fawceti.
4S
106
chapter v
THE CUBE
It will be increasingly evident to the student that familiarity with
the cube is extremely important in both simple and complicated struc-
tural developments. In later chapters we shall find ourselves needing
great facility in drawing cubes when confronted by a variety of forms
that can best be rendered by relating them to this basic geometric
solid. In the chapter on the circle, for example, the cube helps us to
determine the proportion of ellipses that represent circles in various
positions.
So the student should be continually drawing cubes with the model
before him, of course-until he can almost draw them with his eyes
shut.
On pages 38 and 46 there are suggestions for cube practice. Consider
first page 46. Here we work with a cube that, when subdivided as
shown, is made up of 64 smaller cubes. Before proceeding with the
various arrangements-and others that will suggest themselves-be
sure that your cube is absolutely correct to begin with. Drawings should
be made at least one-and-one-half the size of those on the printed page.
First sketch the cubes freehand, drawing directly from a model of
the cube. When the drawing looks right test it by extending the con-
verging lines till they meet on the eye-level. Use T-square and triangles
for these tests. It may be necessary to lay the drawing on another
very large sheet in order to find the vanishing points at considerable
distance from the cube. The lines extending at the right should, of
course, meet at the same point ; those at the left at another point on
the same horizontal eye-level. When the converging lines have been
corrected the question still remains: "Is it a cube?" It might be too
narrow or too wide.
One way to check on proportion is to lay a windowpane over the
drawing and, with an architect's ruling pen and india ink, trace the
cube lines carefully. The glass surface is not easy to draw upon but
it will actually take the ink. (You will need a brass-edged ruler.)
Now hold the glass at the side edges near the top so that it will hang
vertically and at right angles to your direction of sight as you view
the cube through it. You are really looking through the picture plane,
and if your drawing is correct its lines will cover those of the model.
If they do not, correct the drawing and test it again.
This may be a tedious business, for you may have to make several
tests before you get a perfect drawing. But it is time and effort well
spent. Many artists go through life making cubes too wide or too
narrow because they never really learned what a square hence a
cube-looks like in perspective.
The student with a camera with a lens that will take close-ups will
find it profitable to take many pictures of the cube in different posi-
tions. These photographs can then be used as a means for checking
108 his drawings.
110
49
Now try doing a page of cubes like those on page 38. Of course it is
not necessary to render the cubes in wash as shown but it is excellent
practice and is more fun. Lamp black is diluted with water and applied
with a No. 5 sable brush. If the cubes are first drawn in line on tracing
paper, then transferred to a good sheet for the shaded drawings, the
result will be better.
The cubes on the black background will give an even greater test
of cube skill. The student may want to compose his own arrangement
instead of copying the plate ; but that is unimportant. It will not be
practical to carry out these drawings instrumentally. This test throws
one entirely upon his freehand judgment.
A day or so after completing them, look at your cubes critically
with a "fresh eye." You will be certain to make some corrections. Do
this for several days until you can no longer find fault with them.
When the cube is seen in direct front view, so only its front face and
top are visible, the beginner finds it difficult to realize how greatly the
top face is foreshortened ; usually he makes it too wide from front to
back, as at A, fig. 109. To appreciate the extent of the error in this
figure we have only to project lines down from cube A to show how this
figure would look (B) when seen at a lower level, where its proportion
can be more accurately judged. Instead of a cube, we now see that we
have drawn a rectangular solid more than five times as long as its
square end (E).
The cubes C and D were drawn by the author from actual measure-
ments taken in the manner shown in fig. 110. The cube D rested on a
table just twenty inches below the author's eye-level and three feet
away. Squinting along the edge of a ruler, the front to back width of
its top face appeared to be slightly over one quarter the cube's height.
The cube C rested on a shelf only eight inches below eye-level, hence
its top face appeared much narrower.
If the cube had been nearer, the top face would have shown greater
depth because the nearer to the eye, the more nearly one looks down
upon it. This kind of meticulous measurement is occasionally advis-
able ; it helps in educating the eye to such an accurate judgment that
109 the use of the model can soon be dispensed with.
A number of elementary perspective facts are demonstrated in fig.
111. Cube No. 1, placed midway between its vanishing points 1 and 2
presents two equal vertical faces. That means that the diagonals AB
and CD (dotted lines) are horizontal and the diagonals EF and GH
are vertical.
No. 2 cube has been set off to the right so that its right vertical face
is turned considerably more toward us ; so much so that its long con-
verging lines vanish at a point far off the page at the right, while
those of the left face turned sharply away-find a vanishing point not
far to the left of the cube. Its AB, CD diagonals now are not horizontal ;
if carried out to the left, being parallel they would meet at a vanishing
point on the eye-level far off the page.
No. 3 cube is one-quarter the size of No. 1, whose left face has been
divided into quarters by the intersection of the diagonal line ( AG) with
a horizontal bisecting line from K. Note that although the small cube
has not been turned-having merely been pushed forward from cube
1, as it were its right face is wider than its left.
