Sorry for the long wait! I didn't mean to leave it quite this long. Homework after work takes quite a punch. Or perhaps is one.
Today, I'll cover perspective, as promised.
I'll be covering it basically as described in Ernest R. Norling's classic book Perspective Made Easy, which was originally published back in 1939, and has been a staple in schools for a long time. It's a recommended quick and easy reference book, and is not even very expensive. Just 13.50$CAN. As well as looking at some actual examples from a recent name that was done by myself.
Perspective, if you've ever looked at planning sketches of Leonardo Da Vinci and things like that, can get pretty mathematical, but it doesn't have to. Since there's a lot of step by step books on the market, I'm going to jump around a bit, and fill in some real life examples and such, define terms, and underline some stuff that was perhaps not entirely clear to me way back. It's a tutorial, so I'm going to fill in the role of tutor on this one. Buy a good book specializing in this to become a master. The one I listed is the cheapest, and comprehensive too. Or look around and find one that suits the way you think.
First, let's define some terms. First, we have the horizon. That's pretty simple. Keep in mind that even indoors, there's a horizon, which we call the horizon line. This is where you're going to place your vanishing points. This is a, or multiple spots on the horizon where everything points to. There's no limit in a picture, depending on what it is, to how many of these there can be, but most pictures have one, two or three-point perspective. An example of infinite-point perspective might be a mass of floating balls. Seeing as you can just draw circles and shade them, I think infinite isn't very practical, more mathematical... Anyway, finally eye-level. This is the level at which the 'camera' or the viewer's eyes are at.
Let's look at an example.
Eye-Level - Ernest R. Norling
The term eye level was new to me when I was looking for solid material for this particular tutorial (I talk through my hat only when I can't find material, or you surprise me -_- ). I tend to do a lot of my perspective intuitively because it's one of the first things I learned and I'm very used to it. I had a very textbook development... In any case, it may be new only because of the reference to the eyes - these days, it might always be called 'camera'. So, you might think, what's the point of this if the drawing's all in on a sheet of paper anyway? Why do I have to figure out where I'd be standing? So eye level is a bit confusing, if apt.
A camera, because it takes pictures which become flat, is a bit easier to understand. Though these days cameras are not held at eye level any more as a rule.
The thing to remember is that the horizonline and eyelevel correspond. Norling was very particular about this point in his book, and I had never really thought about it. I suspect this fact may further helping me out in the future.
Now that you know about the parts, let's see about constructing an image. The image above is one-point perspective. Note how lines point to a particular place. If there were power lines on one side of the track, how do you think they would be drawn? The tops of these power poles will be over the horizonline. That means that the invisible line from the top of one pole to the next, the next the next, would in fact point downwards. I'll draw it in. I'll need this in colour due to all the ink the guy has in this drawing... Witness my Photoshop drawing skill!!
Let's add poles
I eyeballed the bottom part, and when I was done, I noticed perhaps I shouldn't have. Take a look at the second pole.
Mistake demonstration
For me, eyeballing is much harder on the computer, and high contrast doesn't help. Either way, it's a lesson that even something slightly off can harm the authenticity of your drawing. Knowing how to use perspective can save drawings, often those where you're not sure what you did wrong.
On paper, my method frequently is to draw roughly what I want to see, find the approximate vanishing point, then rework everything to fit nicely into it. It's hard to think of your vanishing points first, place them down pre-emptively and then have your image still match what you saw in your head, so I would say that after practice with camera angles, drawing roughly first then cleaning up is the easiest way to go about it. But this is where those thumbnails and name come in. Let's look at some very rough work. It's not the example I was thinking of, but I don't have the vast majority of the work here with me at my home. So, let's look at a different page.
Bugger Pg 10 - Name
The example's panels read from left to right.
Okay, not the best work ever, but it demonstrates a few perspectives, which I made using the method I described above. I sketch roughly what I want to see, then draw rough perspective lines that help me keep everything in line. On actual manuscript paper then, I would start strait away with perspective lines, now that I know it will give me what I want to see.
The first panel is two point perspective. This is an example of something called warped perspective and is something you're technically supposed to avoid. However, I wanted the paper to have that particular shape in the panel. Makes it a bit more interesting. There will be signatures on the bottom, and it makes it look a little bit more like the reader's eyes are very close to the surface of the paper - enough to skew his vision. Hold up a pencil box very very close to your eye, similar to how the paper is positioned in this panel. If you were to draw it just how you saw it, it's nothing like a rectangle any more, is it? It gains a strange teardrop sort of shape. Lots of things in our world warp like this when veiwed, but our brains compensate so that you never really question the actual shape of the object. You didn't think at any point that it was an oddly-shaped paper on the table, did you? It's no different in real life, save that you take real life to 'look real' a lot more easily. If you explore your world keeping this sort of thing in mind, you start to have a lot more "If I drew that, it would look wrong" or "I see how I'd have to draw this for it to look right" moments.
