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THE VANISHING POINT
The artist's business is to be able to draw an object so that it will look solid and not flat like the surface of the paper on which it is drawn. In so doing the artist employs a method that we call perspective.
Perspective is used not only to make the object appear to have dimensions but also to cause it to appear close up or in the distance or to suggest a feeling of space.
Let us follow the railroad tracks out on the plain where there is level land in all directions as far as we can see. All around us we can see the sky meeting the distant plain in a long even line. This is called the horizon.
The ideal example of the horizon is seen when viewed across a large body of water where no distant shore is seen. At sea the horizon is one continuous line.
We may consider the horizon as continuous. This is true though the view may be obstructed by an object: a hand, a building, or a mountain. The horizon is still there though we go into the building and close the door. If objects became transparent the horizon could always be seen. This is illustrated on the opposite page.
THE VANISHING POINT
Now we stand between the two shiny rails and look along the track. These rails go on and on across the level plain until they reach the horizon where they are lost from sight in the distance.
We call the place where they disappear the vanishing point.
Now look down at your feet. There you see the track. Raise your eyes and look fifty feet beyond. You still see the track although you are not looking directly down upon it.
Then look straight ahead. You see the track as it climbs to a height level with your eyes and disappears at the horizon in the distance. This height can be called the eye-level.
Here the horizon and the eye-level become one and the same thing.
THE HORIZON AND THE EYE-LEVEL
Now sit down on the track and look about. You will find that your eye-level has lowered. The distant horizon also appears lower in order to meet this change of eye-level.
If we ascend in an airplane we shall find that the distant horizon rises with our height. It appears to remain at eye-level.
This accounts for the peculiar basin-like appearance of the earth when viewed from a great height.
We can now understand why the drawing of the corner of a room looks different when sketched from a low stool as compared with one sketched from the top of a stepladder.
The height of the eyes becomes a very important factor in freehand drawing.
We use perspective in drawing a brick so that it appears as a solid object.
The horizon is that distant line where the earth and the sky seem to meet.
The vanishing point is the place on the horizon where the rails of the tracks appear to meet.
The horizon is the height of your eyes no matter where you are above the ground.
The eye-level is the height of your eyes no matter where you are.
Draw a brick, a box, a book. Do you know just why you draw it as you do?
If you are in level country or near the ocean look for the horizon. Experiment by looking from different heights: from the ground, from a window, from the top of a building. Must you ever look up or down to see it?
Locate vanishing points in things other than railroad tracks.
Make a sketch from the center of a level street with the sidewalks representing the two rails of the track.CHAPTER 2
THE EYE-LEVEL AND ITS RELATIONSHIP TO PERSPECTIVE DRAWING
THE EYE-LEVEL IS ALWAYS REPRESENTED BY A STRAIGHT LINE
You are seated sketching the interior of your room. Someone makes a mark around the wall the same height from the floor as your eyes. This mark will appear as a straight line across your drawing. It is the eye-level.
Notice in the drawing that the visible horizon seen through the window is the same height as the eye-level mark on the wall.
"THE EYE-LEVEL IS LEVEL WITH THE EYE"
The eye-level is level with the eye.
You may smile at the simplicity of the above definition, yet it is a surprising fact that it is ignored in practice even by professional artists. Its importance, however, is immeasurable.
Let us look into it.
On the preceding page is the drawing of the room corner; there are the pictures on the wall, the chair, the lamp, the window, and the drapes.
Now let us consider the lamp.
We are seeing the underside of the lamp shade; in other words we are looking from below up into the shade. Now let us look at the base of the lamp; it rests on the floor and it is necessary to look down upon it. The shade is above the height of our eyes while the base is below. Somewhere between is the eye-level, a place that is exactly the same height from the floor as are our eyes.
We show this eye-level by means of a straight line across the drawing.
We find that we have control over this eye-level line. We can look under the table and see the underside. We accomplish this by lowering our eye-level. We stand on tiptoe or step up on a box to see over the heads of people in a crowd. We do this to raise the eye-level. New pictures are constantly being formed before our eyes by our various ways of raising and lowering the eye-level.
It is interesting to watch for the effects and changes in a landscape when viewed from an automobile driven over a hilly road. Showmen have taken advantage of this fact and have built the Ferris Wheel, a mechanical means of swiftly raising and lowering the eye-level. The quick change of picture helps to intensify the experience.
We find that the objects we draw are in two classes: the ones that are above and the ones that are below the line that indicates the eye-level.
Now let us go into it further.
THE HIGH-WATER MARK
Imagine yourself wearing a diving helmet and seated in your room making a sketch of the interior. As you sit there the room is filled with water until it just reaches the height of your eyes. Now then; everything in the room that is under water is "Below the Eye-Level," everything that is not under water is "Above the Eye-Level." The "High-Water Mark" around the walls and on everything else that it touches in the room is "The Eye-Level" itself. No matter in what direction you look this high-water mark appears to your eye as a straight level line across the objects of the room.