Note also the directions of the EF and GH diagonals of cube 3;
they converge with the EF diagonal of the parent cube because those
diagonals are actually parallel. That geometric relationship is often
useful, as it was here in determining the location of the small cube's
point F. Points E and G were found by projecting forward from and
P of cube 1. Next SO was projected forward, giving the correct width
of the narrow face.
It will be seen that the further the cubes are placed to the left, the
wider their right faces and the narrower their left. The opposite
applies to cubes at the right of the center.
Incidentally, the drawing of cubes placed like 4, 5 and 6 offers a
means of testing the accuracy of cube 1. If through error of judgment
cube 1 had been made too wide, a cube in the position of 4, 7 or 8 might
present a wide face actually wider than its height.
EYE i r v r i
ill
cm H o R i s o N
chapter vi
112
FORESHORTENING AND CONVERGENCE
I suppose it would be an unpardonable break with tradition not to
use the railroad track to demonstrate the simplest of all perspective
facts : the fact that objects appear progressively smaller as their dis-
tance from the eye increases-the railroad ties and the telegraph poles
and the fact that, therefore, the rails and the wires converge and
(in a picture) come together at a vanishing point on the eye-level. The
space between the ties and between the poles decreases progressively
with the increase of distance.
The position of the observer in fig. 112 is in the center of the road-
bed, between the tracks ; and as he looks straight ahead toward the
horizon (the level of his eye) all the railroad ties are at right angles
to his direction of sight. That is the way they would look in a photo-
graph. In one-point perspective all such parallel, horizontal lines in
the subject (according to the rule) are represented by horizontal lines
in the picture. There are exceptions, as we shall see.
When the observer steps off the tracks to the left of the roadbed and
views the tracks from that position, what he sees is illustrated in fig.
113. The rails converge to a point at the left; and the ties, instead of
appearing as horizontals, take a slanting direction and converge to a
point on the eye-level outside the picture at the right. This is known
as two-point perspective.
In fig. 114, which represents the observer's relation to the scene as
pictured in fig. 112, the direction of sight is at right angles to the ties
which are parallel with the picture plane. In fig. 115, which represents
the observer's relation to the scene in fig. 113, the ties are not parallel
with the picture plane ; their left ends are nearer the picture plane and
the eye than are their right ends. Hence they converge to the right.
In fig. 112 (and in fig. 114) the observer is exactly in the center of
the picture. What happens when, as in fig. 116, he moves over to one
side, but not beyond the tracks as in figs. 113 and 115?
In theory his direction of sight remains parallel with the rails and
at right angles to the picture plane and to the ties. Now the left ends
of the ties actually are further from the eye than are the right ends ;
but both ends are equidistant from the picture plane which, in theory,
is the determining condition. Therefore, in the drawing, the ties,
according to the rules, should be drawn as horizontal lines. Hence
there would be but one vanishing point, as in fig. 112.
CHANCE But a drawing made that way would not look as satisfying as it does
in the drawing (fig. 117) by Fred Chance, where the observer stands
on the track in about the position indicated in fig. 116. From that posi-
tion it certainly is natural to turn the eye to the left of the vanishing
point, particularly since the picture's interest the horn and whistle-
lie in that direction. The camera would practically reproduce what Mr.
Chance has done if it were held in the same position taken by the artist
as his point of observation. If, however, a third track were to be added
(in Mr. Chance's picture) at the right side, the situation would be the
same as in fig. 112; then the ties would have to be made horizontal.
Prove this for yourself by tracing Mr. Chance's picture; sketch the
third track at the right and give the ties the same direction as those
of the other two. Note the unnatural effect.
113
Drawing by Aldren A. Watton.
114
115
116
PICTURE
PLANE
Drawing by Fred Chance.
Courtesy American Locomotive Company.
117
118
119
Just to demonstrate further how Fred Chance's drawing violates
the strict rules of scientific perspective, we have laid a rectangle say
a panel of wallboard-upon the track (traced from his picture), see
fig. 118. Now place a rectangle of paper on the table before you so
that you view it as the tracks are viewed in fig. 116. Can you turn it
in such a way that it resembles the rectangle in fig. 118? No, as soon
as line A is slanted up from the horizontal (as in fig. 118) line B takes
a direction indicated by the dotted line in fig. 118 and by the drawing
in fig. 119. Yet if you experiment further by laying a piece of white
paper (cut like the rectangle in fig. 118) on the track in Mr. Chance's
drawing, it probably will look natural enough.
It would be interesting for the student to experiment further with
this subject by making a drawing similar to Mr. Chance's but drawing
the ties horizontal. The advantage of the Chance procedure will be
quite evident in the comparison of the two effects.
If Mr. Chance had established his vanishing point but slightly to
the right, just outside the picture (as in fig. 119) he would have con-
formed strictly to the "law" of two-point perspective. Then, you see,
the rectangle laid on the track would have met the test. But it is obvious
that by keeping his vanishing point within the picture he concentrated
interest upon the horn and whistle as he could not have done so suc-
cessfully by following the plan in fig. 119.
The old rule stated, in effect, that we cannot have two-point per-
spective with one of the vanishing points within the picture's limits.
As we shall see, it is a rule that is constantly and effectively violated.
