Introduc on to Perspec ve

Hello, and welcome to my Perspec ve Tutorial!

First, feel free to download anything about it, both images and text. It's free, and available for any and all.

The reason for it is quite simple: unlike style, use of colors, subject ma er, or any number of ar s c features that are subjec ve- that is, a ma er of taste (some love manga, others hate it)- the hints and lessons on perspec ve here are mostly objec ve. For example, in the part on how to draw a proper cube, the steps shown will work every me, and give a good cube. It's not a ma er of taste, it simply is one way of doing it, and it does work...the way 2+2 does=4.

But as for the why?

Most of what you see in my gallery is the result of years of eﬀort, some mes focused, some mes stumbling on un l it came out right (at least, sort of). It's mostly self-taught, and only very, very recently did I ﬁgure out many things about perspec ve. So much, in fact, that it's the "third true advancement" in my style - the others being from 1986 and 1997. This was no doubt triggered in large part by interac on with the other ar sts here at DA. Only problem is, I'm 44 as of this typing. Oh, bother!

There are many ar sts here, much younger than I am, who may well be exactly where I was in 1986. Some who are superior to what I was, some at the same level, others not quite there yet. But- how much further, and how much sooner, would those younger ones, who are now where I was in that oh-so-diﬀerent world 24 years ago, be in just a few years, or even sooner, if they did not have to rediscover and reinvent the wheel?

Perspec ve is key to so much. It can guide one when drawing anything from a city to a natural corridor in the forest, or a passage in some dark cave of a dungeon. A building seen from a ﬂying car's perspec ve if futuris c, or maybe a temple if from a sorcerer and a dragon steed.

It can guide one to drawing a chair si ng on a ﬂoor, or even a checkered ﬂoor.

Tracks or a road, going oﬀ into some distant place...and the train or vehicle on it!

With the use of perspec ve, one can shi from an objec ve viewpoint to a subjec ve one (where you see a much bigger Miss Sharon from the viewpoint of a ny Golem-Lin, for example).

Thus...this tutorial!

There are several parts to it here, but it isn't so much a progression from simple to more advanced, as a tour through the worlds oﬀered by each part. The ﬁrst part, for example, is about the use of a Single Vanishing Point, the second the use of Two Vanishing Points, and the third will be about (oh, you can see this one coming, can't you?) the use of Three Vanishing Points. And maybe beyond.

Yet, there are mes where an ar st, be he- or she!- at 1/10th my skill level, or ten mes my superior, will only want to use the Single Vanishing Point. Even one eventually understands and can create images with SIX or more (), there are mes when only one is called for.

One can combine the types. You can draw a tunnel or hallway with one, and then draw a ﬂoa ng cube using two- all in the same picture.

This tutorial is only meant to show one the concepts, and a few ways, of doing this. But it would be all but impossible for any tutorial to completely explore, to fully show, the vast, vast worlds that this can open up.

Maybe it will do nothing more than bring together bits and pieces you already knew about.

But if it can advance your eﬀorts so YOU don't have to be middle-aged to reach my current levels, if it can give new excitement or inspira on, then this was all worth it.

Enjoy! And good luck!

Perspec ve: What is it?

"Perspec ve" can essen ally be summed up as "Point Of View," that is, how you are viewing something.

Since most media is two-dimensional, you can only really present up/down and le /right. That is all that is really there.

However, for most images, you will also want to show a third dimension: close/far, or depth.

You therefore must create an illusion of this.

If you ﬁnd a long, level ﬂoor and neatly place iden cal s cks on it, one behind the other, horizontally, equally spaced, away from you, and then view them from one or the other end, what does it look like? It seems as though those s cks are ge ng closer and closer and smaller and smaller the further away they are.

Yet, you KNOW that they are not- they are equally spaced and the same size.

So their shrinking size and ge ng closer and closer is illusion. This is one way we perceive depth, which here is real.

Now, if you were to draw this scene, how would you do it? Why, you'd draw the s cks smaller and smaller and closer and closer. So here, their shrinking size and ge ng closer and closer is real, but the "depth" isn't there- that's illusion.

Art must use illusion to show reality. Art and reality here are opposites when it comes to depth.

And this is usually done with "Vanishing Points."

Vanishing Points are points that are the basis for an ar st's perspec ve in art. They help give a neat, realis c look to things in pictures, since reality follows certain laws; vanishing points imitate this. As the name implies, things "move into the distance" when going towards vanishing points.

