Learning perspective

How to use perspective.

Although we live a world with three dimensions, you only have two dimensions when drawing a picture on paper. The third dimension, the one that will give depth to the painting, sketch, draft or whatever is created by using the rules of perspective. Even if you are only sketching still-life objects on a table, you'll need to understand and master the principles of persepctive. Learn the difference between a plan, elevation and perspective.

Compare the human eye to a camera.

A guide to drawing perspective

• Viewoints
• The horizon
• Planes
• Altitude
• Angle of view

Drawing objects which are parallel in a landscape. How subjects move from the foreground to the background to give depth.

The visual ray and principal point, the horizon line, plane, natural horizon, vanishing point, viewpoint are some of the terms used in perspective.

Here are three views of a shed - seen from above, face on, and a three-quarter view. The first drawing is seen in (plan) outline, the second is (an elevation) elevated and the third is in perspective. In the first picture we can make out the vegetation but we can't recognise the chimney or rather (determine) the height of the chimney. In the second picture, we can appreciate the height of the chimney but it is difficult to grasp the exact position of the vegetation. The last picture shows as much as the other two put together, but what really counts is that this is the only drawing which gives a certain sense of depth, the impression that the hut is in right in front of you, that it has a certain reality about it and that it takes up a certain volume in space.

Do you like grammar? Neither do I! Nobody - apart from the odd specialist - is particularly interested in grammar. We accept that it helps us to express ourselves better (provided that we don't have to reach for the grammar book before we dare open our mouths)! We conjugate verbs and construct sentences entirely automatically and without thinking about it. We're able to do this because we've listened to these same grammatical constructions literally thousands of time.

It's much the same thing with perspective. In itself, the science of perspective is of little interest to most of us. We are only interested in it insofar as it can help us to draw better. In other words, there are two ways of approaching perspective: the scientific or theoretical way and the practical way. With the theoretical approach, you'll learn a set of abstract rules and you can be sure you'll very quickly get bored.

So of course I suggest that we approach the question of artistic perspective from a practical point of view. All you have to do is to observe what I show you with a minimum of attention and you will learn the secrets of perspective quite naturally.

It would be possible to do without perspective but it would be a great pity. Perspective is the most powerful way of lending realism and depth to your drawings and of making them more striking. Without perspective, the means at your disposal (your results) would be limited. Here's why.

Perspective is a hidden but vital element of a landscape, an object or a portrait. It is in fact an optical illusion that applies to everything you see. Remember that drawing is not the same as sculpting. The challenge facing you is to reproduce on a flat sheet of paper something which in fact possesses a third dimension: depth. I repeat, perspective is merely an optical illusion applied to everything you look at. That's why we need to know a little about how the eye works.

Historically, it was some time before artists came to terms with perspective. A lot of medieval works of art are very beautiful but they show things as they are and not as the eye sees them.

You can see the logic at work in this illustration. The chessboard is seen without relief but the pieces on the board are seen in profile and turned in the direction in which they are set up on the board. The capitals of the columns are practically represented in cross-section. And the women are rather curiously positioned. In other words there are several different "points of view" in the same picture, and it's rather off-putting.

This Turkish miniature dating from 1720 is another example of a partial lack of perspective. Once again, several different points of view are merged into a single picture. And we notice that that the horses furthest away are as large as those in the foreground. In perspective they would, of course, be smaller.

How the view deceives the eye This winding road seems to get smaller and smaller as it moves away from our point of observation. In actual fact, of course, the width is always the same - otherwise there wouldn't be enough room for the cars! Looking at this picture, we get the impression that the two rails will end up by joining together. Visually speaking, this is true, but visually speaking only. Reason and the eye are engaged in an endless combat Reason tells the brain: "These rails are parallel and horizontal". The eye says to the brain: "As you can see, the rails climb towards the sky and become thinner towards the top". The brain replies: "The rails are always parallel otherwise the trains would be derailed. But I don't want to use my reason. I want to draw so I'll listen to what the eye tells me. As you'll see, it's always difficult to forget our knowledge of things when we try to transcribe them. And yet we must learn to concentrate exclusively on visual perception. You are confronted by a landscape, stretching out before your eyes towards the horizon. Your brain registers the depth which moves from the foreground into the distance. You have no problem in placing what you see to your left and right onto the left and right sides of the sheet of paper. But how are you going to render the depth?

Here are three suggestions which you can use separately or together. 1. Draw the trees close to you in front of those which are further away - this will have the effect of hiding part of them. 2. Draw the trees further away from you more lightly; this will give an effect of distance. 3. Draw the trees in the distance smaller than the ones close to you. Don't make a special effort to remember these three tips; just observe how they are present in this drawing.