Interestingly enough we have another Fred Chance railroad draw-
ingthe Fortune cover (fig. 120) in which the vanishing point of
the track is in almost the identical position as in fig. 117. In this design
he has followed the rule which says that when a vanishing point falls
within the picture, other horizontal lines at right angles to the retreat-
ing lines must be horizontal in the drawing. Thus we see that the illus-
trator uses his judgment in these matters; he is much less governed
by perspective rules than by what suits a particular situation.
Cover design by Fred Chance.
Reprinted by special permission of the editors of Fortune.
120
FAWCETT
In the painting for an advertisement for the Association of Ameri-
can Railroads (fig. 121) we see a violation of the rule laid down at
the beginning of the chapter : the rule that in one-point perspective all
horizontal lines should be parallel. We note in this picture that the
ties on the tracks at the sides are not parallel ; those on the right con-
verge to a point on the eye-level at the right ; those at the left seek a
vanishing point on the left. In this "one-point" perspective we have
three vanishing points, an effect contrary not only to scientific perspec-
tive but to what the camera would give us.
Here we should remind ourselves again of the difference between
the camera eye and the human eye. The camera, with its lens pointed
straight ahead will focus upon every detail within the frame of that
picture; it will see each detail clearly. The eye to take in the same
scene must change its direction, looking to the left to take in the left
part, and to the right to see that clearly. One would even have to turn
the head to do it. When we look at the picture of this scene we do the
same thing. When we look toward the right it is natural for us to expect
the convergence of the ties we see there. Focusing upon them we are
but vaguely conscious of the left tracks, even of the center track. It
would be interesting for the student to make a drawing of this situa-
tion, "correcting" the picture by making all the railroad ties horizon-
tal, then judge for himself which effect looks better. That, after all,
should be the determining factor.
Another very interesting handling of the railroad problem will be
found in the drawing by George Giusti and design by Bradbury Thomp-
son on page 63. We encounter this modification of one-point perspec-
tive in many situations, notably in the rendering of interiors as demon-
strated on pages 56 and 57, where we have experimented with differ-
ent methods of drawing a kitchen in perspective, borrowing Robert
Fawcett's illustration of the woman and stove as our motive.
121
Courtesy Association of
American Railroads.
frOO*
122
123
124
125 A
125 B
126
Courtesy Abbott Laboratories,
North Chicago, Illinois.
127
Visitor* Information Center,
Portland, Oregon*
In the interior (fig. 122), we adhere strictly to the rule for one-
point perspective, sometimes called parallel perspective because the
planes at right angles to the eye (the facing wall and the end of the
stove and the front of the cabinet in the drawing) are parallel with
the picture plane. In this drawing the eye-level is the same as that of
the wonjan, and the vanishing point is in the center of the room. This
is the effect that would be produced by photography when the lens of
the camera is viewing the room from the same vantage point.
Now if we move over to the right of the room, rather close to the
wall, and direct our camera somewhat toward the door, we get an
effect like that in fig. 123. The facing wall is no longer a rectangle;
its floor and ceiling lines converge to a point on the horizon far to the
left, as do all other lines parallel to them. This is a much more agree-
able effect for the simple reason that an arrangement of lines and
shapes, as in fig. 125B, is more interesting, less static, than that in
fig. 125A. Abbott Laboratories' Brief Summaries (fig. 126) is a good
illustration of the superiority of a design layout based upon the per-
spective procedure of fig. 125B. This is a violation of the old per-
spective law as is the photograph of the Visitors' Information Center
in Portland, Oregon (fig. 127) .
There is no reason why, if the effect in fig. 123 is agreeable, we
should not keep the observer's position in the center of the room and
converge the facing wall lines to a left vanishing point as we have
done there. But we have to be careful not to bring the left vanishing
point too close to the picture, as has been done in fig. 124, where the
drawings of the cabinet and the chair become very distorted. In this
kind of problem, as in all others, the illustrator's judgment will rule.
We have to find a way of measuring every piece of furniture in the
room ; the heights of the stove, the chair, and the cabinet in relation
to the figure (see fig. 122). We are assuming here that the housewife
is a little over five feet, her eye exactly five feet above the floor. Since
the height of the range is the same, we have a five-foot measurement
on the wall. Any vertical on that wall between the floor and the eye-
level likewise is five feet long AB for example. Dividing AB into five
one-foot parts we can measure on it the height of the chair (18 inches
--one and one-half feet) . A line on the wall from this point to the VP
cuts the corner of the room at X. A horizontal on the facing wall,
through X, dictates the height of the chair seat. The cabinet dimen-
sions are 30 inches high to the top of the drawer section ; almost six
feet from floor to top of cabinet. We carry these measurements around
the walls in the same way. We make the door seven feet high.
59
128
An advertisement for
Hanes Hosiery, Inc., by Bobri.
BOBRI Bobri, the creator of the interesting advertising illustration (ftg.
128) , is one of our most skillful draftsmen, as well as a highly original
designer. In this picture he has taken liberties with perspective which
enhance his design without appearing to violate natural effect.
