But the system of formal perspective is not without problems. Followed to the letter, strictly applied perspective rules can result in rather dry and rigid drawings. Perhaps the most serious problem with the formal perspective system is that it is so "left-brained." It employs the style of left-hemisphere processing: analysis, sequential logical cogitation, and mental calculations within a pre-prescribed system. There are vanishing points, horizon lines, perspective of circles and ellipses, and so on. The system is detailed and cumbersome, the antithesis of R-mode style with its antic/serious, pleasurable quality. For example, in anything but the simplest one-point perspective setup (Figure 8-10), vanishing points may be several feet beyond the edge of the drawing paper, requiring pins and strings to mark them.
Fortunately, once you understand "informal" perspective (sighting), you don't really need to know formal perspective at all. That's not to say the study of perspective is not useful and interesting. In my view, knowledge never hurts! But sighting is sufficient for basic drawing skills.
Graham Collier, professor of art, states that in the early days of the inception and development of Renaissance perspective it was used creatively and imaginatively to impart what must have been a thrilling sense of space to art.
"Effective as perspective is, however, it becomes a deadening influence on an artist's natural way of seeing things once it is accepted as a system—as a mechanical formula."
— Graham Collier
Form, Space, and Vision, 1963
Fig. 8-10. The classic perspective illustration. Note that vertical lines remain vertical; horizontal edges converge at a vanishing point (or points) on the horizon line (which is always at the artist's eye level). That's one-point perspective in a nutshell. Two-point and three-point perspective are complex systems, involving multiple vanishing points that often extend far beyond the edges of the drawing paper and requiring a large drawing table, T-squares, straight-edges, etc., to draw. Informal sighting is much easier and is sufficiently accurate for most drawing.
A brief practice in sighting before you do a "real" perspective drawing
What you'll need:
• Your drawing board
• Several sheets of scratch paper
• Your drawing pencils, sharpened, and your eraser
• Your plastic Picture Plane and your felt-tip marker
• Your larger Viewfinder
What you'll do:
First, you will practice sighting proportions and angles, using your pencil as a sighting device. Once you've practiced a bit, then you'll do your "real" sighting drawing. Begin by seating yourself in front of a doorway, at about ten feet away.
Hold up your Viewfinder/Picture Plane and compose your drawing so that you can see the whole doorway. Hold the Picture Plane very still and use your felt-tip marker to draw the top of the doorway on the plastic plane. See Figure 8-11. (The line will be somewhat shaky.) This is your Basic Unit. Transfer this unit to a piece of paper, estimating the size and position so that it is the same as on your Picture Plane. Set the Picture Plane aside. See Figure 8-12.
Now, pick up your pencil. Hold it at arm's length toward the top of the doorway with the flat (eraser) end out and with your elbow locked. Close one eye and move the pencil so that the end coincides with one side of the top of the doorway. (Choose either the outside of the molding or the inside edge.) Then, with one eye still closed, move your thumb along the pencil until your thumbnail coincides with the other side of the doorway. Hold that measure. You have "taken a sight" on the width of the doorway.
A test: What happens if you open both eyes or if you relax your elbow?
Keep your thumb at the same position and try bending your elbow just slightly, just barely pulling the pencil toward you.
What happens? The "measurement" has changed, hasn't it? Therefore, the reason you must lock your elbow when sighting proportions is to maintain the same scale. When your elbow is locked, you are always taking sights using the same position.
Then, relock your elbow, and resight the width of the doorway on your pencil (Figure 8-13). We'll call this your Basic Unit, or your "One." Now, keeping your thumb in the same position, turn your pencil vertically and find the relationship (the ratio or proportion) of width to length.
Still holding the pencil at arm's length, and still with one eye closed and your elbow locked, measure from the top corner: "One (width), to one (height)" (Figure 8-14), then drop down, measure "One to two" (Figure 8-15), drop it again and measure the remainder, "One to two and two-thirds" (Figure 8-16). You have now "taken a sight" on the proportion of the width relative to the height of the doorway. This proportion is expressed as a ratio: 1:22/3, or, in words, "One to two and two-thirds."