Look at this picture for a moment. This time it's an indoor scene and there's a certain impression of depth. We might even suppose that the artist was situated just a few feet from the figures. Can you see how the three ideas I mentioned above have been incorporated in the picture so as to render the depth?

Is the outdoor scenery painted in more lightly than the rest of the scene? Yes. Do the figures in the foreground partly conceal those further back? Yes. Are the figures further back smaller than those in front? No, not at all. The size of the figures is dictated solely by their age and build.

It's the perspective which gives the impression of depth; it represents the room not as it really is but as the eye perceives it. Drawing in perspective is really the art of drawing "wrong" so that the (end) result seems "right". Or to put it another way, it's the art of closing one eye so as to see better. Let me explain. First of all, let's take another look at the picture. You'll be able to make the same observations in a minute when you look round the room you happen to be in. The walls are at right angles to each other, there's a window with small panes, a door and a tiled floor. Look at the lines formed by the edges, the ridges and the corners of the walls and windows, or the stone tiles. The lines are for the most part vertical or horizontal and are perpendicular to each other. This is perfectly natural since the architect has designed everything at right angles, and the builder has used a plumb line, a set square and a spirit level in order to respect the architect's plan. It would really be too good to be true if things were as easy as that for the drawer.

If you superimpose a piece of tracing paper marked with white horizontal lines on the picture, and then trace in blue the vertical lines visible on the picture, you will notice something rather curious. The vertical lines are indeed vertical. But the horizontal lines in the picture are quite different from those on the grid. They slant off in different directions. The artist has distorted the objects by using these diagonal lines to put them in perspective. But how are you going to attack this problem when you have to deal with this kind of drawing?

Grasping the idea of perspective

Try to imagine the problem from the point of view of a blind man. He cannot appreciate the depth of a place unless he has actually been able to move inside this space. Unlike those of us blessed with sight, he does not have the ability to, as it were, "travel with the eye". If someone blind from birth were suddenly able to see, he would have the horrible impression that everything was being thrown at his face. But while a blind person cannot drive a car, a one-eyed man or woman certainly can. In other words, having only one eye does not stop one from appreciating the depth of a place or the distance separating, for example, two cars. Three-dimensional vision is not the only way of receiving information about depth. We might say that a one-eyed person driving a car "reads" the depth in the perspective whereas you, when you draw, "write" this perspective in order to give the illusion of depth. The procedure is virtually the opposite.

Perspective passes through an incredibly sophisticated piece of photographic equipment - your eye. Just think of it: the film can be reused as often as you like, the memory card is built-in, the connections are supplied, the shutter is sensor-controlled and the viewfinder (system) is automatic! We are in fact incredibly lucky in possessing a dual system with all the advantages of 3D vision. But 3D view - the result of the merging of two different images each received by an eye - is not the same thing as view in perspective.

You can link up a printer to this wonderful camera. It consists of a piece of paper, a pencil and your hand. Once again everything is pre-installed!

Now all you need is a good software program to drive your equipment. Day after day, you will become more proficient in operating your own software. Learning to draw is really a questioning of exploiting your software. And very soon the software will be guiding your hand intelligently and accurately.

Before a person makes a speech in public, he tries to find out something about his audience. Before take-off, a test pilot carefully studies the configurations of the aircraft. In the same way, we are going to embark on a little conducted tour of your eye. It will be time well spent!

The objective eye

Things sometimes take a curious turn. The camera took its inspiration from the eye. For a long time people thought it would never be possible to incorporate the eye's automatic focus system in a camera. Yet nowadays this is a feature of even the most basic cameras. What's more, cameras are neither short nor long-sighted. Could it be that the pupil has outstripped the master? One thing is certain: most people know more about the working of a camera than they do of the eye! Simplified and exploded view of a camera

Look at this representation of a camera. You see all the main elements: the objective and its lenses, the diaphragm, the camera obscura and the film.

Simplified and exploded view of an eye

Now look at the eye.

Here we find the lenses (the cornea marked 1 and the crystalline lens marked 3), the diaphragm marked 2 (the iris and its pupil), the camera obscura (the upper chamber and the vitreous humour, here marked in orange) and lastly the film, marked 4 (the retina). The reversed image is projected onto the film after the crossing of the rays at the focal point The principle of photography

An object illuminated by light sends rays to the objective. A film sensitive to light is situated in a camera obscura or dark room situated behind the objective. It is marked at the point where it is reached by the rays of light. The rays start by passing through a series of lenses. Obeying the laws of optics, and after meeting at the focal point, they transmit to the film a reduced and reversed image of what was seen in the eyes of the objective.