Let us look first at the buildings and the checkered pavement. We
might naturally assume that all converging lines of these objects are
parallel and therefore seek a common vanishing point at the eye-level ;
as, indeed, they appear to do at casual glance. But, laying our tracing
paper over the drawing and testing these lines, we discover that instead
of one vanishing point there are two, as shown in fig. 129. They are
not very far apart, to be sure, but from the standpoint of design the
variation is important. Fig. 130 shows how awkwardly violent the
light side of the structure on the right would be if its lines converged
to VP 1 . The design is better as Bobri has arranged it.
What he has really done is to give that building (fig. 128) the shape
of a parallelogram. Side Y in fig. 132 is parallel to the horizontal lines
of the pavement, but side X cuts diagonally across them.
Another interesting violation of scientific procedure is seen in the
direction of the lines of the battlements of the building on the left
(indicated by heavy lines) in fig. 129. These, being parallel to the
picture plane, might be expected to be horizontal in the drawing;
instead they slant down to the left and all of them are parallel. This
might seem to be an accidental minor detail, but to a meticulous
designer like Bobri nothing in the picture is accidental.
Now we come to something that is indeed surprising. That is the
relation, in size, of the figures. We are at once aware, of course, that
the girl's figure is out of scale with other elements in the picture and
for an obvious reason ; but we are not so conscious-if at all-of the '
gigantic size of the guard with the halberd in relation to the distant
figures and the height of the building itself.
But fig. 131 demonstrates that this personage is about three times
the height of the distant figures. Projecting lines forward from VP 1
through the feet and head of one of the distant figures until they reach
the plane in which the guard standsthe tinted plane-reveals the
proper height for the guard, if Bobri had wished to be photographi-
cally correct instead of a designer.
When we see such things done by an expert they seem so simple,
as do most things that are right, and it is hard to realize how subtle
these adjustments between design and perspective are. It is only when
the beginner makes his own attempts that the skill of the experienced
designer-draftsman in these matters is appreciated.
GIUSTI George Giusti's drawing (fig. 133) shows the solution of an interest-
ing problem. As shown in Westvaco Inspirations, this advertisement
spread across two 12 by 9-inch pages. That factor in itself will explain
certain "irregularities" in perspective procedure.
First, let us look at the tonal section in the upper-right corner. That
rectangle isolates what might be called a normal view : it covers about
as much terrain as might comfortably be included in a picture of this
kind. As a matter of fact it tells the whole story. It is extended beyond
its borders only to create an unusual layout and thus further dramatize
the idea.
129
Pi ^
ll 't
"N
eye
180
182
Thit it a plan of tk* building and pavement
09 Bobri ha* drawn them.
131
Now if a student presented that drawing (the tonal section) in a
perspective class, his instructor might point to his error in the render-
ing of the railroad ties. These, he might say, should be horizontal lines,
since the subject is drawn in parallel perspective with the vanishing
point nearly in the picture's center. And he could demonstrate the
logic of that rule by drawing two diagrams (figs. 134 A and B) in which
converging lines to the right of the track are made into additional
tracks. He could point out that if the direction of the ties of track X
(fig. 134A) is correct, those of tracks Y and Z, being parallel with
them, must be drawn as shown. But the absurdity of that effect is evi-
dent. The device of a third vanishing point for the right track (fig. C)
seems equally so. (However, please refer to the painting of locomotives
on page 55 where this device has been employed successfully. But in
that picture the slant of the ties of the side tracks is so slight that the
divergence is scarcely noticeable.) The logical rendering of the two
tracks is that seen in 134B. The fact that actually these other tracks do
not exist in Giusti's drawing does not justify him theoretically for
what he has done. But in breaking the rules he has done the most
effective thing.
When the converging lines of the ties (within the tonal area) are
extended, it will be seen that they meet at a vanishing point far to
the left. But, it will be noted, there is no convergence at all of the tie
lines outside the tonal area ; they are mostly parallel. Indeed some in
the foreground diverge slightly. Furthermore, it is the work of two
persons. The tonal picture is a drawing by Giusti for a Gruen Watch
Company advertisement; the extended tracks and the figures below
the picture were added by designer Bradbury Thompson in creating
a two-page spread for Westvaco Inspirations, for which he is art direc-
tor and designer. Therefore, what we have here is really not a picture
but a design, a design which involves two distinct views, one toward
the right-hand page of the spread, the other toward the left page.
While the attention focuses upon one page the other is out of focus,
hence not really a part of a unified picture, although it is part of a uni-
fied design. Although one would expect the perspective inconsistency to
be disturbing, it is not because the reader, turning from the train
which is the focal point of the spread to follow the rails as they come
forward on the opposite page, turns the head as he would if he actually
were on the spot staring at the rails themselves. Thus there are two
separate focal points in a single picture, a feat that demands arbitrary
handling of perspective devices.
Another interesting point in this design is the treatment of the
figures. Note that while the figures diminish in size perspectively, those
in the distance are much larger than they would be if treated realisti-
cally in perspective. Converging lines drawn through all the extended
hands find a vanishing point considerably above the horizon line. Who
cares? The effect is much stronger than otherwise. In this connection,
refer again to Bobri's figure treatment in the Hanes advertisement,
page 58.