The most basic example is this: draw a point in the middle of a piece of paper, and from it draw two lines going down, to make an upside-down "V." Now, between those two lines, draw horizontal lines, and what happens? As you get closer to the point, the lines get smaller- just as in the s cks example that follows.

That one vanishing point imitates the real-world fact that something going oﬀ into the distance seems to get smaller and smaller.

Although this tutorial became far bigger and with far more than I'd ever imagined it would become when I started it late in the Fall of 2010, turning into the "Third Advancement," perspec ve usually involves one, two, or three vanishing points. Of course, there are more, and I've seen pictures using as many as SIX, but for the most part three is the limit.

One Vanishing Point pictures deal with a single vanishing point, and the whole picture centers around that one point. Such pictures are VERY strong on depth, and any line that does not radiate from that one point is usually automa cally horizontal or vercal. The classic angled checkered ﬂoor picture, with the horizontal lines, is an example of this.

Two Vanishing Point pictures cover what a single vanishing point cannot: squares, rectangles, blocks, buildings, etc. at an angle, such as looking at the corner of a building straight on. If you want to draw a checkered ﬂoor at any kind of an angle, without the usual horizontal lines, you'd have to use two vanishing points. Such pictures do not show depth with the same intensity. Mostly, lines not using the two vanishing points are automa cally ver cal.

Three Vanishing Point pictures in a way combine the above two. You get the beneﬁts of two vanishing points, but with the depth one vanishing point can give. There are usually NO "automa c" lines here, so such pictures take the most eﬀort. A building drawn with two vanishing points seems as if you are looking straight at it; if drawn with three vanishing points, it will seem as if you are looking up or down at it.

It is also possible to combine these techniques while keeping them separate. You may draw a corridor with a single vanishing point, for example, yet have a block in it drawn with two vanishing points- it is not truly a "three vanishing point" picture, but rather a single VP picture and a two VP picture in the same place. And, very important, is the...

...Horizon!

One thing most pictures using perspec ve have is "The Horizon." This is the level of your view, where the ground and air meet in the distance. Assuming one is looking straight ahead, a six-foot person will see the horizon at a certain height; a mouse would have a much higher horizon, while a giant would have a much lower one.

For the most part, the horizon is an imaginary horizontal line drawn through a single vanishing point, or an imaginary horizontal line connec ng two vanishing points. The horizon is VERY important for how one sees something: a ﬂat square, perfectly level with the ground, would be a thin line if exactly on the horizon; if it is above the horizon, you'd see its underside; if below, you would see the top of it.

And what of three vanishing points? That's trickier, because in such cases you might NOT be looking straight ahead. Hover in front of a tall tower at about, say, ﬁ y feet while looking straight ahead- you can use only two vanishing points to draw it. BUT- look upwards or downwards at it; you are at the same height and the horizon is at the same level, but now your view has changed and a third vanishing point is needed. But by how much are you looking up or down? The third vanishing point determines this.

Because I drew and wrote this tutorial as the Third Advancement was happening, it is o en in chronological, rather than subject-based, order. This is why the part on how to divide up a three vanishing point wall appears in the sec on on two vanishing points, for example. Never fear, though- there is an Index to clear up any awkwardness!

I men on this several mes throughout the tutorial, and here is a good start: you do NOT have to do everything exactly as I explain it here. What ma ers is the end result, and if you rearrange the steps given to get there for something, go right ahead.

Another thing is this: DO NOT ever not try something diﬀerent for something speciﬁc. Draw a par cular line four inches long to constantly get cubes in a picture? Why not ask what happens if it is two inches or eight inches long; what sort of shapes would you get?

For a two vanishing point picture draw a neat upsidedown "V?" What happens if you lt the "V" to one side or the other, so the 45 degree point (this is explained in the 2VP pages!) is no longer directly dead center between them?

What happens if you move the third vanishing point around? Do vanishing points even have to be on the paper I am drawing on? (Answer: Absolutely Not!)

What I do recommend is this: Again, start from the beginning, even if you move quickly through it. Not only might there be something in even the 1VP secon you didn't know about, but almost everything in the later sec ons is simply a more complex version of something from the earlier sec ons.

And so, good luck, and have fun.

"Perspec ve" normally follows lines to or from Vanishing Points, be it anywhere from 1 to 6- or beyond. The idea is to give an illusion of depth, of things close and distant.

Vanishing points are great for ar ﬁcial things, like buildings, roads, and the like...but what about natural scenes? Where straight lines are uncommon at best? Where curves are the norm, where trees and clouds can be big in the distance while small ones are closer?

