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Thread: Perspective 101

October 13th, 2007 #1
Perspective 101
Welcome to Perspective 101! Every illustrator needs to know what perspective is, and how to use it. There are many books out there on the subject – but until you’ve learned a bit about the basics, those books can seem intimidating. So, this thread is meant as an introduction to perspective. From here you can dive into those books with enthusiasm instead of fear; or you can just pick up the basics and run with that.
Before I go on, a word of warning. Unlike most other skills in art, perspective is logical. Because of this, one mistake that people make with perspective is to give it a quick glance, understand it, and then because they understand it, they assume that they can use it at will without ever practicing it. (I was guilty of this at one point.) This is about the same as assuming that since you know what a piece of music sounds like, that you can play it on the piano.
Perspective and piano both require practice. Fortunately for you, perspective is the easier of the two to learn. I have suggested assignments with each subject below.
Index
What is Perspective?
OnePoint Perspective
Assignment: Rectangular Volumes in OnePoint Perspective
TwoPoint Perspective
Assignment: Rectangular Volumes in TwoPoint Perspective
ThreePoint Perspective
Assignment: Rectangular Volumes in ThreePoint Perspective
ThreePoint Perspective, Continued
Assignment: More Rectangular Volumes in ThreePoint Perspective
How Many Vanishing Points Do I Need?
Assignment: Rectangles with Different Numbers of Vanishing Points
Drawing From Observation Using Perspective
Assignment: Apply Perspective to a Drawing from Observation
Drawing Shadows in Perspective
Assignment: Draw Boxes with Shadows
Finding the Center
Assignment: Mess Around with Centerpoints
Circles in Perspective
Assignment: Ellipses
Drawing Shadows Part Two
Assignment: Draw More Boxes With Shadows
This is a work in progress. I will be adding more to it over time. If you see an error or have a request, please send me a PM and let me know!
If you do the assignments, please post your results elsewhere. I would like to keep this thread strictly as a reference. However, if you have a particularly good example of something that you think would make this thread a better resource, let me know!
For a much more thorough look at perspective, Elwell recommends a couple of books: Creative Perspective for Artists and Illustrators, by Ernest W. Watson, and Perspective! For Comic Book Artists, by David Chelsea. These books are inexpensive, and from the quick skimming I’ve given them so far, I am thoroughly impressed with the knowledge they contain. (I was going to add a third book to this list, but I seem to have misplaced it the darn thing. But it’s no big loss, because the former two books seem far superior.)
For discussion on perspective, there’s a thread in progress in the Fine Arts, Studies, And Discovery section.
Happy reading!Last edited by Seedling; October 22nd, 2007 at 01:58 AM.
I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.
Perspective 101, Concept Art 101, Games Industry info,Oil Paint info, Acrylic Paint info, my sketchbook.

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October 13th, 2007 #2
What is Perspective?
As things move away from you in space, they appear smaller and smaller, until they vanish from sight. When you are drawing this 3D phenomena on the 2D plain that is a sheet of paper, then you are faced with a challenge: how do you know for sure that you are drawing your distant objects small enough? This is what “perspective drawing” is for.
There is only one rule in perspective drawing that you have to know: parallel lines in space are parallel forever, but those same parallel lines, when drawn on that 2D paper, converge at a point. That point is called the “vanishing point”, because it is the point at which those lines appear to vanish.
The most clichéd demonstration of this, of course, is the train tracks going off to the horizon.

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October 13th, 2007 #3
OnePoint Perspective
That traintrack images has a single vanishing point, so we call it “onepoint perspective”. There are three types of lines in onepoint perspective: lines that go horizontally across the page (such as the railroad ties in the previous drawing), lines that go vertically (imagine a line of telephone poles marching alongside those tracks), and lines parallel to the train tracks that all converge at the vanishing point.
With those three sets of parallel lines: horizontal, vertical, and recedingintothe distance, you have to tools you need to make rectangular volumes.
Assignment: Rectangular Volumes in OnePoint Perspective
Draw a horizontal line across your paper – and use a straightedge. That’s the horizon. Put a point on that horizon line right in the middle. That’s your vanishing point. Then above, below, and crossing that line, draw assorted rectangles. (A) They should be orthogonal – that is, at tidy right angles to the line.
Then, using your straightedge (if you don’t have a ruler handy, try using a folded sheet of paper) connect the points of those rectangles to the vanishing point. (B) That turns your rectangles into rectangular volumes that extend all the way to the vanishing point. You can then shorten those superlong shapes by adding in more horizontal and vertical lines. (C)
You’ll notice I’ve left lightlydrawn lines all over my drawing. You’ll want to do this as well, because that scaffolding will come in very handy when you get into more complicated shapes. I suggest drawing lightly with a hard pencil, so that when you really mess up you can erase, and when you’ve got a line in the right place, you can make it stand out by darkening it. Also, draw your shapes as if they are made out of glass. That is, you want to be drawing the far edges (the ones that are blocked from view) of the boxes as well as the near edges. This, again, will be necessary later when you’re drawing more complicated subjects.
Try doing some variations on this exercise as well. Do things such as moving the vanishing point way off to the top, bottom, or side of the page, or punching holes in the boxes, or creating other shapes. The goal with these explorations will be for you to find out where this technique ceases to give good results, and get you thinking about what is necessary to accurately construct other sorts of shapes in space.