134 A
134 B
134C
Two-page spread in Westvaco Inspirations
designed by Bradbury Thompson
around a Gruen Watch Company advertisement
by George Giusti.
94
FAWCETT This dramatic picture by one of America's top illustrators reveals
interesting perspective tactics involving four vanishing points. The
horizontal lines of the room in which the action takes place converge
toVPl.
Now the casual observer senses that the wall of the further room
(gray in our diagram) is parallel with the corresponding left wall of
the near room. But when we carry out the converging lines we discover
that they seek a vanishing point considerably to the right ( VP 2) . This
means that the further wall is not parallel with the near one; the wall
is turned more toward us.
Why should this have been done? The answer is obvious. The effect
is more pleasing than if the wall were in more violent perspective,
in that case affording less opportunity for the display of its fine panel-
ing, a most interesting background feature. Oddly enough, however,
the floor line of that room converges to VP 1, thus strengthening the
impression that the far wall is actually parallel with the near one
a very subtle treatment !
The table, we note, is not parallel with the wall of the room as we
would expect it to be and as the casual observer suspects ; its long sides
converge to VP 3. This is a matter of design ; imagine how awkward
it would be, had that long line converged to VP 1 !
We have still another vanishing point; that of the opened door
VP4.
Until one has analyzed this picture as carefully as the author has
done, tracing some of its details, he cannot appreciate the perfection
of the drawing of every incidental object. Study the lamp, for example,
and the still life objects on the table. Nothing is slighted ; each prop
is authentic and convincing. And to demonstrate how this illustrator
makes even inanimate objects respond to the action that is taking
place, note the tilt of the liquor in the near bottle a minor bit of strat-
egy to be sure, but a master does not overlook the importance of "bit
parts."
136
136
Illustration for Collier's by Robert Fawcttt.
ATHERTON
137
An advertising illustration
for Coty, 7nc.>
by John Atherton.
In fig. 138, which is shown above, the chaise longue is drawn as it
actually would appear when viewed from the angle which the artist
assumed when he established the direction of the long side (X). This
can be substantiated by observation of any rectangular piece of furni-
ture. When seen in this position, the short side of the chaise longue
(Y) comes into full view.
But had the furniture been drawn in the "correct" manner (as in
fig. 138) the design of the picture would have been scattered and
ineffective, with the distant door thrown outside the range of interest
that should of course be focused on the girl.
Had the same relative position of door and chaise longue (as in
Atherton's drawing) been maintained as in fig. 139 and had the chaise
longue been drawn "correctly," the design would have been most awk-
ward. In fact, it would have been impossible.
Now suppose that, insisting upon a "correct" drawing of the chaise
longue we turn it as shown in fig. 140. In this positionthe long side
being horizontal-the end lines converge "normally" to the distant door
which is their vanishing point. But, as is obvious, the design is static;
it lacks the grace of Mr. Atherton's drawing.
Although this is a relatively simple bit of perspective strategy it
represents the practiced skill of one who knows how to distort natural
appearance in order to achieve unity and elegance of design.
yp MOR/ZOW
chapter vii
141
The figures give scale to the tanks
which are ten times the height
of the figures, or sixty feet.
The scene is drawn as though the artist
is on some eminence that brings his eye
about eighteen feet from the ground
-three times the height of the figures.
The figures beside the oil truck were
drawn first. Their height carried
horizontally to Aon tank $ and then
projected forward, giving
the proper height for
the foreground figures.
THE CIRCLE
How infrequently a circular object is viewed from the one direction
-"straight on"-in which it appears as a perfect geometric figure that
can be drawn with a compass ! But of course a circle always looks like
a circle whatever its relation to the direction of sight ; and if the ellipse,
which is its perspective appearance, is correctly rendered by the artist
it will indeed look like a circle. If, however, its ends are made either too
pointed or too rounded it certainly will not look like a circle. Nor will
it if it is not perfectly symmetrical.
The student should, at the outset, acquire facility in drawing ellipses.
Otherwise his progress in working out problems involving the circle
will be greatly hampered. He should do a lot of drawing from models-
cardboard circles, plates or other circular forms laid on the floor, the
table, and at various other levels.
Try sitting back from the drawing board and swinging in the ellipses
with full arm movement. While at first this will be awkward and the
first ellipses thus made will fall short of being perfect figures, they are
likely to be better than those constructed laboriously by finger move-
ment.
The tracing of ellipses from photographic reproductions in maga-
zines and newspapers will help to develop the correct concept of ellip-
tical figures. Keep up your practice until the drawing of ellipses is
really easy and until you are sure that you are making true figures.
A practical test of the symmetry of the ellipse is to fold it on its
short diameter to see if one side falls exactly over the other, as it
should ; and to fold it again on the long diameter to test the similarity
of the front and back halves. The drawing, of course, has to be on
transparent paper for this test; if not, a tracing of it on transparent
paper can be made quickly.
Fig. 141 demonstrates some of the perspective facts of the circle
when it is associated with the cylinder. At the eye-level (which is also
the horizon line) the circular section lines of the tanks appear as
straight lines. Above and below this level they appear as ellipses that
are progressively "rounder"-to coin an adjective that is useful in
discussing proportion-as their distance above and below the eye-level
increases. The top ellipses of the tanks are more nearly round than the
bottom because their distance from the eye-level is greater.