When you are sketching outdoors this "water level" explanation will still hold true. Fences, buildings, haystacks, people, all have a "High-Water Mark" which is the artist's eye-level.
If you are seated on the ground sketching, or if you are on a roof, the "High-Water Mark" explanation still holds true.
IMPORTANCE OF THE EYE-LEVEL
It is easily seen that you would get two entirely different views of your table if you made a sketch while standing beside it, or if you sat on the rug and sketched the same table from that position.
The whole system of perspective drawing is based on the height of this eye-level; whether or not the eyes are above or below the thing that is being sketched.
The horizon is shown by a straight line across your drawing.
In a room you can create your own horizon. This is an eye-level mark around the wall.
We look up to see things above the eye-level and down to see things below the eye-level.
The eye-level is the high-water mark when the water is eye deep.
This line is the first thing we locate in making a perspective drawing.
The visible outdoor horizon is not to be confused with the Horizontal Line (HL) in mechanical perspective as explained in the last step of this book.
Draw a line on the blackboard the height of your eyes when you are standing. This will appear as a straight line, though it may be in the corner of the room where the line is on different walls.
Change to a seated position and take notice of the line in the corner of the room. Does it still appear as a straight line where it joins at the two walls? Stand on a chair and note the result.
Go outdoors and locate your eye-level mark on the various things you see around you. Imagine where the eye-level line would cut across these different things if you were making a drawing.CHAPTER 3
PARALLEL LINES AS WE SEE THEM
PARALLEL LINES RELATED TO ONE-POINT PERSPECTIVE
PARALLEL LINES AS WE SEE THEM
The two rails of the track are always the same distance apart.
When two or more lines always remain the same distance apart they are called parallel lines.
In a perspective drawing we do not actually draw these lines parallel. Why not?
Let us look straight down on a person standing on the track and see what is happening.
When he looks down at the track at his feet his eyes must take in a wide area in order to see both rails.
He sees this width in front of him, as indicated by the heavy black line.
As he raises his eyes and looks fifty feet in front of him he sees the same width of tracks but within a much narrower area.
For this reason the track appears narrower as he looks farther away.
The shaded portion on the sketch shows this area.
The portion he sees fifty feet away is shown by the black line.
As he raises his eyes to the horizon the same width of track appears in so narrow an area that it looks like no width at all. This is the vanishing point.
Thus the nearer he looks, the wider appears the spread of the track, and the farther away he looks the narrower it appears until it becomes a point at his eye-level.
This wide or narrow area is perhaps better understood if we think of the person drawing these widths on a piece of glass held upright as shown on page 28.
The above sketch shows how the man, in order to see farther along the track, must raise his eyes.
PARALLEL LINES AND ONE-POINT PERSPECTIVE
Parallel lines are two or more lines that extend in the same direction and remain the same distance apart.
The two opposite sides of a table are parallel, the boards of the floor, the rails of a track.
We know that the two parallel rails of the track appear to converge at a point in the distance. Now take notice of the fences and telegraph wires that follow the .tracks; they also converge at this same point.
A group of parallel lines in a perspective drawing, if extended, meet at the same point.
There are two exceptions to this rule. These exceptions are shown in the drawing.
(1) When we face the vanishing point of a group of parallel lines (as in the picture) we have one-point perspective; in this case the left-and-right lines, like the ties of the track, are all parallel with the horizon. There is no vanishing point.
(2) Up and down (perpendicular) lines, like the telegraph poles and fence posts, are also drawn parallel but without a vanishing point. (Perpendicular lines are explained on page 45.)
The general rule for (1) and (2) is that parallel lines which are also parallel to the picture plane do not appear to converge at a point. The picture plane is explained on the next page.
A good example of parallel upright lines is a forest of tall straight trees. The trees farther back in the forest appear smaller, thus suggesting depth or distance.
THE PICTURE PLANE
Hold a sheet of cellophane or glass upright before your eyes. You can see the object or scene before you through the transparent sheet. If you trace this scene as you see it on the sheet you will have a drawing in perspective. The transparent sheet can be thought of as a sheet of drawing paper or an artist's canvas. When held in this position it may be called the picture plane. We think of perspective drawings as made on this picture plane.
The picture plane stands upright (perpendicular) between the artist and the object he is drawing. Also, the picture plane is placed directly across (at right angles to) the line of direction in which the artist is looking. The diagram at the right explains this.
Drawing in perspective on the picture plane can be self-explained by standing in front of a window and with a china marking pencil tracing on the glass the outlines of the buildings as you see them.