What you'd have there is some mes called a "zero" or "non" vanishing point image. This is when you cannot really use vanishing points, because the scene is too disorderly or inconsistent.

Luckily, certain rules usually apply, and can help.

For example, all else the same, things that are close have more detail than distant things. A maple tree up close is one with details you can see, right down to tears in the bark and spots in the leaves- but from a mile away, it becomes much less detailed. In the distance, a slope covered with maple trees is more a misty green mass than actual trees.

When you draw things closer and closer to the horizonwhere sky and ground meet, or eye level- they are ge ng further and further away. Couple that with the fact that it would have less detail, and you can show that even a much larger object is in fact far away, while a smaller one is actually close.

An obvious way of showing something being closer is to draw it in front of something else.

So, the following basic rules can help:

1) The closer things are, the more details can be seen.

2) The closer something is, the bigger it looks.

3) Objects in front of others are closer.

4) If something curves, the curves get ghter in the distance- as a rule.

5) The closer something is drawn to the horizon, the more distant it is...as a rule. There are excep ons, as will be seen here in Fig. 2.

In Fig. 1, we see a meadow. The grass up close has the strongest coloring, the blades are drawn largest, and there is the greatest amount of detail. The grass further back has less detail, weaker coloring, and the blades are drawn smaller. The part in the back is much, much less detailed, has the weakest coloring and detail, and the blades- what are drawn- are the smallest. All of this creates the illusion of three levels of distance: close, further away, and far.

Fig. 2 shows a simply-drawn meadow (although note the size of the grass blades up close and distant) with ﬁve bushes on it. Once again, detail and coloring are strongest for the closer ones.

This me, however, the sizes are NOT uniform. Bush 4 is bigger than bush 3, although they are the same distance away. To show that, both have the same color strength and amount of detail and- this is so important here!- they are both right on the horizon! Bush 2 and bush 5 are drawn the same size and distance from the horizon, but are NOT the same distance away. The amount of detail and color strength in bush 5 is much greater, and this me I drew a shadow- under bush 5, showing where it is ﬂoa ng. That's right, ﬂoa ng- (bear with me here...please...)- imagine how much less this would work without it. It looks closer than bush 2.

Fig. 3 shows how objects drawn in front of others look closer. The faded coloring helps here, and the trees behind the front ones were drawn "higher up," as were the bushes in Fig. 2.

Fig. 4 shows a natural scene, along with some "0VP" signs, to illustrate what's been done so far. The signs get smaller and less detailed the further back they are. The river's curves are ghter in the background. Details are less in the background. This me, however, I darkened the river in the distance; there are mes you'd do that. Other mes, things can get lighter. It depends on the situa on.

Fig. 5 is an example of not following those rules. The trees all have the same level of detail, coloring, and size, no ma er where they are. The meadow is drawn the same everywhere. There is no scale, no shading, nothing- the result is a very simpliﬁed image with very li le sense of depth, beyond the fact that you simply "know" which trees are closer and further away

(largely due to distance from the horizon).

Fig. 6 Is similar to Fig. 3, except the clouds are of diﬀerent sizes. Since the small cloud is in front of the big one, has stronger outlines and more detail, and has somewhat stronger color, it is clearly closer.

As with land objects, things in the sky that are closer to the horizon are usually further away, unless you showwith detail, shadow, or such- that it is in fact hovering not too far above the ground but is s ll drawn above the horizon.

Fig. 7 is a picture with EVERYTHING wrong. The river's curves are the same everywhere, the coloring and details of everything is the same, objects that are pre y much the same size are not drawn larger or smaller regardless of distance. The two trees in the lower right also show a problem...

There is an old photographer's trick and joke: You take a picture of someone up close at the foot of a gently sloping hill, but behind that person, some distance away, is someone else standing up a ways on the hill. If you posion them just right and take the picture, it will look like a ny person standing on the head of the ﬁrst person. While the picture is not faked and is technically correct, you would s ll try to avoid such a situa on.

So it is with art. If two trees, the one behind the ﬁrst is larger and up a hill a ways, you'd end up with something similar to what you see in Fig. 7, although one tree would be more detailed and colored more strongly. It's usually best to avoid this sort of thing if possible.

Zero/Non Vanishing Point pictures are a good deal more subjec ve than 1+ VP pictures. While there are certain rules you can follow, they are not absolute and at mes simple judgement and experience must apply. And that is up to you, not me or this tutorial.