The proportion of the ellipsesthe proportion of short to long dia-
meters-also depends upon the distance of the cylinder from the eye.
The nearer the eye, the more nearly round ; the further away, the thin-
ner. Seen at a considerable distance they appear as nearly straight
lines.
Another point to be noted here is that the long diameter of the
ellipse is at right angles to the axis of the cylinder (shown by white
line) . We must draw ellipses of all upright cylinders-this means all
circles on horizontal planes-upon horizontal long diameters. They
always look that way to us, though not always to the camera. A photo-
graph of the tanks would show the ellipses with long diameters slanted
down toward a vanishing point at the left on the horizon. The effect
would be one of unnatural distortion.
This is one of many differences in camera and human eye vision.
It must be said that some distortions of camera vision are not as objec-
tionable to the average person as they were before photography began
to accustom the eye to unnatural odd angle effects which fill our picture
magazines. Our eyes have been re-educated or conditioned, as it were.
Artists have adopted some of these camera distortions and they use
them in common practice, as we shall see later. But the rule that the
ellipse, representing a circle on a horizontal plane, must be drawn on
a horizontal diameter is inviolable ; here the camera distortion is not
acceptable to the human eye.
What about the ellipses of cylinders seen in the positions other than
upright, standing on their circular ends? The drawing in fig. 143,
traced from a photograph of rolls of newsprint paper, demonstrates
that regardless of the position of the cylinder the long diameter of its
ellipse appears at right angles to the cylinder's axis.
The photograph of the grinding wheels (fig. 142) and the diagram
(fig. 144) a tracing from the photograph reduced in size reveal some
interesting additional facts.
First we note that the long diameters of the ellipses are at right
angles to the axis lines of cylinders of which they are the circular
ends. This relationship of diameter to axis is constant no matter what
the position of the cylinder ; axis and diameter of ellipse are always at
I Courtety Penninaular Grinding Wheel Company.
143
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n
right angles to one another. When the ellipse to be drawn represents
a circle that is not actually part of a cylinder, as the circular face of
a rectangular clock (fig. 145), the artist imagines the cylinder whose
sides and axis line converge with the side lines of the rectangular solid
which they parallel.
Always we must remember that the long diameter of the ellipse is
not a structural line of the object: it is merely an imaginary line-
useful only for drawing purposes. It is never the same as the geometric
diameter of the circle which the ellipse represents. We note, for
example, that ends of the ellipses' diameters in fig. 144 do not touch
the circles where they rest upon the ground or at their uppermost
points. And we see that the numerals VI and XII on the clock's face
are located on its structural, vertical diameter, having no reference
to the ellipse's long diameter which changes direction as the clock is
turned one way or another and raised and lowered.
Referring again to fig. 144 we observe that the long axes of the three
ellipses are not parallel to each other : that of cylinder 1 deviates from
the vertical slightly more than number 3. All three diameters converge
upward and, if extended, would meet at a point somewhere in a ver-
tical line, called a vanishing trace, through VP 1 which is far off the
paper at the left. The vanishing trace is demonstrated in Chapter IX.
In fig. 144 the side lines of cylinder 1 have been projected backward,
to the right, toward their vanishing point ; and two other ellipses have
been drawn within them to indicate how the proportion of ellipses
changes (length of long diameter to short) according to distance from
each other and from the eye. The photograph of the freight car wheels
(fig. 146) illustrates this very clearly. The camera appears to have
been quite close to the wheels. A picture taken at a greater distance,
though from the same direction, would show less difference in the
proportion of the ellipses of the two wheels. Refer to fig. 164 on page 77.
145
147
Advertising drawing of
Sydney Harbour, Australia,
for the British Commonwealth
Pacific Airlines, Ltd.
148 A
In the drawing of the bridge (fig. 147) we have an interesting
application of the principles we have been discussing throughout this
chapter. Although the lines of the bridge are not perfect arcs of circles,
they are sufficiently related to circles to make the accompanying anal-
ysis useful. It shows how essential is our knowledge of the appearance
of the circle in all situations where it is even but a part of the object's
form. Without such knowledge the artist can make serious errors, even
when he has photographs to use ; these will not always illustrate his
subject in the position in which he is required to view it.
Our analysis (fig. 148 A) represents, at least approximately, the
relation of the bridge's span to circles which appear to carry the curve
of the trusses for some distance. The perspective diagram (fig. 148B)
is self-explanatory. We see that the long diameter of the ellipse (dotted
line) is at right angles to the axis line of an imagined cylinder and
that it lies considerably in front of the circle's actual center (Y), a
phenomenon that is discussed presently.
Come back to this subject later when studying reflections. Making
a drawing of the bridge with its reflection in the water will be a
rewarding exercise.
148 B
150
The Observatory on Palomar is another good illustration of the same
principles. Here, the ellipses' long diameters slant but slightly from
the vertical since the cylinder's axis line, being not far above the eye-
level, is nearly horizontal. As in the bridge drawing, only segments of
the ellipses become parts of the structure but we need to draw the
entire ellipses in order to be accurate with the segments.
