Rob Adams a Painter's Blog painter's progress

April 20, 2011

Windows in Perspective part 1

Filed under: Drawing,How to do,Perspective — Rob Adams @ 1:41 pm

In this post I want to cover how you put windows into a building or find the next one on a long line of telegraph poles. There is some geometrical construction but not I hope much more than joining up dots. The there is certainly no algebra! Poor perspective is one of the most common faults in paintings either painted from imagination or life. Unfortunately any viewer will feel that something is wrong even if they don’t quite know why it doesn’t quite work. These little tutorials are aimed at painters or other artists who need to get it right enough to make the viewer comfortable with what they see not really for architects who need to get things spot on. To this end I am starting as simply as possible. I am assuming the reader knows the absolute basics such as lines join up at the horizon at what is usually termed the vanishing point and that the horizon is always at the viewer’s eye level. I will cover these very basic topics in the future but not in these posts. I am doing the first section in a back to front way in that I am starting with a row of telegraph poles and then showing why they are in the places they are and the basic principles that caused them to appear in those positions. So, off we go.

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perspective, drawing, tutorial

Here is the only geometric construction we are going to use in this tutorial. If you draw a diagonal cross from corner to corner (the red lines) of a square or rectangle then they will cross at the middle point. If you draw the green lines through that middle point then it will divide the original shape into identical quarters. The blue line shows that you could do this again and again chopping the rectangle into ever smaller pieces. If you think of the black rectangle as a window opening then the green line might be the window bars separating the glass panes.

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perspective, drawing, tutorial

So here are our telegraph poles evenly spaced running off to the horizon. You can clearly see they get smaller as they get further away and the spaces between them get narrower too. But what exactly controls why each pole is in the place where it looks right to the eye. I have made a black mark on each pole which is halfway up. So next we will draw some lines over the picture to find out.

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perspective, drawing, tutorial

First thing is to mark the Horizon with the blue line. The Horizon is always at eye level. If you are painting outside then if you hold a brush horizontally close in front of your eyes it will lie along the horizon. If you are working from a photo, say of buildings, then if you find a window ledge or other level feature that is aligned with the top or bottom of the picture and neither slopes up nor down then that is also the horizon. You can also join up the tops and bottoms of features such as the poles above to find where they meet and that is once again the horizon level.

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perspective, drawing, tutorial

Here I have done just that with the black lines. We learn something else from this as well and that is the Vanishing Point which defines where all the tops and bottoms of our poles is. Next we use the Geometry rules in the first diagram to see what is going on.

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perspective, drawing, tutorial

Here I have drawn a red line through all the centres, note it also meets at the horizon an all horizontal lines will always do. Then as in the first Diagram I have added a blue cross. As you would expect the lines cross on on the red line. If you wanted to add a post exactly between the first two where the blue lines cross is where it would go.

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perspective, drawing, tutorial

Now here is the clever bit. Look at where the green line goes. Because three posts together make a big rectangle with the second post in the middle the green line will always cross at the middle of the second pole. This means that even if we only have the first two poles in our drawing we can find the right place for the third pole, it is always where the green line hits the top black line. Once we have the second and third pole we can then use them to find the fourth pole and so on until they are too small to see.

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perspective, drawing, tutorial

Here I have drawn a few of them in to show that it really will carry on finding the pole positions until the horizon, though I would start guessing long before that. In the next part I will show how you use these very basic methods to put windows into a building. If anyone finds anything unclear please comment and I will either answer the query in a comment or update the post if  others have the same difficulty.

Part 2 is here.

April 19, 2011

The Problem With Columns

Filed under: Drawing,How to do,Perspective — Tags: , — Rob Adams @ 12:42 pm

This is the second of an occasional series of posts about perspective. Many people believe that geometrical perspective, single point, two point and three point are actually an accurate representation of what we see. Cameras see in this way after all so it must be right mustn’t it? Well actually no, it is a compromise as are all methods of making our very three dimensional world fit conveniently on a flat surface. Here I am going to deal with a very old problem that perplexed Renaissance artists as they struggled to find solutions to the problems of illusory painting. Vredeman de Vries and other artists published learned books full of geometrical construction but certain problems seemed impossible to resolve. Columns were a big feature of architecture of the time and they often occurred in long arcades, perfect fodder for the perspective method you would think. However it turns out that round columns are exactly the type of object that causes the neat geometrical rules to fall apart. What I intend to do here is highlight the issues as clearly as I can and then point the way to the various solutions that later artists arrived at. It is a sad fact that all modern books on perspective that I have seen do not even seem to realise that the issues are there, let alone giving any practical advice to overcome them.