Let's draw on the panel and find the perspective I used. I remember that I did this little sketch by eyeballing, so let's see.

It is revealed that the pen is slightly out of perspective. I wonder if it was noticeable before...? It's not too bad at least. Note how the beer glass is not getting larger or smaller at the top or bottom - it's not being very perspecty. This is because parallel lines going up and down, even imaginary ones (think of the glass inside an invisible cube) in this image are going to remain parallel when depicted. It's two point perspective, so all the lines in a dresser, or a box on the table will all point strait up and down. This changes if you're doing three point perspective. It's mainly used for depicting tall buildings, since the warp becomes pretty severe once you start pinching smaller the tops of buildings, for example. I may talk more about 3-point later, but no promises. If you understand 2-point, that's fine. Three just changes this vertical-parallel lines rule to add a third vanishing point. It doesn't need the horizon line and can be placed anywhere on the vertical axis of the object. Playing with these is the best way to learn. Just remember to spread the points out far!
What makes my example skewed or 'warped' is how close one of the vanishing points are. Ever wonder why drafting tables are so big? It's not just to draw on really big paper. In most drawings both vanishing points will be way, way off the page, like the second vanishing point in this example. Many serious artists cover their draft tables with huge paperboard so they can pin or draw vanishing points in to keep track of them. Bringing the other vanishing point up close to the other is what causes warp - and should be in most cases avoided. Here's an example by Norling.
Beds - Ernest R. Norling
You can have a point in close, but the other one has to compensate. In my example, it didn't compensate nearly enough for how close point 1 was. This causes warp, but I decided to use it for visual direction.
Panel 2!
This panel was drawn using one point perspective, full on so you're looking strait down the image into the point, like that classic rail roads image.

From an artistic perspective, and I'm not sure why artbooks don't mention this, one point perspective may be less interesting than two point, but it's excellent for visual direction. Now, one thing I was never happy with this panel for was that I seem to be directing the reader to look at Antonio's navel, the guy in the middle. What is so important about his navel? Nothing. It's his expression that is of note, if nothing else, and it's Barry's line anyway. So this isn't the best example, but at least you know what's wrong with it. I also wasn't happy with the size of the table. Still, here, I used perspective lines to figure out how big to draw each head. The rest didn't go so well. I would have liked to place the vanishing point off the page somewhere behind Antonio who is at the end of the table and put Barry in the focus of the panel. This would mean all horizontal lines in the picture would point towards Antonio and his smirky face, leading the eye to him eventually, while keeping Barry the centre of attention while he speaks his line. This way, I can attend to both important things in the panel, and Walter, who is inbetween those two characters but technically in the middle, won't hog all the attention. Or I could put Barry's speech bubble on top of him, haha. --But I'm working off a script, and I don't have that freedom.
The next panel is a good example of approximated perspective, or working perspective backwards, which is a common practice and especially important if you're working off a script where certain people have to be inside the scene.
Panel 3
Two point perspective.
The boys are all sitting around a rectangular table, as I hope is clear by now. There's only one shot that will show all the speaker's faces. Luckily, Eddie, the man in the foreground is talking to himself, so he's literally having an aside. I turned his face. He's not directing his comment at any of the four people with him, so he's not making any contact with them. If I had him looking strait ahead, it would look like he's joining in with the other two's conversation. Lucky. So now that I have it planned in my head, I drew Eddie's head first. I drew the circles for the other two's heads until I was happy with the placement. This gives me enough information, along with the line of the table to draw the rest of the scene if I wanted to. I never drew the line for the booth they're sitting in, so I've placed it in now, in red. I don't even quite need to find the vanishing point to do so.
What if, for some reason, I wanted to draw more? I can keep working backwards to find out where to place more of my image. There's another guy beside the man in the foreground. Let's figure out where to place him. I'll draw one new line that goes right through Eddie (foreground guy) and Barry's heads. Now, I'll do the same with Walter, since this new guy will be sitting right across from him... --but I don't have enough information to place this line! Don't I need two lines to find the vanishing point? --You can estimate by using the horizon line, which we've already 'found' with the last points. Figure out about where it will be and it will give you where to start your new line. Draw a line from the point over the top of Walter's head, and you get the top of the new guy's!