Refer to the Peter Helck drawing in later pages for further study
of this phenomenon.
Many beginners, especially those who are mechanically minded, are
quite surprised to be told that the diameter of a circle and the long
diameter of its elliptical appearance are never the same lines ; and to
discover that the long diameter of the ellipse is always in front of
(nearer the spectator) the circle's structural diameter.
Even more convincing than the diagrams here that prove it on
paper is a simple experiment with a cardboard circle, preferably a
very large one. Hold the model in a horizontal position at arm's length
a few inches below eye-level. Better yet, lay it on a shelf about ten
inches below eye-level. Now place the point of a pencil on the back
rim of the circle and slowly move it forward on the circumference
toward the front until it reaches a point that seems to be the extreme
right-hand boundary of the circle. Mark this point on the model. Do
the same on the other side. Now take the model down and connect the
two points with a line. That line, it will be discovered, is not the dia-
meter of the circle : it lies in front of it. Now draw the actual diameter
of the circle with a dotted line and put the model back on the shelf.
What is seen will resemble fig. 150.
The explanation is simple enough. Though actually shorter than
the circle's diameter, the long-axis of the ellipse looks longer because
it is nearer the eye. The closer the observer is to the circle the more
widely separated are the axis of the ellipse and the diameter of the
circle. This fact the student should verify by his own experiments.
The photograph of automobiles parked in a circle on Great Bear
Lake, on page 76, is an excellent demonstration of this phenomenon.
The Observatory at Palomar, California.
151
EVE' LEVEL
H
153
154
155
After these convincing experiments it seems hardly necessary to
demonstrate further the phenomenon by such diagrams as figs. 152 and
153 which represent the spectator viewing the circle from different
distances. However, there are other factors to be considered here.
In fig. 152 we see that the circle's diameter AB is a shorter line on
the picture plane than CD, the diameter of the circle's elliptical appear-
ance from that view point. Fig. 153 demonstrates how increased dis-
tance from the circle brings the two diameters closer together. And
when the circle is small-as in the clock's face (see page 71) -the
ellipse's diameter comes very close to the circle's structural center.
In larger objects like the bridge (page 72) the ellipse's long diameter
is likely to be considerably in front of the circle's structural center.
Now let us consider the problem of concentric circles which is illus-
trated in figs. 154 and 155.
Here we have three concentric circles which, in plan, fig. 154, are
seen to divide the diameters AB and CD into six equal parts.
After we have drawn the square in perspective and have found its
diameters and center, we can divide AB, the horizontal diameter of
the square, into six equal parts to give us points through which the
ellipses must pass on that line. On the greatly foreshortened diameter
CD these points must be so placed as to give a gradual diminution of
the six spaces (perspectively equal) between the ellipses from front
to back.
The ellipses, as we know, have to be drawn so that their long di-
ameters lie in front of the circle's center. The diameter of the smallest
ellipse is so near the center as to practically pass through it.
CHAPIN A practical application of this phenomenon is seen in the accom-
panying diagram of the solar system, the orbits of the planets forming
a series of concentric circles. That the artist knew his perspective
facts can be proved by testing the drawing on an overlay of tracing
paper.
156
TIME drawing by R. M. Ckapin, Jr.
Courtoty TIME. Copyright TIME, Inc., 1949.
160
161
The New York Times advertisement (fig. 157) presents yet another
illustration depicting the globe with the encircling plane which carries
the lettering. The top view (158) indicates the relative dimensions
of the plane and the globe.
Since we look down upon the globe, the poles (A & B) would not
be on its circular contour line; the axis would be foreshortened as
in fig. 159, and the center would be slightly below actual center.
In fig. 160 we see the globe encircled at this perspective center. It
requires a somewhat cultivated judgment to know whether the ellipse
is correct in proportion (long to short axes) considering the position
of the globe-below eye-level-which we established when we indicated
its poles. In fig. 161 we apply the procedure of fig. 155, consulting the
top view for the relative measurements of the various circles.
,^^;;
162 fee fUhinff on Great Bear Lake. Photograph Associated Free .
Hud9on type locomotive of the Chesapeake and Ohio Railroad
We now come to the consideration of another and most important
relationship of the circle and the square. It can conveniently be studied
on pages 78 and 79 in the problem of wheels on a railroad track.
Only one of the four ellipses can be correctly proportioned for a
wheel seen on that particular track and in that position on the track.
(The conditions are identical in all four diagrams.)
When the track is at right angles to our direction of sight; that is,
when our direction of sight parallels the ties, the wheels of course
appear as perfect geometric circles. On tracks that are viewed at an
angle the wheels are seen as ellipses varying in proportion (of short
to long diameters) according to the angle the track takes to our direc-
tion of sight. On a sharply receding track the ellipses are very thin.
164
TOP VfEW Or WHEELS
p/crusr PMMf
FOtf 01jSRVtt.