1VP1— Examples of the Single Vanishing Point

Well, here it is, page one of my tutorial!

This shows the extremely basic views.

For this one, we must start from the upper le , and then move to the right.

The ﬁrst view is of six s cks, seen from directly above. They are of the same size, equally spaced.

Next to it is a direct front view. Naturally, you can only see the nearest s ck, since the others are blocked by it.

The next view is one that is in between the ﬁrst two. Here, you see all six s cks, but from one end, at an angle. As a result, the near ones look bigger than the ones in the distance, and you'll also no ce that the distant ones look closer together.

Now, right a er that, we see two parallel lines, seen from directly above. They are, well, parallel.

But what's this? Next up are those two lines, seen from an angle, and now they seem to form a sort of "V," coming together in the distance- AND, they seem to be thicker when up close.

This, of course, is mere illusion in real life. Objects like those six s cks do NOT really get smaller the further away they are, and equally-spaced objects do NOT really get closer the further away they are.

Parallel lines of uniform thickness do not thicken or get skinnier, nor do they actually meet in the distance. It is merely subjec ve, an illusion- but vital, because without it, we'd have no depth percep on.

In any artwork on any ﬂat surface, be it paper, canvas, or computer screen, we are all just reproducing this illusion.

And so, here are a few helpful laws to remember- if you do, 60+% of it all becomes easier:

1) As an object is more and more distant, it looks smaller and smaller.

2) Equally-spaced objects, as they are further and further away, seem to be closer and closer together.

3) Parallel lines, seen from an angle, seem to converge (meet up) in the distance.

Star ng on the second row, the ﬁrst image combines the above, into a sort of ﬂat train tracks. It merely obeys the three laws above- that's it.

But now, it's me to introduce something that is going to be central to this, the ﬁrst tutorial- the SINGLE VANISHING POINT. This is where the image ul mately seems to go, where it vanishes.

For the next image, the third dimension will be brought in (an illusion on paper, but...). This is seen from above, so the "sides" cannot be seen. No ce how a ﬂat, long triangle is made "3-D" by drawing the rectangle at the near end.

Last, and far from least, are several images, all coming from the same vanishing point. A couple are "solid colored," while the rest are "transparent," as if made from glass. No ce the diﬀerence, how the triangle/ prism is made that way by drawing in another triangle? See how the transparent cube looks like a transparent cube by drawing in another square?

Erase the lines not involved in the shape you want, and it looks like a lone 3-D object. No ce which lines need to be erased for the "clear" and "solid colored" ones.

But, above all, no ce how all corners connect to that SINGLE VANISHING POINT.

This simple page is the basis of all else here. Know it, and the rest merely builds up from it, piece by piece, like a building made of toy blocks.

Well, here we are...the World of the Single or One Vanishing Point (1VP)!

The main feature of the 1VP is to create a strong sense of DEPTH: that is, of things moving away from you. Standing in a hallway, looking down a road or tracks, staring down a pit...this is what 1VP is really all about.

On the previous page you've seen a few examples of what the 1VP can do. Here, we'll see some more examples, but more sophis cated. Over the next pages, you'll see more complex 1VP images, but for now, here are the basics.

The image at the top of the page shows a sort of "street" going oﬀ into the distance. Take a moment to see which of the lines actually go to (or come from, however you'd like to look at it!) the vanishing point; they are the ones you are not directly facing.

The object at the lower le of that image shows something very important: diagonal lines that do NOT go to the vanishing point. As you saw on the previous page with the triangle, you are not limited to ver cal and horizontal lines; this is how le ers can be drawn going oﬀ into the distance.

Clearly, the sense of depth is very strong here. That is what 1VP images do best!

In the middle of the page are two pictures of a pit. The le one has a centered VP, so the lines from the corners go right to the very center. No ce how the squares get smaller and closer together as they go "down;" this follows two of the basic rules of perspec ve, as with train tracks.

The pit on the right, however, has the VP moved up and to the right. That one diﬀerence has completely changed the view of the pit. Since everything in a 1VP image centers on that VP, moving it must change everything. In this case, it no longer looks as if you are looking straight down the pit as with the one on the le - now it looks as if you are more to the right and up. If you want to show the point of view of someone looking over the edge of a pit, then you should move the VP to where the viewer would be looking down.

The bo om image is simply six blocks going oﬀ into the distance, BUT- this me, they do not go all the way to the VP. No ce how the ver cal and horizontal lines are lined up? This is a good way to draw a part of a city from overhead.

