Perspective
 Recently someone emailed me asking me to explain perspective. I soon realised that explaining perspective in an email was like getting a marshmallow into a piggy bank but I did feel that I could explain the basics on a web page if I included lots of pictures. I am an expert in perspective drawing but not a teacher so please bear with me as I attempt to explain and please be patient as the page loads all the graphics. I will explain the technical aspects of perspective mainly to show what you should be aware of to make 3D graphics look as real as possible. I don't expect you to get out the drawing board and start setting up perspective points but being aware of where they are helps an artist get things ( in perspective ).

Points I will cover.
Reality and the way our subconcious mind alters the way we see it.
Single point perspective
Two point perspective ( 3 D )
Circles in perspective
Measurements are possible
The effects of distance on colour
Correctly sizing objects in a painting

Perspective, the way we use it in paintings, is really quite easy to understand but it is not reality.

Let me explain.

I learned technical perspective drawing as a young man when I used to draw and paint room interiors to present to customers.

This is a black and white photo of one of those paintings measuring about 36" x 24"

You will notice that all vertical lines are done with a set square and tee square and if extended would never meet.
This is what the human brain expects when looking at a normal painting and what we think we see when we look at the actual room
In reality all parallel lines do meet at some point if extended far enough, as far as our vision is concerned, because the farther away an object is the smaller it appears.
When we take a photo we often think that the camera has distorted the image because walls or telephone poles are not upright. PSP even has a perspective correction tool for this.
In actual fact the camera is right but our brain doesn't see it that way.
What the camera sees below is correct but I know that the 2 posts in the picture are upright and it upsets my eye to see them at an angle.

To correct this I used PSP and now it looks correct to me even if I am kidding myself.

Consequently

We can dispense with perspective for upright lines which makes things much easier to understand.

As I have mentioned all parallel lines, except uprights, will meet at some point so all we need to do is find that point.
For all intents and purposes we can say that the point will be at eye level which will be an imaginary line running horizontally through the picture, usually the horizon.

I am sure that you have already heard the railway track example when talking about perspective so let's get that out of the way right now and hook it up to our eye level.

Below is a picture of a railway track. I have superimposed lines showing how the parallel lines actually meet at eye level.

Now let us go back to that room drawing I did so many years ago.

When I started the drawing I first drew a line for my eye level ( horizon )and then chose where I wanted to stand in the room. ( At the right side looking down the room )
I made a pencil mark on the horizon at the correct place and then every line parallel to the side of the room had to go through that point.
Just like the railway track.

Now I am sure the more astute among you have noticed that the lines running across the room also slant towards some distant point far off to the left side of the picture.
Had I drawn those lines parallel the room would appear to grow in size towards the left side.
I went to a lot of trouble to get this correct in that picture but all you need to remember is that the lines will meet eventually and they meet at eye level.
This happens because the room is a 3 dimentional box having height, width and depth.
The height we have already dispensed with ( we ignore it ) but we then need 2 points where all other parallel lines will meet.

These points will be on the horizon line but the position along that line decides how we look at the object.
If the points are equal distance to right and left we are looking at it directly from the corner.

Closer to one point or the other turns the object around.

The distance between the points makes the object appear closer when the points come closer together.

That pretty much takes care of the technical basics although you do need to know that a circle in perspective is a perfect ellipse.

 I remember drawing a room with circular recesses in the ceiling and after positioning squares where they should go I asked my boss how a circle should be drawn in perspective. He told me it was a perfect ellipse bounded by the lines I had set up. As usual my mouth started before my brain was in gear and I asked him for the technical proof. He didn't know so I set out to prove it myself. Over the next few weeks I spent many hours trying to figure this out and finally had the answer which was something Pythagoras would have been proud of. Believe me you don't want to go there but take my word for it a circle in perspective is a perfect ellipse no matter how you slice it although it must be tilted to fit correctly.

One of the nice things about PSP and other graphics programs is the ease with which you can draw an ellipse. In Selections or Preset shapes you can make a perfect ellipse as easily as falling off a log.
Anyone who has attempted to draw an ellipse with a pen and paper knows what a technical nightmare it is.

The only thing to control with a perspective circle is how flat it will be and the tilt if needed.

Take 3 ellipses of different heights.

Move them into position with the flattest at the top.

And you have a perspective drawing of a hat box.

Measuring

Measurements are possible but unless you are drawing a row of houses or something like that you will probably not be trying to use this.

It all hinges on the fact that we can measure the first vertical line we draw.

For simplicity let us draw two boxes spaced the same distance apart as the side of the box

First we draw our horizon and then a vertical line as the front corner of the closest box.

Now place 3 points on the vertical equal distance apart.

Join these points to perspective points on the horizon

There is a very complicated way to measure this next point but I find it much easier just to use my eye and make it look right.

Draw 2 vertical lines making the lower two lines into a box.

Now by drawing a line through the corners of that square we find the position of the next square on the line above.

Do this again with the next square you just created to find the back of the second box.

The measuring is now all done and all other corners of the boxes can be found by intersecting perspective lines like this

Strengthen the lines you need and erase the perspective lines and your boxes are complete.

The circle on the side of the first box is a perfect ellipse.
The trick is to tilt it so that the closest part of the ellipse is in the correct place.
In this case the top needed to be close to centre ( In perspective of course )

More complicated variations of this can be used to measure points anywhere in a perspective drawing.

I have shown you this to show that perspective has rules and can therefore be controlled.
When creating art work you need only be aware of these rules to keep everything looking correct but it is good to know what you are looking for.

Perspective Colouring in painted landscapes.
The air we breathe is not invisible.

Easy proof that air is not entirely invisible can be found by looking at a blue sky.
If air was fully transparent the sky would be black as it is in space.
I am not sure how to tell you what colour the air is because it is connected up to light refraction and doesn't really work the same way in PSP but you can get an approximation by doing this.

The sky is actually bluer than this but it shows why the sky overhead is deep blue ( looking through less air ) and the sky at the horizon is much paler ( looking through lots of air ).
Knowing this it becomes obvious that distant hills or mountains are a pale blue/gray while at close quarters they may be deep green, brown or countless other colours depending on the mountains or hills themselves.

Notice in the picture below the colour of the foreground trees.
The not too distant mountains behind are covered in exactly the same trees but have become blue/gray in colour.

A setting sun does turn distant sky and hills orange but it is much more pronounced when there is a little light cloud ( or pollution ) in the air making the air even less transparent.

I realize this has been a very simplified and short explanation of perspective but if you know only this you will be able to produce lifelike graphics.

All that remains is to show you how I set up perspective in order to place images in PSP.

We will start with the picture I used above, add a removable layer called perspective and draw our eyeline across.

Now on another layer I'll add a family picture and on the perspective layer draw a line across the field from his feet.
Another line from the new perspective point to his head.

Now I'll add 3 more layers with the same picture but reduce them in size 70%, 50% and 30% respectively.
Move the new layers so that the feet are on the line and the head touches the upper line.

Now all four images are in perspective standing on the field.
Naturally you would be adding some shadow etc. to make them more real but the perspective is correct.

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