We are viewing all four tracks at exactly the same angle. The ques-
tion is, which of the wheels is correctly drawn? The person with a
trained and discriminating eye knows that only the ellipse seen in
fig. 166 can be correct. He does not need to be convinced by the experi-
ments on these pages which are intended to prove it for the inexperi-
enced student. Even our demonstration will not prove it for the student
who has not, through much practice drawing of cubes, learned exactly
what a cube looks like in perspective for, as we shall see, the cube
helps us here to make decisions.
However, we will assume that the student has in fact acquired a
reasonable concept of the cube's appearance in perspective views. He
will at once identify fig. 170 as a cube. That means of course that the
ellipse drawn on the side (which is the same as that of the wheel
in fig. 166) is the correct rendering for a wheel on that track. Fig. 169
is too wide to be a cube and figs. 171 and 172 are too narrow to be
cubes.
In order to make this experiment as simple as possible, the track
has been drawn so that the rail and the ties cross a horizontal (AB
in fig. 173) at the same angle. This means that a cube resting on the
rail will present two equal faces; that the diagonal of the top and
bottom faces (dotted lines) are horizontal and that the back corners
are vertically above the front ones.
Now let us extend the track as in fig. 174. Cube No. 2A occupies the
same relative position on the tracks as that in fig. 170 ; its two vertical
faces are equal. The other cubes are placed in such positions on the
tracks that the ellipses inscribed within them correspond with the
ellipses in figs. 169, 171 and 172. Thus we see that the proportion of
the ellipses on the same track depends upon their nearness to the eye.
An interesting application of this principle is seen in the locomotive
wheels (page 77) where the small front wheel is very nearly a circle
and the furthest driver is a relatively narrow ellipse. The camera man
who made the photograph from which this drawing was traced must
have been very close to the locomotive.
The diagram in fig. 164 illustrates the logic of this differential in
proportion of ellipses. Observers A and B view the two wheels from
different distances. The dotted lines represent the central directions
of their sight approximately central between the two wheels. The pic-
ture plane for each is, of course, at right angles to the direction of sight.
Note that the differential in width, in what would be seen as ellipses,
is greater for observer A than for observer B.
On the following pages we make an analysis of a very interesting
picture by Peter Helck which demonstrates many of the points covered
in this chapter.
173
B
2A
I A
174
80
175
Advertising painting for the New York Central System
by Peter Helck.
81
HELCK No living American artist knows more about perspective or uses it
more expertly in his work than Helck. The subject here illustrated is
simple, compared with many that he is called upon to illustrate. Such
industrial scenes as the interiors of steel mills, with their intricate
machinery, involve about every kind of perspective problem that can
be imagined ; busy railroad centers, shipbuilding yards and the myriad
activities of business, farm, and commerce put Helck's knowledge and
skill to the acid test.
There can be no guesswork in the rendering of such illustrations as
the one chosen for this demonstration. As we proceed with our analysis
we shall see that every detail of the painting has been constructed with
such accuracy as can only result from meticulous observation of scien-
tific method.
Of course Peter Helck did not go through the steps presented in
this demonstration ; his knowledge of perspective is so thorough and
he has employed it so continuously over many years that the pro-
cedure here outlined was purely automatic. None the less it was active
in his subconscious mind as he made his painting.
The establishment of the eye-level is an important consideration in
every illustration; the picture's effectiveness depends in no small
measure upon the point of view from which the scene is to be viewed.
In order to dramatize the size and power of the large locomotive, Helck
established a low eye-level, such a vantage point as might be had by
a spectator standing in the ditch below the roadbed. The eye-level is
seen to be a little above the foundation slab.
Before discussing problems involved in the circular formsarches
of the bridge and the locomotive wheels-let us take a look at what
happens to the straight lines.
Vanishing points 1 and 2, we note, control all the horizontal lines
that are parallel either with the length of the bridge or its thickness,
also they control the lines of the locomotive on the bridge. But we
discover that the horizontal lines of the front of the lower locomotive
give us a different vanishing point. That point ( VP 8 ) is slightly below
the eye-level on the vanishing trace. How is this explained? (For
explanation of vanishing trace refer to Chapter IX.)
176
B
A heavy paper model of an engine
that would be useful to the student
in studying this problem.
It is explained by the fact that the locomotive is traveling on a
curved track. How do we know this? By the way the locomotive leans
as it does when rounding a curve, the inside rail of the curve being
lower than the outside rail. If the track were straight, and both rails,
therefore, on the horizontal ground plane, we would be able to see
the further rail, the roadbed being below our eye-level.
In order to demonstrate the perspective facts of this situation in
the clearest manner, let us reduce the problem to its simplest possible
terms by resorting to models (page 83) that represent the bridge and
the locomotive. We can use a rectangular prism for each, since we are
considering only their rectangular aspects. We have drawn the models
below the eye because by looking down upon them the points involved
can better be demonstrated.
Fig. 179 demonstrates the situation if the track were straight and
at right angles to the bridge as shown in fig. 177A. With the track
straight, the locomotive would not lean; its upright lines would be
vertical.
177B shows the tracks curved as in Mr. Helck's painting. But the
locomotive (in our plan) is seen to have the same position as when
the track is straight (assuming the center of the circle, of which the
curved track is an arc, to be on the axis line of the brid