The VP is not exactly centered; see how that aﬀects the blocks? Moving the VP simulates moving your point of view, which is useful if you want to draw several comic panels showing ﬂight over a city.

So far, we've seen a bit of what can be done in the world of the Single (One) Vanishing Point (1VP)- here's a bit more!

The Single Vanishing Point will usually be on a line called "The Horizon," also known as "Eye Level." This is very important to keep in mind as it also involves points of view. A small creature will have a low horizon, while a bigger one will have a higher one. If you want to draw a floor from the point of view of a mouse and a giraffe, you'd have two different points of view, and this would be based on how high the horizon is. This will be covered in greater detail a bit later.

With a 1VP view your focus is on that one vanishing point. What you see of objects depends on where they are in rela on to the vanishing point.

The image at the top of this page shows four shapes. They surround a vanishing point.

Take a moment to no ce what you can see of them. Since the top one is over the VP, you see its underside. The one beneath it? You see its top. The one to the le is showing its right side; the one to the right shows its le side (based on your point of view).

You can actually try this in real life with any object. Try it with a block or a book. This is actually something you see all of the me in everyday life.

For comic ar sts, this is something that must come easily. To show someone walking past a crate or a building requires one to know how to do this. For tradi onal or computer anima on, it is just as important. If you are passing a building while on a bus or a train, watch to see how you see it as you approach it and then go by it.

Real life and art come together here.

The next image has two structures: a staircase and a strange object. Between them is a vanishing point. Keeping in mind that the horizon is usually a horizontal line going through the vanishing point (but not always!), look and see what you can see of the objects. The same rules from the top image apply here. But- in addi on, you can see that any ﬂat, level surface exactly on the level of the VP is ﬂat to you. That is because it is perfectly level with your eye level. same horizontal line? And how it happens to be 45 degrees, as if drawn from the corner of a square? Drop a line down from Point A, and you'll get a square!

It might seem tricky at ﬁrst- un l you apply what you already know from real life to it. Because they are the same here, almost exactly!

The next image shows two blocks. One is "standard," with ver cal and horizontal lines up front, while the other is turned so it is a diamond shape. This IN NO WAY aﬀects how the corner lines go to the VP. It just shows that you can rotate such an object in that way and s ll have a 1VP image. Any line that does not go the the VP DOES NOT automa cally have to be ver cal or horizontal.

The World of the Single Vanishing Point is not so limited. In fact, it has a lot of room.

The ﬁnal image shows a corridor. It is a pre y standard 1VP corridor: ver cal and horizontal lines if they do not go to the VP; it is very much like what you'd see with late 1970s and early 1980s role-playing computer and video games.

The only diﬀerence, as with the pits on the previous page, is where the VP is. Once again it is centered on the le one, but moved over with the right. No ce how this aﬀects the image. It is as if you stepped to the le . Again, this is how it would be in real life.

If you moved the VP down very low, then you'd see the corridor as a mouse would. The floor would be drawn more "flat," while the ceiling would be more angled. The walls would also be affected, as would any doorways.

As a side note, you'd have to keep in mind what changing the point of view might do. A human would see the top of a table, a mouse would not- but that mouse would see the underside of the table, while a human would not. A mouse might not only see what is in another room through the gap under a door, but would see the underside of the door too!

But for now, don't worry too much about it. Take it one step at a me, so you can both build upon and understand what all of this is about, and the later things will come much easier, since it all builds up bit by bit.

Now that the very basics of perspec ve have been covered, let's do something with it- why not the classic "checkered floor," which was my first (mostly) successful effort back in that distant world of 1986?

Here we go, this me (I hope!) be er prepared...

Step 1: First, draw a dot. This is your vanishing point. Somewhere below the vanishing point, draw a horizontal line.

Drop a line straight down from the vanishing point to the horizontal line. Where they meet is Point C; in this case, that center line is 7 cm.

From Point C, on both sides, draw dots. Make sure that they are the same distance apart (I put them 3 cm apart).

Now, connect each of those points to the vanishing point.

Finally, draw a horizontal line through the vanishing point; this is the "Horizon." How far to each side? Exactly as far as Point C is from the vanishing point. This is very important!

(Note: "The Horizon" is usually the level of your view, and it assumes that you are looking straight ahead. If you draw a block and it is below the horizon then you will be able to see the top of the block; if it is above the horizon then you will see the underside of the block; if the top of the block is exactly as high as the horizon then it will be perfectly level with your vision.)