Backwards perspective
Note also the imaginary square it creates. This square should look just like it could really be floating there. If it doesn't, something's probably wrong, and you'll need to be more precise. For this example, I never did figure out exactly where that other vanishing point was. The green line was placed down completely arbitrarily, where I thought it might be given where the lines were going off to. It was all guessing, but that's often enough, as much as it shouldn't be encouraged! It takes a lot of time to be precise, and this is production art! Be precise when you're practising, so it doesn't matter when you have to do it for real! If you do have time though, you'll never regret it.
Panel 4
This is another example of one point perspective that was perhaps done a bit better. Other than visual direction - I have the weight of the image hung mostly on one side, between new guy David and Antonio, it leaves lots of unimportant space at the bottom of the panel for lots of speechbubbleness.
Panel 4
Here, you can see the actual lines I did a bit better. I did this panel the same way I did the others. I drew in Antonio and Walter, to his left, then figured out the rest by drawing in the appropriate lines by finding the vanishing point.
The next two panels don't particularly have perspective at all, and are sort of unfinished.
Some other things to note about perspective, before I leave this topic:
Put everything in boxes if you're having trouble with what something looks like. Foreshorten the boxes and this will give you a clue as to your next step with your object. This even goes for body parts. If you're having trouble with the foreshortening of musculature, what you're looking for is foreshortening - and there are a lot of good books on this too, like the Atlas of Foreshortening, which is unfortunately because of all the picture plates, ungodly expensive (about 80$CAN). This is where good figure drawing classes come in handy. But those are 200$CAN+, if you go to Concordia. (But there are free or almost free classes as well.)
Reflections have the same vanishing point as well, not their own!
Floortile - Ernest R. Norling
What about shadows? Your 'vanishing point' for a shadow is the light source. Say a candle. Draw from that point, down around the edges of the object onto the 'floor'.
What about shadows cast on stuff? Draw through, as if the obstructing object were not there. Where the invisible lines touch the object in question helps form the shadow on that object.
Pages in a book: Keep in mind that the book is like a circle at it's edges. The pages are held in the centre of this circle, and rotate around it. Draw a cylinder in the perspective for your drawing and fill in the pages.
Slopes - Ernest R. Norling
Buildings with irregular faces - Ernest R. Norling
If any of that has sparked your interest, http://www.quadrilateralperspective.c om/ might also be of interest to read. It's very strange, but perhaps it's the next big thing, using very different fundamentals. Still, it hasn't caught on simply due to the fact that it's different from the way we've always done it, traditionally.
Today, I'll cover perspective, as promised.
I'll be covering it basically as described in Ernest R. Norling's classic book Perspective Made Easy, which was originally published back in 1939, and has been a staple in schools for a long time. It's a recommended quick and easy reference book, and is not even very expensive. Just 13.50$CAN. As well as looking at some actual examples from a recent name that was done by myself.
Perspective, if you've ever looked at planning sketches of Leonardo Da Vinci and things like that, can get pretty mathematical, but it doesn't have to. Since there's a lot of step by step books on the market, I'm going to jump around a bit, and fill in some real life examples and such, define terms, and underline some stuff that was perhaps not entirely clear to me way back. It's a tutorial, so I'm going to fill in the role of tutor on this one. Buy a good book specializing in this to become a master. The one I listed is the cheapest, and comprehensive too. Or look around and find one that suits the way you think.
First, let's define some terms. First, we have the horizon. That's pretty simple. Keep in mind that even indoors, there's a horizon, which we call the horizon line. This is where you're going to place your vanishing points. This is a, or multiple spots on the horizon where everything points to. There's no limit in a picture, depending on what it is, to how many of these there can be, but most pictures have one, two or three-point perspective. An example of infinite-point perspective might be a mass of floating balls. Seeing as you can just draw circles and shade them, I think infinite isn't very practical, more mathematical... Anyway, finally eye-level. This is the level at which the 'camera' or the viewer's eyes are at.
Let's look at an example.
Eye-Level - Ernest R. Norling
The term eye level was new to me when I was looking for solid material for this particular tutorial (I talk through my hat only when I can't find material, or you surprise me -_- ). I tend to do a lot of my perspective intuitively because it's one of the first things I learned and I'm very used to it. I had a very textbook development... In any case, it may be new only because of the reference to the eyes - these days, it might always be called 'camera'. So, you might think, what's the point of this if the drawing's all in on a sheet of paper anyway? Why do I have to figure out where I'd be standing? So eye level is a bit confusing, if apt.
A camera, because it takes pictures which become flat, is a bit easier to understand. Though these days cameras are not held at eye level any more as a rule.