The reversed image is projected onto the retina like the sensitive film of a camera The eye works in the same way. The rays pass by the iris, cross the crystalline lens and come up to the sensitive retina. The image is reduced and reversed.

The focal point moves according to the shape adopted by the crystalline lens. As long as the lens remains supple we enjoy good eyesight

In a slightly different way to the camera (even an autofocus camera), focusing is carried out by deformation of the crystalline lens (A). The system used to give the image sharpness is too complex to describe here, but the end result is to modify the curve of the two sides of the crystalline lens, thereby varying the focal point and not the distance separating the lens from the sensitive part to be acted on: the retina.

The retina is merely the development of the optical nerve swallowing up visual information

But here's the most extraordinary part. Our eye has no need of consumables such as a film. Everything works like a digital camera. The retina serves as a film and is lined with tens of thousands of sensitive cells: cones and rods.

This complex, completed by cells and nervous fibres, sends information to the processor, in other words our brain. How is it sent? By radio? No, it's a cable connection, for the retina is simply the development of the optical nerve. This nerve swallows up the information rather like a funnel. But it has a little defect! The retina is simply the development of the optical nerve which swallows up the visua information. À couper je pense ?

A camera film is flat whereas the retina is curved. Fortunately the brain deals with all that without much difficulty. There is, however, a little snag. The retinal surface has not kept the same sensitive properties in the bottleneck where the retina becomes a tube. This is an area where our eyes do not see, where things are hidden from us.

If you don't believe me, here's a little experiment you can try. This experiment designed to expose the blind spot can also be tried after printing out this page

Cover up your left eye and look at the snow crystal with your right eye. Focus on the crystal and you will make out the star. Now move your face fairly slowly closer to and further away from the screen, all the time looking at the crystal with the right eye. At a particular moment the star disappears completely. It is in the retina insensitivity zone. The symmetrical experiment is just as conclusive. The retina has another zone which, as though to console us for this infirmity (disability), is fitted with improved sensitivity. This is the macula. The macula is lavishly provided with cones and takes better "photographs" than any other part of the retinal surface.The quest to find the laws of perspective gave rise to the (an) experiment with the interposed glass pane. The experiment took place at a time when photography was still unknown

The experiment is known as "Leonardo da Vinci's window". In this photograph, taken in 1890, the artist views the perspective of the mulberry tree ou on garde le nom français ? courtyard of the Paris School of Fine Arts. By placing a pane of glass vertically in front of you, closing one eye and keeping your head very still, you can trace the contour of what you see, just as you would trace an image already reduced to two dimensions. The fact is that when you close one eye, all effect of depth is crushed. So what you get is a perfect drawing in perspective without knowing the slightest thing about the theory of perspective! When masters like Leonardo da Vinci and Dürer studied the results, they noticed that certain lines, in reality parallel, sur la vitre converged towards the horizon, while others remained resolutely parallel to each other.

Of course, it wouldn't be very practical to set up a glass pane every time you wanted to draw, so we'll make do with closing one eye and paying careful attention to what we see. This will be enough to get rid of any effect of depth. When you close one eye, the real world becomes an image in exact perspective which you can use for your drawing. A photographer doesn't complicate things by worrying about the rules of perspective. What was far or near in reality paraît is far or near in his photo. The easiest way to understand perspective is from a photographer's point of view, the difference being that you don't actually need a camera, just your eye.

Stand in the corner of a room and turn round to face towards the middle. Stretch out your arms and hold the two ends of a ruler horizontally in each hand. Close one eye and "take a photograph" with the other one. Don't move your eyes and move the ruler over the photograph , taking care to keep it horizontal. You see that the horizontal lines are biased and slanting just as in the picture we studied a moment ago. How many lines which are horizontal in reality still seem horizontal with one eye closed? Almost none. So all you have to do is to transpose your observations as faithfully as possible onto your drawing paper. You can't go very far wrong as far as perspective is concerned.

At the outset, it's always easier to draw a subject which exists physically in front of your eyes. In this way you can observe and take note of measurements, proportions and angles. But very soon you will want to draw from memory or your imagination and here your knowledge of perspective will come in useful. If you have encountered a sufficient number of different situations you will know how to avoid the tricks which perspective will try to play on you. I promised you that I wouldn't bore you with a lot of rules. But in this case I must at least show you the dangerous corners, where perspective lies in wait for you and tries to spoil your drawings…

How to give an impression of depth

Several "tricks of the trade" work very well in drawing. You have already observed some of them such as the superimposing of two drawings, the use of shadow, relief and of course perspective. It is also possible to combine several methods. The two most often chosen by artists are relief and perspective. When used together they can lend an astonishing impression of realism to a drawing. See if you can find the different means used in these vignettes.