Step 3: Draw the new horizontal lines based on that long diagonal line. To go beyond that, draw another angled line from the center line, as shown; where it goes through the lines are where the horizontal lines go.

Just as shown. You have a checkered ﬂoor!

By the way, did you no ce how the second angled line from the center line is not 45 degrees, but rather 36 degrees? This is because that line must end in the same point as before, in this case Point A. This is really important to remember!

For other ﬂoors, you could use Point B, and the opposite lower corner, if you'd like...or both. Or use lines from the center lines...or a combina on. But they should all give the same horizontal lines.

(Note: Since the horizontal lines are the same distance apart with this method, you could apply this part to drawing a corridor with its sec ons each the same size, if you wish. Since this advancement did not occur in a neat orderly fashion, I drew those corridors elsewhere in the 1 VP sec on before ﬁguring out this part.)

On to...Step 4

So far, we've drawn a ni y grid. Now, we will do something with it- including the promised Checkered Floor!

For Step 2, from one of the lower corners, draw a diagonal line to one of the ends of the top horizontal lines, as shown in the illustra on. From Point C, do the same thing to the same point as before.

See where the long diagonal line from the lower corner goes through the other lines? Those points will be where you draw the new horizontal lines!

No ce how the angled line from Point C gives you the

Step 4: Color in the squares on the ﬂoor, being sure to alternate them, as shown. You do not have to, say, make the square on the lower le dark, but then the one to its right must be dark. It's up to you.

There you go- a genuine Checkered Floor!

BUT- you can do more, and since I have the extra space, why not?

From the lower le corner, draw a ver cal line. For this example, make sure it ends somewhere above the vanishing point. Connect the top of that line to the vanishing point.

Extend the bo om horizontal line out to the le a li le. Draw a ver cal line up from there, and make it just as high as the other one. Connect their tops, as shown...

O.K., from the upper le corner, draw a ver cal line unl it reaches the line going to the vanishing point.

And you have...a wall!

Since the top of the wall is ABOVE the vanishing point, you cannot see it (unless the wall is transparent). Remember, the vanishing point in these cases usually at the horizon; the level you are looking at.

For the other side do the same thing, except the ver cal lines from the corner must end BELOW the vanishing point. Connect those ver cal lines, and see what happened?

You can draw not one, but TWO lines to the vanishing point. Why? Since the wall is below the horizon (your line of vision), you can see it. The opposite of the le wall in that way, too!

Draw those two lines to the vanishing point.

From the upper right corner, draw a ver cal line un l it touches the line as shown.

From that point, draw the li le-short line to the other line going to the vanishing point.

You have the other wall. Study it for a moment, see how it worked. Step 4 is done.

It's what you see all the me in real life; now you've seen a way to draw it, too.

Now you can draw something that is the cornerstone to so much involving basic perspec ve. Since the squares are all the same size, for example, you can equally space objects on that ﬂoor- anything two squares above something is the same distance away as something two squares to the le , for example.

What, am I going to leave all that white space?

Never!

For Extra 1 (why not?), everything was done the same way as Steps 1, 2, and 3, with one excep on: I moved what was Point A a ways to the right, to about 5 cm.

Look at the result: rectangles, "upright," and the Point C angle is 54 degrees, not 45. One look at that long diagonal line to the 5 cm point shows why.

Also no ce how the horizontal lines are higher than before?

Try moving Point A to the le . You'll get rectangles, but "on their sides," squat. And the horizontal lines will be lower than before, too.

You can control what kind of shapes you get just by moving that one point! It's that easy, and shows that you should never be afraid to experiment with these things; the results can teach plenty!

For Extra 2 (imagina ve, aye?), I moved all of the points on the bo om horizontal line 1 cm to the right (moving them all 2 cm to the le would do the same thing). Otherwise it was all done as in Steps 1, 2, and 3.

No ce how everything has been "shi ed over." Also no ce- very important!- that the horizontal lines are all at the same levels as before.

Also no ce the 41 degree angle, and where it starts from? Point C is not used here this me.

This would be useful for anima on, too, if a character was walking by such a ﬂoor.

Well, that's it! Now you have even more than a mere ﬂoor!

And if that last line didn't make you want to leave, well, then- on to more in the world of the Single Vanishing Point!

1VP6—The Classic Rectangular Corridor Receding into Distance

Well, well- what have we here? Looks like a corridor, and a tricky one at that!

Such a thing was quite in mida ng to me once, because I did not keep in mind the basic steps. Had I done so, even just the ones from Page One, this would've been much easier.

