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Description
Page 2…

What would happen if everything wasn’t so centered, as on the previous page?
The horizon tends to show where one is looking. As a result, anything drawn over the horizon would be viewed from below, while anything drawn below it would be seen from above. Since the block on the previous page was drawn dead center, it was as if you were looking at the very middle of the block.
In Fig. 6, this block is drawn the same way as the one before, with one exception- this time that middle line, line 1, is drawn so more of it is above the horizon than below. Right away, you can see that as a result, lines 2 and 3 end up the same way, but there’s something else- see how the angles on top of the block are steeper than they were before, and how the angles on the bottom are more shallow? This is exactly what would happen if you started to shrink or crouch down while viewing the block from before.
Want to know what would happen if you drew that middle line so more of it was below the horizon? Turn the page upside-down. Now it looks as if your point of view was raised!

So far, the block was always drawn with the horizon passing through it. Now- what if it isn’t? If the horizon does not pass through something, then you are either viewing the object from above or below.
In Fig. 7, there is what seems to be a formidable-looking block. But in fact, drawing it is very much like the ones from Fig. 4 and Fig. 5, with a bit extra. As before, you draw a vertical line- line 1- but it is below the horizon. Also as before, you draw lines from the two vanishing points to the top and bottom of that line, so you end up with a sort of “V.” On each side, the same distance from line 1, draw in two vertical lines so each connects the two diagonal lines coming from the vanishing points. Those are lines 2 and 3.
From each of the vanishing points draw a line to the bottom of lines 2 and 3. Do the same to the tops of lines 2 and 3.
See how they intersect? Because we lined up the front and back corners, two of them meet on line 1- just as before, but this time (!) the other two meet ABOVE line 1!
From the tops of lines 2 and 3, darken the lines connecting them to that intersection. Do the same from the tops of lines 2 and 3 to the top of line 1.
And there you have it so far- a solid block viewed from above.
If you want a transparent block, then darken the lines going from the bottom of lines 2 and 3 to where they meet, which just happens (in this case) to be on line 1. From where the two lines meet above line 1, just draw a vertical line straight down (line 4). Now you have a transparent block!
If you want to know what would’ve happened if you had drawn line 1 ABOVE the horizon, again just flip the page upside down. The way you’d draw it would be the same, just stay inside the lines.
Now, Fig. 8 is going to be trickier, because this time the block is going to be off-center, unlike all of the others!
Draw line 1, below the horizon and to the left of the center, as shown. As always, this is the base of what you’ll draw. Just as in Fig. 7, draw lines from the vanishing points to the top and bottom of line 1, but this time you’ll have a strange-looking, uneven “V.” Don’t let that worry you- you do the same thing as before!
Once again, you draw lines 2 and 3 the same distance from line 1, but this time notice that line 2 is lower and longer than line 3. This is because line 1 was to the left- so we should have seen less of the left side and more of the right.
( If this is giving you any trouble, just find a block, put it on a table so you are viewing it right on the corner, nice and even, and then slide it to the left. You will also notice that what here is line 2 will be closer to line 1 and line 3 will be further away. But since for now we just kept them at the same distance from line 1, what we end up with looks more like a rectangle than a square block.)
Once again, draw lines from the vanishing points to the tips of lines 2 and 3.
This time, you will see TWO places where those lines intersect. Once again, darken the lines going from the tips of lines 2 and 3 to the tips of line 1, and from the tops of lines 2 and 3 to where the lines meet above and to the left of line 1. This is as far as you need to go if you want a solid-colored object.
For a transparent object, darken the lines from the bottom of lines 2 and 3 to that intersection below the top one. Now, connect those two intersections with line 4- as shown.
And there you have it- a solid (or transparent, depending on how far you went!) object seen from above and moved to the left. If you flip the page upside down, you will see it from below and moved to the right. Try moving line 1 around when you try this again, and see how the perspective changes.
If this is giving you any trouble, don’t worry- just go through it again a few times, and it’ll fall into place. I didn’t learn about this, really, until I was 20 back in 1986!