Visual ray and principal point Wherever you look, you "cast" a visual ray in a direction. The ray travels in a straight line from your eye to the centre of the image it perceives and moves with your eyes. Take aim with an imaginary rifle on a target. The visual ray corresponds to the trajectory of the bullet. The point where the bullet reaches the target is called the principal point.

Your vision is more or less conical. That is to say, when you look in a particular direction, the width of your vision is no more than 20 centimetres or so in the foreground , and a few hundred metres in the distance. The further you look, the wider the field around the principal point. Depending on the orientation of our visual ray, objects appear distorted to our eyes, obeying the laws of optics and perspective.

This sketch, which is deliberately short on detail, shows that the same distortion of perspective is perceived when looking at a railway track or ladder as it appears to us when stood upright against a wall, aiming towards the highest rung. The ladder is vertical, the railway line horizontal but their transposition in perspective is exactly the same. Here is the essential point to grasp: an object is distorted not according to it its position in space but according to the angle by which the visual ray reaches it.

So when you begin a drawing it is important to work out the height and orientation of your visual ray and to keep to it. This means choosing a single point of view. If you overlook this point and combine several points of view, your objects and figures will appear very awkward.

Imagine a horizontal disc centred around your head at eye level and stretching into infinity. This disc gives expression to a major element of perspective: the horizon plane.

The horizon plane is an imaginary line situated at eye level and stretching into infinity. It is marked in red in these three illustrations.

You would of course only see a section of it - a horizontal line spread over 360°.

This line is called the horizon line. Now suppose you transport yourself - along with your imaginary disc - to a coastline. This is what you would see. You would notice that the line exactly divides the landscape between the sky and the water, merging with what we usually call the horizon. While we're at it, let's continue to use our imagination a little.

Climb up the tallest coconut palm on the island and see if the natural horizon has now passed below the disc which you have kept at eye level. You will notice that this is not the case. The horizon, the horizontal plane, the horizon line and your eye rise and fall together. The thing to remember is that the horizon line is always situated at eye level.

It is the same with a photograph. The horizon rises with the camera.

Here are two images of the same scene. The first picture is seen by a spectator (you) whose eyes are at the same level as the figure on the right. So the two horizon planes are merged.

The second image places the observer higher up than the first one. This time, your eyes are at the level of the higher figure. The horizon plane is still merged with the natural horizon which seems to have risen at the same time as you - but be careful!

The draughtsman's horizon plane, linked to his viewpoint, determines the height of the natural horizon. If other figures are placed below or above, they see the horizon higher up or lower down.

When you choose the height of the horizon in a drawing, you impose a point of view on anyone looking at the picture. Your choice will determine whether the spectator is in a dominant situation in relation to the subject. Look at these pictures. Try to feel the secondary effects due to the choice of viewpoint. Sharpen your artistic sensibility by trying to analyse what has an impact on you. Feel how the choice of viewpoint leaves an impression. In other words, think about the relation established between the subject (the actor) and you (the spectator). Don't worry if it is not immediately clear to you. Your perception will gradually gain strength as you exercise it.

Here, you dominate the figure represented but in a somewhat benign way since you are looking down on him. However, his position at the centre of the picture gives him a certain importance.

This viewpoint creates an impression of confrontation between the figure and yourself. The centred composition, the horizon line placed at mid-height gives the picture a symmetry which removes the human aspect apparent in the preceding image.

This time, with the viewpoint below, the figure dominates you. He has gained a certain ascendancy over you and you seem to be in his power.

The same situation, but this time with an off-centre and very low-angle view, leaves a different impression. The figure still dominates but you yourself are not under his domination, or at least not as much as in the preceding image.

So you see, perspective is not just a tool for representing something accurately, it is also a means for enlarging your artistic vocabulary. Le cadrage Don't confuse viewpoint with composition. The same scene, viewed from the same place, can be centred differently as a matter of aesthetic choice. The viewpoint determines perspective distortion whereas the composition selects the surface exposed to the eye.

Here are three different compositions or frames of the same picture. The result makes us feel that we are looking at three different images.

And yet the viewpoint is exactly the same.

The red line represents the horizon plane of both the figure and the spectator. The horizon plane is at the same level in all three pictures.