Now, turn back to your sketch
By sighting the doorway, you determined that the width-to-height proportion of the doorway was 1:2 2/3. That is the proportion of the doorway "out there" in the real world. Your job is to transfer that proportion from "out there" into your drawing.
Obviously, the door in your drawing will be smaller—much smaller—than the real doorway. But it must be proportionally the same, width to length.
Now, therefore, use your pencil and thumb to take a new measure: the width you have drawn on your paper (Figure 8-17). Then turn the pencil to vertical on your paper and measure off "One to one, two, and two-thirds" (Figures 8-18, 8-19, and 8-20). Make a mark and draw in the two sides of the doorway. The doorway you have just drawn has the same proportion—width to height—as the real doorway you were looking at.
To set this idea, draw a new "One," smaller than the first one. Now, measure that width with your pencil and again mark off the proportional height. This doorway will be smaller, but it will be proportionally the same as your first drawing and the real doorway.
Summing up: In sighting proportions, you find out what the proportions are "out there" in the real world and then, holding the proportion in your mind as a ratio (your Basic Unit or "One" — in relation to something else), remeasure in the drawing to transfer the proportion to the drawing. Obviously, in drawings, sizes are almost always on a different scale (smaller or larger) than what we see "out there," but the proportions are the same.
As a clever student of mine put it: "You use your pencil to find the ratio 'out there.' You remember it, wipe the measure off the pencil, and remeasure with your pencil in the drawing."
The next step: Sighting angles
Remember, sighting is a two-part skill. You have just learned the first part: sighting proportions. Your pencil, used as a sighting device, enables you to see "How big is this compared to that?" "How wide is that compared to my Basic Unit?" And so on. Proportions are sighted relative to each other and to your Basic Unit.
Sighting angles is different. Angles are sighted relative to vertical and horizontal. Remember, both angles and proportions must be sighted on the plane.
Take up your Viewfinder/Picture Plane and your felt-tip marker again and seat yourself in front of another corner of a room. Hold up the Picture Plane and look at the angle formed where the ceiling meets the two walls. Be sure to keep the Picture Plane vertical in front of your face, on the same plane as the plane of your two eyes. Don't tilt the plane in any direction.
Again, compose your view, and use your marker on the Picture Plane to draw the corner (a vertical line). Then, on the plane, draw the edges where the ceiling meets the two walls, and, if possible, the edges where the floor meets the walls.
Then, put your Picture Plane down on a piece of paper so you can see the drawing and transfer those lines to a piece of drawing paper.
You have just drawn a corner in perspective. Now, let's do that without the aid of the Picture Plane.
Move to a different corner or a different position. Tape a piece of paper to your drawing board. Now, take a sight on the vertical corner. Close one eye and hold your pencil perfectly vertically at the corner. Having checked, you can now draw a vertical line for the corner.
Next, hold up your pencil perfectly horizontally, staying on the plane, to see what the angles of the ceiling are relative to horizontal (Figure 8-21). You will see them as angles between the pencil and the edges of the ceiling. Remember these angles as
Verticals in human-built structures remain vertical. Horizontals—that is, edges parallel to the face of the earth—appear to change and converge and must be sighted. But you can pretty much count on verticals remaining vertical. In your drawing, they will be parallel to the edges of your paper. There are exceptions, of course. If you stand at street level, looking up, to draw a tall building, those vertical edges will converge and must be sighted. This situation, however, is fairly rare in drawing.
shapes. Then, again estimating, draw the angles into your drawing. Use the same procedure for the floor angles (Figure 8-22).
These fundamental sighting movements or measuring gestures in drawing are not difficult to master, once you have a real understanding of the purpose of the movements.
• The purpose of closing one eye, as I explained earlier, is to see a 2-D image only, not a 3-D binocular image.
• The purpose of locking the elbow is to ensure using a single scale in sighting proportions. Relaxing the elbow even slightly can cause errors by changing the scale of the sights. In sighting angles, it is not necessary to take the sights at arm's length, but you must stay on the plane.