Description
Page 2…

What would happen if everything wasn’t so centered, as on the previous page?
The horizon tends to show where one is looking. As a result, anything drawn over the horizon would be viewed from below, while anything drawn below it would be seen from above. Since the block on the previous page was drawn dead center, it was as if you were looking at the very middle of the block.
In Fig. 6, this block is drawn the same way as the one before, with one exception- this time that middle line, line 1, is drawn so more of it is above the horizon than below. Right away, you can see that as a result, lines 2 and 3 end up the same way, but there’s something else- see how the angles on top of the block are steeper than they were before, and how the angles on the bottom are more shallow? This is exactly what would happen if you started to shrink or crouch down while viewing the block from before.
Want to know what would happen if you drew that middle line so more of it was below the horizon? Turn the page upside-down. Now it looks as if your point of view was raised!

So far, the block was always drawn with the horizon passing through it. Now- what if it isn’t? If the horizon does not pass through something, then you are either viewing the object from above or below.
In Fig. 7, there is what seems to be a formidable-looking block. But in fact, drawing it is very much like the ones from Fig. 4 and Fig. 5, with a bit extra. As before, you draw a vertical line- line 1- but it is below the horizon. Also as before, you draw lines from the two vanishing points to the top and bottom of that line, so you end up with a sort of “V.” On each side, the same distance from line 1, draw in two vertical lines so each connects the two diagonal lines coming from the vanishing points. Those are lines 2 and 3.
From each of the vanishing points draw a line to the bottom of lines 2 and 3. Do the same to the tops of lines 2 and 3.
See how they intersect? Because we lined up the front and back corners, two of them meet on line 1- just as before, but this time (!) the other two meet ABOVE line 1!
From the tops of lines 2 and 3, darken the lines connecting them to that intersection. Do the same from the tops of lines 2 and 3 to the top of line 1.
And there you have it so far- a solid block viewed from above.
If you want a transparent block, then darken the lines going from the bottom of lines 2 and 3 to where they meet, which just happens (in this case) to be on line 1. From where the two lines meet above line 1, just draw a vertical line straight down (line 4). Now you have a transparent block!
If you want to know what would’ve happened if you had drawn line 1 ABOVE the horizon, again just flip the page upside down. The way you’d draw it would be the same, just stay inside the lines.
Now, Fig. 8 is going to be trickier, because this time the block is going to be off-center, unlike all of the others!
Draw line 1, below the horizon and to the left of the center, as shown. As always, this is the base of what you’ll draw. Just as in Fig. 7, draw lines from the vanishing points to the top and bottom of line 1, but this time you’ll have a strange-looking, uneven “V.” Don’t let that worry you- you do the same thing as before!
Once again, you draw lines 2 and 3 the same distance from line 1, but this time notice that line 2 is lower and longer than line 3. This is because line 1 was to the left- so we should have seen less of the left side and more of the right.
( If this is giving you any trouble, just find a block, put it on a table so you are viewing it right on the corner, nice and even, and then slide it to the left. You will also notice that what here is line 2 will be closer to line 1 and line 3 will be further away. But since for now we just kept them at the same distance from line 1, what we end up with looks more like a rectangle than a square block.)
Once again, draw lines from the vanishing points to the tips of lines 2 and 3.
This time, you will see TWO places where those lines intersect. Once again, darken the lines going from the tips of lines 2 and 3 to the tips of line 1, and from the tops of lines 2 and 3 to where the lines meet above and to the left of line 1. This is as far as you need to go if you want a solid-colored object.
For a transparent object, darken the lines from the bottom of lines 2 and 3 to that intersection below the top one. Now, connect those two intersections with line 4- as shown.
And there you have it- a solid (or transparent, depending on how far you went!) object seen from above and moved to the left. If you flip the page upside down, you will see it from below and moved to the right. Try moving line 1 around when you try this again, and see how the perspective changes.
If this is giving you any trouble, don’t worry- just go through it again a few times, and it’ll fall into place. I didn’t learn about this, really, until I was 20 back in 1986!