First, ignore the walls and ceiling. What do you have le ?

The ﬁrst part of the checkered ﬂoor.

That's it.

And so it is with the other three sides. That is it.

Now, how far do you space the horizontal lines? You could just use angles, like for the checkered floor, drawing a faint center line to start with here, or you could just try to make it "look" right. Just keep in mind that where you draw that second horizontal line, above the first and longest line, will define the size of each segment.

But, the how-to...

First, draw a nice, even rectangle, or at least close to it for now.

Now, connect the corners, so you have an "X" in the center. This is our vanishing point, and as before, is the heart of everything.

Draw a horizontal line above the bo om line. Draw the other three lines, nice and ver cal for the walls, and nice and horizontal, for the ceiling.

You have a smaller rectangle.

In whatever way you want, repeat this, un l you are down to ny rectangles. No need to go beyond that, if you don't want to.

You now have a basic rectangular corridor.

But let's not stop there! Find the middle of the top line on the biggest rectangle- there!- and draw two dots, each the same distance from the center dot on that line.

Now, connect one, and then the other, of those dotsle and right- to the vanishing point.

You now have two lines on the ceiling, converging at the vanishing point.

In each segment of the ceiling, draw in two horizontal lines- but no ce something!- no ce how the space between our- let's call it an overhead light- overhead light and the "near" horizontal line is bigger than the one between it and the horizontal line below it?

Remember the laws of perspec ve, how equal-sized things seem smaller than ones further away? Remember those six lines on page one, how they grew closer together and smaller as they went oﬀ into the distance?

Same thing here. Exactly the same. It all comes from those basic things.

Repeat as you go down.

Now, on the right side, we once again use the vanishing point to draw in the doorway, adding those horizontal lines. Also see how the space on one side of the doorway ("1") is smaller than the other ("2")?

Same as before.

Now, that "window"- this me, two lines from the vanishing point, two horizontal lines of the same length, then TWO MORE LINES FROM THE VANISHING POINT to outline the other side. Add the ver cal line, and it's ready.

And that is all, folks. Just as with math, it all builds up from the very basics.

So far, the vanishing point has always been in the center.

What if it isn't?

This me, we'll move it up and to the right! So...

First, draw the large rectangle, as before. This me, it should be the same size and dimensions as before, so trace the one from the previous page. So far, you're doing what you did with the previous image.

This me, though, draw the dot above and to the right of center.

Connect each corner to it, so you get a weird-looking "X."

What you should now do is this: trace the secondlargest rectangle from the previous page- the ﬁrst one going oﬀ into the distance- onto this picture. Making sure it is aligned ver cally and horizontally, touch the corners to the four lines of the "X." Make sure it isn't lted.

Or, you can simply measure the bo om line of that smaller rectangle from the previous image, and make sure the ends touch the two bo om lines of the "X," keeping it horizontal. Draw in the rest of the rectangle.

Repeat, each me with the next smaller rectangle.

Just keep in mind that the rectangles going oﬀ into the distance are the same sizes as before; they just aren't centered as before. This is very important!

For the ceiling lights- do the same thing as before, except this me, of course, the two lines going from the vanishing point to the two dots are going to be angled diﬀerently. No ce that you are s ll ending them in the same place on top of the big rectangle as before.

So far, so good...

Do what you did before with the doorway and window, keeping in mind that the result will look di ﬀer- ent, because the vanishing point is oﬀ-center- but the procedure is iden cal to page 4. You can actually end those lines coming from the vanishing point in the same places on the big rectangle; watch what happens.

There you go.

Of course, you can do pre y much the same thing with triangles, or squares, or whatever. Instead of horizontal lines for the ceiling, try two raised lines, mee ng on the vanishing point line, for a peakedroof look. Skylights? Just follow the same rules, and it works.

Good luck, and hope this helps!

Whoa- this certainly looks fancy, and if I had to try it back in 1986- or even 1987- it would have been in mida ng!

Unless you keep those laws of perspec ve, and use that single vanishing point. It's true- this is the same as the previous images here, except it has more of the same.

First, this is actually a varia on of the rectangular corridor- the one with the center vanishing point. The most obvious diﬀerence is the peaked roof; this is a pentagon. If you look at the "X" for the side walls, you can see this.

The peaked roof was done merely by drawing in two raised lines instead of a straight horizontal line. Just make sure they start from the ends of the ver cal lines and meet in the same place in the ver cal line drawn from the vanishing point. It'll work automa cally.