• The purpose of comparing angles to vertical or horizontal is obvious. Angles can vary infinitely around 360 degrees. Only true vertical and true horizontal are constant and reliable. And since the edges of the paper (and the edges of the format you have drawn) also represent vertical and horizontal, any angle can be assessed on the plane and transferred into the drawing in relation to those constants.
Some important points about sighting angles
• All angles are sighted relative to the two constants: vertical and horizontal.
• In your drawing, the edges of your format represent the constants vertical and horizontal. Once you have determined an angle "out there" in the real world, you will draw it into the drawing relative to the edges of your format.
• All angles are sighted on the picture-plane. This is a solid plane. You cannot "poke through" it to align your pencil with an edge as it moves through space. You determine the angle as it appears on the plane (Figure 8-23).
• You can sight angles by holding your pencil either vertically or horizontally and comparing the angle with the edge of the pencil. You can also use the crosshairs on your clear plastic Picture Plane or even the edge of one of the Viewfinders. You just need some edge that you can hold up in a vertical or hori-
zontal position on the plane to compare the angle you intend to draw. The pencil is simply the easiest to use and doesn't interrupt your drawing.
• Visual information seen on the plane is nearly always different from what you know about things. Say you are facing a corner of a room. You know that the ceiling is flat—that is, horizontal—and that it meets the wall at right angles. But if you hold up your pencil perfectly horizontally, close one eye, and, staying on the plane, line up the corner so that it touches the center of your horizontal pencil, you will find that the edges of the ceiling go off at odd angles. Perhaps one angle is steeper than the other. See Figure 8-22, page 149.
• You must draw these angles just as you see them. Only then will the ceiling look flat and the right angles of the walls appear to be correct in your finished drawing. This is one of the great paradoxes of drawing.
• You must put these paradoxical angles into your drawing just as you perceive them. To do this, you remember the shape of one of the triangles made by the edge of the ceiling and your horizontal pencil. Then, imagining a horizontal line in your drawing (parallel to the top and bottom edges of your format), draw the same triangle. Use the same process to draw the other angled edge of the ceiling. See Figure 8-21, page 149, for an illustration of this.
I usually recommend that students not try to designate an angle by degrees: a 45-degree angle; a 30-degree angle; etc. It really is best to simply remember the shape the angle makes when compared to vertical and horizontal and carry that visual shape in your mind to draw it. You may have to double-check angles a few times at first, but my students learn this skill very quickly.
The decision whether to use vertical or horizontal as the constant against which to see a particular angle occasionally puzzles students. I recommend that you choose whichever will produce the smaller angle.
I realize that sighting sounds very "left-brained" at this point. But remember we are searching out relationships. The right hemisphere is specialized for the perception of relationships—how things compare. As I said before, the "counting up" of sighting is just a simple way of "tagging" our perceptions. The Basic Unit is always "One," because it is the first part of a comparison. After you practice sighting a bit, you are hardly aware of the process and it is very rapid. Also, with practice in drawing, you will be doing a lot of "eyeballing," meaning estimating rather than needing to sight everything. But for any difficult perception, as in foreshortening, an experienced artist gladly uses sighting. Like negative space, sighting helps to make drawing easy.
Try to remember that drawing always produces an approximate version of the subject, even for a person highly skilled in drawing. Drawing is not photography. The person who is drawing consciously or subconsciously edits, emphasizes (or minimizes), or otherwise slightly changes various aspects of the subject. Students are often very critical of their work because it is not an exact rendition, but the subconscious choices made during drawing are part of the expressiveness of drawings.
Please note that in public places you will attract an audience of viewers who will very likely want to talk with you—not a good situation for maintaining an R-mode, wordless state of mind. On the other hand, if you would like to make some new friends, drawing in a public spot will work every time. For some reason, people who ordinarily would not approach a stranger do not hesitate to talk with someone who is drawing.