The thing to remember is that the horizonline and eyelevel correspond. Norling was very particular about this point in his book, and I had never really thought about it. I suspect this fact may further helping me out in the future.
Now that you know about the parts, let's see about constructing an image. The image above is one-point perspective. Note how lines point to a particular place. If there were power lines on one side of the track, how do you think they would be drawn? The tops of these power poles will be over the horizonline. That means that the invisible line from the top of one pole to the next, the next the next, would in fact point downwards. I'll draw it in. I'll need this in colour due to all the ink the guy has in this drawing... Witness my Photoshop drawing skill!!
Let's add poles
I eyeballed the bottom part, and when I was done, I noticed perhaps I shouldn't have. Take a look at the second pole.
Mistake demonstration
For me, eyeballing is much harder on the computer, and high contrast doesn't help. Either way, it's a lesson that even something slightly off can harm the authenticity of your drawing. Knowing how to use perspective can save drawings, often those where you're not sure what you did wrong.
On paper, my method frequently is to draw roughly what I want to see, find the approximate vanishing point, then rework everything to fit nicely into it. It's hard to think of your vanishing points first, place them down pre-emptively and then have your image still match what you saw in your head, so I would say that after practice with camera angles, drawing roughly first then cleaning up is the easiest way to go about it. But this is where those thumbnails and name come in. Let's look at some very rough work. It's not the example I was thinking of, but I don't have the vast majority of the work here with me at my home. So, let's look at a different page.
Bugger Pg 10 - Name
The example's panels read from left to right.
Okay, not the best work ever, but it demonstrates a few perspectives, which I made using the method I described above. I sketch roughly what I want to see, then draw rough perspective lines that help me keep everything in line. On actual manuscript paper then, I would start strait away with perspective lines, now that I know it will give me what I want to see.
The first panel is two point perspective. This is an example of something called warped perspective and is something you're technically supposed to avoid. However, I wanted the paper to have that particular shape in the panel. Makes it a bit more interesting. There will be signatures on the bottom, and it makes it look a little bit more like the reader's eyes are very close to the surface of the paper - enough to skew his vision. Hold up a pencil box very very close to your eye, similar to how the paper is positioned in this panel. If you were to draw it just how you saw it, it's nothing like a rectangle any more, is it? It gains a strange teardrop sort of shape. Lots of things in our world warp like this when veiwed, but our brains compensate so that you never really question the actual shape of the object. You didn't think at any point that it was an oddly-shaped paper on the table, did you? It's no different in real life, save that you take real life to 'look real' a lot more easily. If you explore your world keeping this sort of thing in mind, you start to have a lot more "If I drew that, it would look wrong" or "I see how I'd have to draw this for it to look right" moments.
Let's draw on the panel and find the perspective I used. I remember that I did this little sketch by eyeballing, so let's see.

It is revealed that the pen is slightly out of perspective. I wonder if it was noticeable before...? It's not too bad at least. Note how the beer glass is not getting larger or smaller at the top or bottom - it's not being very perspecty. This is because parallel lines going up and down, even imaginary ones (think of the glass inside an invisible cube) in this image are going to remain parallel when depicted. It's two point perspective, so all the lines in a dresser, or a box on the table will all point strait up and down. This changes if you're doing three point perspective. It's mainly used for depicting tall buildings, since the warp becomes pretty severe once you start pinching smaller the tops of buildings, for example. I may talk more about 3-point later, but no promises. If you understand 2-point, that's fine. Three just changes this vertical-parallel lines rule to add a third vanishing point. It doesn't need the horizon line and can be placed anywhere on the vertical axis of the object. Playing with these is the best way to learn. Just remember to spread the points out far!
What makes my example skewed or 'warped' is how close one of the vanishing points are. Ever wonder why drafting tables are so big? It's not just to draw on really big paper. In most drawings both vanishing points will be way, way off the page, like the second vanishing point in this example. Many serious artists cover their draft tables with huge paperboard so they can pin or draw vanishing points in to keep track of them. Bringing the other vanishing point up close to the other is what causes warp - and should be in most cases avoided. Here's an example by Norling.
Beds - Ernest R. Norling
You can have a point in close, but the other one has to compensate. In my example, it didn't compensate nearly enough for how close point 1 was. This causes warp, but I decided to use it for visual direction.
Panel 2!
This panel was drawn using one point perspective, full on so you're looking strait down the image into the point, like that classic rail roads image.