The checkered floor was done the same way as before, except I drew the horizontal lines where they were from the first corridor picture- I did not bother to measure angles this me (you can, if you'd like, but then this should be done before drawing the roof in). Do not fill this in yet, though.

The transparent block on the le side was done similar to the walls from the checkered ﬂoor picture.

The doorway on the right? Same as before.

HOWEVER...

The most signiﬁcant diﬀerence here are the supports. These help give a real 3-D look to this corridor. They can be tricky!

But not as much if you look this over, and take it one step at a me.

First, draw lines parallel to the big pentagon here on all sides except for the ﬂoor- I deliberately le crossed lines there, but once ﬁnished, you can erase them. You should have the big pentagon, and a smaller one without the bo om line, neatly aligned with the big one. This is the side of the support facing you.

Now- lightly draw in the "inside" of the support, making it as thick as you want. Start at the sides connected to the floor. With a straightedge, line up the end of the ver cal line of that inner, bo omless pentagon with the vanishing point, and connect that point to the the line next to it, the faint line you just drew. THIS is where the support meets the floor there, and you can see that that diagonal line DOES NOT line up with the one where the floor meets with the wall. This is vital for the 3-D effect.

Do the same for the other side.

Now, draw in another bo omless pentagon, making sure its lines are parallel to the other two pentagons, as shown. With small lines, connect the corners of the smallest pentagon to the corners of the middle one.

There you have it. Try it a few mes, and it'll become easy enough!

On the ceiling, on the right, there is a skylight. You can see where lines from the vanishing point were used; and the far side and near side are merely lines parallel to the supports. But for the thickness, I drew two short perpendicular lines from the support, and merely drew in lines parallel to the inside of the skylight.

The rectangular block on the le side is similar, but I pushed it up against the support.

Important p!- On the support next to the door, to its right, I drew in a faint line in the support; look at the arrows. This is to warn you about a common mistake: when deciding how much space to put on either side of the door, you must know how far it is from the part of the support that TOUCHES THE WALL ON THE DOOR SIDE. This cannot be seen because the support here is not transparent. So keep that small distance in mind, or the it may look a bit "oﬀ."

Well, that's it for now, fellow DA ar sts and guests. You've been given a quick look at the places the Single Vanishing Point can take you, but there's even more! This will be covered in "Subjec ve/Objec ve Viewpoints," but that's a diﬀerent topic.

There are places the SVP cannot take you, thoughlike drawing a cube at an angle, or a mack truck. Something's missing...

And that will be for the SECOND AND THIRD vanishing points! See you there!

Hope this helped...

1VP9—A Perfect Square & Cube with a Single Vanishing Point

So far, you've seen how to draw blocks with a Single Vanishing Point.

But- what if you want to draw a speciﬁc kind of shape, one that is consistent, the same? Like the most basic things of all: squares and cubes- real squares, actual cubes?

Here it is:

First, draw a Vanishing Point. Draw the horizon it's on, as with the checkered ﬂoors.

Next, and this is central to it all, draw a point somewhere directly below the vanishing point, and call it "C." (Well, you don't have to call it "C," but why not?)

Measure the distance from the Vanishing Point to Point C, and then, to the le and the right of the vanishing point, draw in points at the same distance from it- call them Points A and B.

You now have everything you need!

Draw a li le horizontal line somewhere. Connect its ends to the vanishing point. You should have something like Fig. 1.

Now, from one of the ends of that li le horizontal line, draw a line through the opposite side to one of the two new points on the horizon; since the line started from the le end of this horizontal line, I used Point B. Had I started from the right end of the horizontal line, I would've used Point A. You just have to be sure that it goes through one of the vanishing point lines.

Where that line crosses the vanishing point line...simply draw a horizontal line. All of this results in what you see in Fig. 2.

You have your Single Vanishing Point Square! I marked the top corners Points E and D, but it really is this easy!

To check it, draw a diagonal line from the corner opposite of the one you used to the other point on the horizon. If it passes through the other top corner of the square, then it came out right. If I do this with the right p of the ﬁrst horizontal line and draw the line to Point A, it will pass through Point E.

For a cube, all you have to do is ﬁrst draw a regular square with the ﬁrst horizontal line for the top or bo om (in this case, I drew it up). All four sides should be the same length since, like all Single Vanishing Point shapes, you're looking directly at the front of it and it's supposed to be a square. You could have just as easily drawn it downward, too.

And now you have the front of your cube, as in Fig. 3!