A "real" perspective drawing
What you'll need:
• Your drawing board
• Several sheets of drawing paper, in a stack for padding
• Your masking tape
• Your drawing pencils, sharpened, and your eraser
• Your graphite stick and several paper towels or paper napkins
• Your plastic Picture Plane and your felt-tip marker
• Your larger Viewfinder
Before you start:
Tape a stack of several sheets of drawing paper to your drawing board. Draw a format on your drawing paper and tone the paper within the format to a medium gray tone. Draw the crosshairs on the toned paper, i. Choose your subject. Learning how to draw "in proportion" and "in perspective" are the two great challenges—the Waterloo, even — of most drawing students in art schools. You will want to prove to yourself that you can achieve this skill. Therefore, pick your subject with that objective in mind: Choose a view or a site that you think would be really hard to draw — one with lots of angles or a complicated ceiling or a long view down a hall. See the student drawing on page 153. The best way to choose a site is to walk around, using your Viewfinder to find a composition that pleases you — much in the same way as composing with a camera's viewfinder.
• A kitchen corner
• A view through an open doorway
• A corner of any room in your house
• Any street corner where you can sit in your car or on a bench and draw
• An entrance to any public building, inside or out
Set yourself up to draw at your chosen site. You will need two chairs, one for sitting on and one on which to lean your drawing board. If you are drawing outside, folding chairs are convenient. Make sure that you are directly facing your chosen view.
2. Clip your larger Viewfinder and the plastic Picture Plane together. Draw a format edge on the plastic plane by running the felt-tip marker around the inside edge of the Viewfinder opening. Closing one eye, move the Viewfinder/plastic Picture Plane backward and forward to find the best composition—the one you like best.
3. Having found a composition you like, choose your Basic Unit. Your Basic Unit should be of medium size and of a shape that is not too complicated. It might be a window or a picture on the wall or a doorway. It can be a positive form or a negative space. It can be a single line or a shape. Draw your Basic Unit directly on the plastic with your felt-tip marker.
After you have drawn your Basic Unit on the plastic Picture Plane, you may also wish to draw one or two of the more important edges on the plastic Picture Plane, but be aware that the line will be very shaky and uncertain. The essential piece of information is your Basic Unit, and that is really all you need.
4. Set aside your Viewfinder/plastic Picture Plane on a piece of white paper so that you can see what you have drawn on it. You will next draw your Basic Unit on your paper. It will be the same shape but larger, just as your toned format is larger than the Viewfinder opening.
5. Transfer your Basic Unit onto the toned paper using your crosshairs as a guide. On both the Picture Plane and on your toned paper, the crosshairs divide the drawing area into four quadrants. Refer to Figures 8-11 and 8-12 on page 146 for how to transfer your Basic Unit from your Picture Plane to your toned paper by using these quadrants.
How to re-find your composition: Sometimes it is useful to go back to the Picture Plane to check on an angle or proportion. To re-find your composition, simply hold up your Viewfinder/plas-tic Picture Plane, close one eye and move the plane forward or backward until your Basic Unit "out there" lines up with the felt-tip drawing of Basic Unit on the plastic plane. Then check out any angle or proportion that may be puzzling you.
For most people just learning to draw, the hardest part of drawing is believing their own sights of both angles and proportions. Many times I have watched students take a sight, shake their heads, take the sight again, again shake their heads, even say out loud, "It [an angle] can't be that steep," or, "It [a proportion] can't be that small."
With a little more experience in drawing, students are able to accept the information they obtain by sighting. You just have to swallow it whole, so to speak, and make a decision not to second-guess your sights. I say to my students, "If you see it so, you draw it so. Don't argue with yourself about it."
Of course, the sights have to be taken as correctly and carefully as possible. When I demonstrate drawing in a workshop, students see me making a very careful, deliberate movement to extend my arm, lock my elbow, and close one eye in order to carefully check a proportion or an angle on the plane. But these movements become quite automatic very quickly, just as one quickly learns to brake a car to a smooth stop.