From an artistic perspective, and I'm not sure why artbooks don't mention this, one point perspective may be less interesting than two point, but it's excellent for visual direction. Now, one thing I was never happy with this panel for was that I seem to be directing the reader to look at Antonio's navel, the guy in the middle. What is so important about his navel? Nothing. It's his expression that is of note, if nothing else, and it's Barry's line anyway. So this isn't the best example, but at least you know what's wrong with it. I also wasn't happy with the size of the table. Still, here, I used perspective lines to figure out how big to draw each head. The rest didn't go so well. I would have liked to place the vanishing point off the page somewhere behind Antonio who is at the end of the table and put Barry in the focus of the panel. This would mean all horizontal lines in the picture would point towards Antonio and his smirky face, leading the eye to him eventually, while keeping Barry the centre of attention while he speaks his line. This way, I can attend to both important things in the panel, and Walter, who is inbetween those two characters but technically in the middle, won't hog all the attention. Or I could put Barry's speech bubble on top of him, haha. --But I'm working off a script, and I don't have that freedom.
The next panel is a good example of approximated perspective, or working perspective backwards, which is a common practice and especially important if you're working off a script where certain people have to be inside the scene.
Panel 3
Two point perspective.
The boys are all sitting around a rectangular table, as I hope is clear by now. There's only one shot that will show all the speaker's faces. Luckily, Eddie, the man in the foreground is talking to himself, so he's literally having an aside. I turned his face. He's not directing his comment at any of the four people with him, so he's not making any contact with them. If I had him looking strait ahead, it would look like he's joining in with the other two's conversation. Lucky. So now that I have it planned in my head, I drew Eddie's head first. I drew the circles for the other two's heads until I was happy with the placement. This gives me enough information, along with the line of the table to draw the rest of the scene if I wanted to. I never drew the line for the booth they're sitting in, so I've placed it in now, in red. I don't even quite need to find the vanishing point to do so.
What if, for some reason, I wanted to draw more? I can keep working backwards to find out where to place more of my image. There's another guy beside the man in the foreground. Let's figure out where to place him. I'll draw one new line that goes right through Eddie (foreground guy) and Barry's heads. Now, I'll do the same with Walter, since this new guy will be sitting right across from him... --but I don't have enough information to place this line! Don't I need two lines to find the vanishing point? --You can estimate by using the horizon line, which we've already 'found' with the last points. Figure out about where it will be and it will give you where to start your new line. Draw a line from the point over the top of Walter's head, and you get the top of the new guy's!
Backwards perspective
Note also the imaginary square it creates. This square should look just like it could really be floating there. If it doesn't, something's probably wrong, and you'll need to be more precise. For this example, I never did figure out exactly where that other vanishing point was. The green line was placed down completely arbitrarily, where I thought it might be given where the lines were going off to. It was all guessing, but that's often enough, as much as it shouldn't be encouraged! It takes a lot of time to be precise, and this is production art! Be precise when you're practising, so it doesn't matter when you have to do it for real! If you do have time though, you'll never regret it.
Panel 4
This is another example of one point perspective that was perhaps done a bit better. Other than visual direction - I have the weight of the image hung mostly on one side, between new guy David and Antonio, it leaves lots of unimportant space at the bottom of the panel for lots of speechbubbleness.
Panel 4
Here, you can see the actual lines I did a bit better. I did this panel the same way I did the others. I drew in Antonio and Walter, to his left, then figured out the rest by drawing in the appropriate lines by finding the vanishing point.
The next two panels don't particularly have perspective at all, and are sort of unfinished.
Some other things to note about perspective, before I leave this topic:
Put everything in boxes if you're having trouble with what something looks like. Foreshorten the boxes and this will give you a clue as to your next step with your object. This even goes for body parts. If you're having trouble with the foreshortening of musculature, what you're looking for is foreshortening - and there are a lot of good books on this too, like the Atlas of Foreshortening, which is unfortunately because of all the picture plates, ungodly expensive (about 80$CAN). This is where good figure drawing classes come in handy. But those are 200$CAN+, if you go to Concordia. (But there are free or almost free classes as well.)
Reflections have the same vanishing point as well, not their own!
Floortile - Ernest R. Norling
What about shadows? Your 'vanishing point' for a shadow is the light source. Say a candle. Draw from that point, down around the edges of the object onto the 'floor'.
What about shadows cast on stuff? Draw through, as if the obstructing object were not there. Where the invisible lines touch the object in question helps form the shadow on that object.
Pages in a book: Keep in mind that the book is like a circle at it's edges. The pages are held in the centre of this circle, and rotate around it. Draw a cylinder in the perspective for your drawing and fill in the pages.
Slopes - Ernest R. Norling
Buildings with irregular faces - Ernest R. Norling
If any of that has sparked your interest, http://www.quadrilateralperspective.c
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