The framing is no more than a purely aesthetic choice of presentation or composition. Take a look at this picture. There's something special about the perspective.

The vertical lines formed by the edge of the wall hanging, the side of the dresser and the axis of the clock remain vertical in perspective. So far so good.

The lines which are horizontal in reality, the two unoccupied sides of the table, are still horizontal when put in perspective. Is this a coincidence? What do you think?

All the other lines which are horizontal in reality, such as the shelves of the dresser and the left and right side of the table, are at an angle in the painting. What's more, they all converge on a single point. They seem to be receding towards a precise point of the horizon. That's why this point is known as the receding or vanishing point. It is exactly at the level of the painter's eye, i.e. at the level of the natural horizon. If the wall in the background were transparent and if the house were beside the sea, the sky and the sea would indeed be separated by the red line. And this would be the case whether the house is situated on the beach or on top of a rocky coastline.

The question is, then, what is special about this perspective view?

The artist has chosen a frontal view for this picture. If we are to understand the impact of this choice on the perspective we need to do something: we need to establish the plan of the room.

Here is the basic plan. What do you notice? You see that all the items of furniture are parallel to the walls. The artist, whose visual ray culminates at the red point, did not take up a position in a corner but squarely opposite the wall at the back. He could have placed himself in a corner and have his visual ray culminate at the same point. If he had done so, all the articles of furniture would have been presented to him by an angle and not by a side. So here the artist has chosen to present all the sides of the objects and the walls either at right angles to his visual ray or parallel to it, but never diagonally.

In a frontal view, the perspective is said to be "parallel". We note also that all the lines parallel to the visual ray converge on the principal point. This time we can call it the vanishing point since it fulfils the two roles simultaneously. All the other vertical and horizontal lines, perpendicular to the visual ray, remain vertical or horizontal once placed in perspective. It's quite simple really.

Now you have a plan and a horizon line. You know where the principal point (which is also sometimes the vanishing point) is placed. So you will now be able to build a very simple scene in which you can put your newly acquired theoretical knowledge into practice.

You are going to draw an object which is familiar to us all - a shoe box. You notice I use the simpler and more expressive word "box" rather than "regular parallelepiped".

You want to put this box in perspective so that you can show the three dimensions in a single picture. Your drawing will unquestionably appear more solid, more constructed, if you bear in mind what you know about the viewpoint. For an accurate representation of the scene, you will start by choosing a viewpoint. You want the box to be just in front of the spectator but slightly lower than his eyes. The box will be below his horizon plane, lower than his eyes, and therefore under the horizon line.

Seen from the side, the box is placed slightly under the visual ray. So you will see the top but not the bottom, the front but not the rear.

When you look at the scene from above, this is what you see:

• the visual ray linking the eye to the principal point passes through the median axis of the box
• the right and left sides of the box are parallel to the visual ray
• the front and rear sides are perpendicular to the visual ray

You have all the necessary knowledge for building up this perspective.

Lines remaining vertical or horizontal Receding lines, parallel to the visual ray The box is seen face on and is therefore in parallel perspective. In such cases, as you already know:

• the vertical lines will stay vertical in the drawing
• the horizontal lines perpendicular to the visual ray will stay horizontal
• the horizontal lines parallel to the visual ray will all converge on the principal point; they recede towards the horizon hence their name "receding lines" or "vanishing lines"

Now look at the box and you will see that it corresponds perfectly to these criteria. The horizontal lines remain horizontal or recede in relation to the visual ray. The vertical lines remain vertical.

Now what would happen if we moved the box to the right or the left or even up or down? Lines remaining vertical or horizontal Receding lines, parallel to the visual ray

If you did this, one of the sides would appear and the others would disappear, but as long as these movements are not accompanied by a rotation of the box, the same rule applies.

La perspective angulaire On the other hand, if you were to rotate the box on its vertical axis, things would change considerably. Here, new rules would apply since you would be leaving the world of frontal perspective and entering the more complex realm of angular perspective. We shall in fact shortly be exploring this notion.

Lines remaining vertical or horizontal Visual rays Receding lines, parallel to the visual ray

Now take a look at these three pictures. The outline view emphasises the sides parallel to the visual ray (in turquoise blue) and the sides perpendicular to it (in yellow). As you see, the box can be centred on the visual ray or moved to one side or the other.

The visual rays traced in blue help us to understand which parts of the box will be visible on the drawing Next, here are the three possible positions for the box in elevation: above, on and below the visual ray. Three times three makes nine, so there are nine types that you are going to come across regularly.