To complete your perspective drawing:
1. Again, you will fit the pieces of your drawing together like a fascinating puzzle. Work from part to adjacent part, always checking the relationships of each new part to the parts already drawn. Also, remember the concept of edges as shared edges, with the positive forms and negative spaces fitted into the format to create a composition. Remember that all the information you need for this drawing is right there before your eyes. You now know the strategies artists use to "unlock" that visual information and you have the correct devices to help you.
2. Be sure to use negative spaces as an important part of your drawing as in Figure 8-24. You will add strength to your drawing if you use negative space to see and draw small items such as lamps, tables, signs with lettering, and so on. If you do not, and focus only on the positive shapes, they will tend to weaken your drawing. If you are drawing a landscape, trees and foliage in particular are much stronger when their negative spaces are emphasized.
3. Once you have completed the main parts of the drawing, you can focus on the lights and shadows. "Squinting" your eyes a bit will blur the details and allow you to see large shapes of lighted areas and shadowed areas. Again using your new sighting skills, you can erase out the shapes of lights and use your pencil to darken in the shapes of shadows. These shapes are sighted in exactly the same way as you have sighted the other parts of the drawing: "What is the angle of that shadow relative to horizontal? How wide is that streak of light relative to the width of the window?"
4. If any part of the drawing seems "off" or "out of drawing," as such errors are called, check out the troublesome area with your clear plastic Picture Plane. Look at the image on the plane (with one eye closed, of course) and alternately glance down at your drawing to double-check angles and proportions. Make any corrections that seem reasonably easy to make.
Artist/teacher Robert Henri sends a stern warning to his students:
"If in your drawing you habitually disregard proportions you become accustomed to the sight of distortion and lose critical ability. A person living in squalor eventually gets used to it."
After you have finished:
Congratulations! You have just accomplished a task that many university art students would find daunting if not impossible.
Sighting is an aptly named skill. You take a sight and you see things as they really appear on the picture-plane. This skill will enable you to draw anything you can see with your own eyes. You need not search for "easy" subjects. You will be able to draw anything at all.
The skill of sighting takes some practice to master, but very soon you will find yourself "just drawing," taking sights automatically, at times even without needing to measure proportions or assess angles. I think it's significant that this is called "eyeballing." Also, when you come to the difficult foreshortened parts, you will have just the skills needed to make the drawing seem easy.
Fig. 8-25. Charles White, Preacher (1952). Courtesy of the Whitney Museum.
This drawing by Charles White demonstrates a foreshortened view. Study it. Copy it, turning the drawing upside down if necessary. You might use the length of the man's left hand from the wrist to the tip of the pointing finger as your Basic Unit. Perhaps you'll be surprised to find that the ratio of the head to the model's left hand is 1:1 2/3.
Each time you experience the fact that drawing just what you see works the wonder of creating the illusion of space and volume on the flat surface of the paper, the methods will become more securely integrated as your way of seeing— the artist's way of seeing.
The visible world is replete with foreshortened views of people, streets, trees, and flowers. Beginning students sometimes avoid these "difficult" views and search instead for "easy" views. With the skills you now have, this limiting of subject matter for your drawing is unnecessary. Edges, negative spaces, and sightings of relationships work together to make drawing foreshortened forms not just possible—they become downright enjoyable. As in learning any skill, learning the "hard parts" is challenging and exhilarating.
Fig. 8-26. Edgar Degas (1834-1917), Dancer Adjusting Her .Slipper (1873).
Courtesy of The Metropolitan Museum of Art, bequest of Mrs. H. O. Havemeyer, 1929. The H. O. Havemeyer Collection
This technique of using the constants, vertical and horizontal, against which to gauge angles is an important basic skill in drawing figures as well as objects. Many artists' sketches still show traces of sight lines drawn in by the artist, as in the Edgar Degas drawing entitled Dancer Adjusting Her Slipper (Figure 8-26). Degas was probably sighting such points as the location of the left toe in relation to the ear and the angle of the arm compared to vertical.
Note that Degas's Basic Unit was from the topmost edge of the hair to the neckband. The artist used the same Basic Unit in Figure 11-6, shown in the chapter on color.
relationships in a new mode: putting sighting in perspective
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