A paper with a hole in it can be set at arm's length to help fix the point of view. Look through this hole and sketch as if the window were the sheet of paper. Simply trace on the glass the buildings and landscape as you see them beyond the window. The result is a perspective drawing.
Suppose we remove the windowpane with this drawing and lay it on the table. On the table it looks like any other perspective drawing done on a piece of paper.
How is it possible to make this drawing without first tracing it on an upright piece of glass? The following steps will explain how this can be done.
The two rails of a track are parallel. These two parallel lines, when shown in a perspective drawing, come together at a point.
When two parallel lines meet at a point all other lines parallel to these two meet at the same point.
You lower your eyes to see your feet.
You raise your eyes to see objects on the ground at a distance.
The picture plane stands upright between the artist and the object he is drawing.
Draw the top view of a man standing at the end of a long narrow table. Show the difference in the area of his vision when looking at the width of the far end of the stable compared with that of the near end.
Stand in the center of a straight level highway. Draw it as you see it—disappearing in the distance. Add a sidewalk parallel to it. Add two rows of telephone poles, a row on each side. Add a fence beside the walk.
Draw a railroad on the prairie sketched from the center of the track. Show a highway crossing it in the foreground.CHAPTER 4
THE THREE SETS OF PARALLELS
LOCATING THE POINT AND THE EYE-LEVEL
THE THREE SETS OF PARALLELS
Here we have an ordinary brick.
It has six sides, but only three sides can be shown in the drawing.
The lines of the drawing indicate where two of these sides join.
If all sides of the brick were shown there would be twelve lines.
The four long lines which indicate the length of the brick are parallel lines.
The four lines of the width are parallel.
The four lines of height (or thickness) are parallel.
Now let us turn the brick so that we are looking straight along the length lines. The sketch on the next page shows it in this position.
We now have the end view of the brick.
LOCATING THE POINT AND THE EYE-LEVEL
Remember how as a child you placed bricks end to end to make a railroad track? Try this.
You see that the facts discovered in regard to the railroad track on the plain now hold true for bricks; the line of the eye-level, vanishing point, and all.
Now let us remove all the bricks but one.
Here it stands. The vanishing point is gone from the drawing, so is the line of the eye- level.
We can easily find the vanishing point and the eye-level by extending the lines that represent two parallel edges of the brick.
The vanishing point is where they meet.
A horizontal line drawn through this point gives us our eye-level.
Thus we can find the vanishing point and the eye-level by extending any two lines that represent converging parallel lines in a perspective drawing.
FINDING VANISHING POINTS AND THE LINE OF VISION
It is an interesting experiment to take cuts of photographs from magazines and then locate the vanishing points by extending the lines that are parallel. Where they cross is the vanishing point.
A straight line through the two vanishing points thus located shows on the photograph just how high the camera's eye was above the ground. This is the eye-level.
Any photograph of a building or a room can be used for this experiment. An easy method is to paste the photograph or clipping in the middle of a large piece of paper and then draw the lines right over the photo and paper.
A brick has six sides. Three of these can be shown in a perspective drawing. We draw a straight line to show where two sides join. Opposite edges are parallel lines.
A row of bricks placed end to end becomes a railroad track. All bricks but one can be removed, still we can find the eye-level and the vanishing point.
Draw an empty cigar box in perspective.
Show which of the sides are parallel. Which lines are parallel?
Draw the box, end-view in perspective.
Draw the box, side-view in perspective.
Find the eye-level and vanishing point of each of these drawings.CHAPTER 5
THE TWO VANISHING POINTS
THE "HEIGHT" LINES
THE TWO VANISHING POINTS
Place the brick flat on the table so that three of its sides can be seen.
Now we have three lines which can be extended, thus locating the vanishing point and the eye-level.
After locating the point and line turn the brick a trifle more.
This changes the vanishing point, but the eye-level is still the same.
The more we turn the brick the more the vanishing point changes, but always along the same eye-level.
Here is another set of parallel lines representing the width of the brick.
Excerpted from PERSPECTIVE MADE EASY by Ernest R. Norling. Copyright © 1967 Ernest R. Norling. Excerpted by permission of Dover Publications, Inc..
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Posted May 14, 2010
This book introduces artists to perspective projection, using one-, two-, and three-point projection examples. It covers much of the material covered by books that cost five or six times as much as this, so it has amazing value. It also will inspire works, no matter how you'd like to use projection in your art.
The complaint I have about this book, and the many other like it in this respect, is that it lacks any formality. In this reviewer's opinion, teaching certain aspects of perspective without formal justification amounts to heresy. Any inquisitive mind will be left wondering "Well, why do measuring points work that way?" or "How will moving the picture plane, station point, or vanishing points affect the drawing?" Unfortunately for the curious or formal-minded, they will have to seek answers to such questions elsewhere.
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Posted June 28, 2011
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