 

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perspective, drawing, tutorial

Here we have a plan view of a simple set up consisting of a row of columns, a cube and a green triangle which marks where our viewer is standing. Below is what we get if we construct using one point perspective what that viewer would see.

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perspective, drawing, tutorial

Well here we are, at first glance it seems sort of OK. Look more closely though and we have some problems. In our plan we can clearly see that all the columns are the same size. That does not however seem to be the case in our perspective projection. The column on the far left is a lot wider than the one straight in front of us. Worse when we look at the plan the far left column it is actually further away from us and should appear smaller not larger. Something is plainly awry. Looking more closely still the base of the far left column seems oddly tilted. This is exactly the result a camera would give on a fairly wide angle lens giving a viewing angle of about 70 degrees. So when you wonder why you looked so fat in that group photo this is the cause and in future you would be best to make sure you are in the middle  of the line! Lets take another case.

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perspective, drawing, tutorialHere is the plan of a simple set up, as before the green triangle marks our viewpoint. We often get rows of things receding from us, looking down a romanesque church nave would be an example. Below is how traditional two point perspective renders the scene.

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perspective, drawing, art, turorial

Once again at a quick glance it all seems well but a closer one shows that the left column again shows problems. These are clearer still when we isolate that part as in the green circle. There is a weird tilt which is plainly not how we would really see the base of such a column. If you then tried to add capitols and bases you would find it very hard to get them believable. Below is an example from an old perspective manual by Jan Vredeman de Vries printed in 1599.

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perspective, drawing, tutorial

As you can see the problem is still present, and remains over the centuries up to the present day. This is because there is no right way to solve this problem. Whatever we do it will still be wrong. The trick is to be pragmatic and make the unavoidable departures from how we really see the world as subtle as possible. Lets look at the dilemma more closely.

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perspective, elipse, drawing, tutorial

Here is our old enemy the ellipse, I won’t go into how to construct one as there are many methods freely available on the web if you are interested. In the real visual world as seen by our eyes when, for example, we look at a coffee mug on the table or any circle that is parallel to the ground, the major axis of the resulting ellipse is always parallel with the horizon line. Try it, put a plate on your table and slide it around. But cameras and 2 point perspective construction produce ellipses that have the major axis tilted. It is this that produces the odd distortions. All we can do is come up with a compromise, a sleight of hand adjustment that is not perfect but improves the believability of our drawing.

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ellipse, perspective, drawing, tutorial

Here is a circle constructed in two point perspective. The problem is that cross and the ellipse with it need to be parallel to the horizon line to look right to the eye. Yet at the same time it needs to fit into the blue box.

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ellipse, perspective, circle, drawing

Here is our compromise. The winners are the ellipse which is now properly aligned to the horizon and also a wee bit narrower to correct for the first problem of “fattening”. The losers are the chequer board floor on to which the column no longer perfectly fits. But as you see the mis fit is quite small and far less worrying to the eye in my opinion. Below is the correction applied.

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It would be easy to tweak the lines of the floor to make the adjustment less noticeable, but I have left it alone as it shows where the changes have been made. Returning briefly to the very first example of the over wide columns left and right one solution here is to make all of the columns the same as the central one. Again a compromise that may throw up other problems but a good starting point. Chequer board floors of course make the whole problem worse. When I was designing for television advertising I once put a chequered floor into a shot that was to be filmed on a wide angle lens. The cameraman was not at all happy and the Director made me paint it out! The next instalment on perspective matters will be how to place arches, doors and windows into buildings in a scene by a few rule of thumb tricks.

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