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October 13th, 2007 #4
TwoPoint Perspective
It takes three sets of parallel lines to make a rectangular volume: horizontal, vertical, and recedingintothe distance. What if we replace those horizontal lines with another vanishing point?
Assignment: Rectangular Volumes in TwoPoint Perspective
This time, instead of one vanishing point in the center of the page, you’ll want to put two  one on the left, and one on the right. Also this time, instead of drawing orthogonal rectangles here and there, just draw vertical line segments. Try one above the horizon, one below, and one crossing over, for starters. Make sure those line segments are between the two vanishing points for now. Then, draw lines from both vanishing points to the ends of each of those line segments. (A) The vertical line segment is now the corner of a building that extends all the way to the horizon. Add in more vertical lines  the far corners of your rectangle. (B) Connect the ends of those new line segments back to the vanishing points to fill in the rest of your box. Those lines will meet at and define the furthest corner of your rectangle.
Everywhere that a corner occurs, there should be lines from that corner to both vanishing points. (And remember to leave all of those light scaffolding lines lying about. The more complicated this gets, the more you will need that information to identify mistakes and to continue your drawing successfully.)
A quick word about tools and precision. When setting up a complex scene involving buildings or spaceships, it will start off exactly like this: a bunch of simple shapes in space. If your drawing contains small errors at this stage, then by the time you are down to the details, those details will be magnified. A good picture can be ruined by small mistakes made at the outset. You may find, for instance, that in a picture of the courtyard of a building, everything on the near side of the image works, but everything on the far side of the courtyard is crooked beyond hope.
The key to keeping a perspective drawing from going badly like that is to keep those vertical and horizontal lines at perfect right angles and perfectly straight. So, either you have to eyeball where you are putting your ruler very closely (and expect that some of your drawings will go terribly wrong), or you must use a tsquare and drafting table.
A tsquare is a ruler with a segment that is designed to hang over the edge of a drafting table to hold the ruler perfectly horizontal. It’s typically used with a triangle and drafting table. It isn’t necessary to have a drafting table to use a tsquare, but some sort of rectangular surface is necessary. The paper is taped down to the surface while drawing to hold it in place.
Here’s an image of how a tsquare, triangle, and drafting table are used: http://etc.usf.edu/clipart/21900/219...uare_21986.htm
You should use a tsquare if you can get your hands on one, to get yourself in good habits. If you don’t have a tsquare available, then at the very least use a straightedge and a careful eye. Don’t be sloppy.
Try out the exercise above, making various sorts of rectangles in space. Perhaps try to figure out how to make other sorts of shapes. Try starting a drawing, and then turning the paper upsidedown, or sideways, and continuing it that way. See what happens if you draw your rectangles outside of the vanishing points. See what happens if you draw your rectangles far above or below the horizon, or if the two vanishing points are closer together. Mess around to get a feel for where this system of two vanishing points works, and where it breaks.

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October 13th, 2007 #5
ThreePoint Perspective
A rectangular volume is made up of three sets of parallel lines. You have now seen that two of those three sets can be pointed at vanishing points. Now let’s try all three.
Onepoint and twopoint perspective are actually simplifications of what our eye actually sees. To see why, in onepoint perspective, think of the lines on the box that you draw parallel to the horizon. Imagine that instead of being entirely parallel, those lines are actually just slightly tilted towards oneanother, so that somewhere, hundreds of feet off the edge of your paper, those lines actually do meet at a vanishing point. The same with the vertical lines in both one and twopoint perspective. Somewhere far above or below the horizon (and off the edge of your sheet of paper) those “parallel” lines meet in another vanishing point.
Those parallel and perpendicular lines in one and twopoint perspective represent a shortcut. Threepoint perspective is actually quite simple: every corner of a rectangular volume must be connected to three vanishing points.
You might be wondering about the horizon. Forget about it. The horizon is something we as humans are used to seeing because we stand on the surface of the earth, and most of our life we are surrounded by big rectangular boxstructures that sit neatly on the groundplane. As long as the boxes that surround us remain neatly orthogonal, and we remain on the ground (as opposed to high above in a helicopter), then one and twopoint perspective suffice for drawing what is around us.
But if you were standing at the foot of a sky scraper and looking up at it, or flying above and looking down, you would need a third point of perspective. That third point would not fall on the horizon, but would instead be up in the sky, or down underground. So for the sake of clarity, we can throw away the horizon for now.
Assignment: Rectangular Volumes in ThreePoint Perspective
Draw three points on your paper in a roughly equilateral triangle. They’ll need to be close to the edges to give you enough room. These are your three vanishing points. Label them “1”, “2”, and “3”. Put a third point somewhere in the center. That point is the nearest point of a rectangular volume in space.
Draw a line from all three vanishing points one to that first corner of your cube. (A) Then pick a second point somewhere between that point and vanishing point 1. That will be the next corner of your box. Draw lines from that point to vanishing points 2 and 3. (B)
This gives you two triangles. Extend two more lines out from vanishing point 1, intersecting each of those triangles. That will give you a shape that looks like a book. (C) That shape is the near sides of your box.
To find the rest of your box, just remember the rule: all corners of the box must connect to all three vanishing points. (I say “find”, because after the initial steps, you no longer get to decide where the remainder of the box goes.) There it all is! Now you just have to sort through the mess of lines for the outlines of your cube. Darken those up so that it stands out clearly.
Try using those same three points to draw multiple boxes in space. Look for the following things to happen:
A. Overlapping boxes. As long as you don’t get lost among all of those scaffolding lines, you can layer as many cubes over oneanother as you like. The tricky part becomes deciding which one is in front of the other. That’s up to you, actually. You can also choose to turn the boxes into conjoined twins. (And as you do, start thinking about how you could make use of this to construct scenes of buildings.)
B. If you were to connect those three vanishing points, you would get a triangle. Notice what happens when a cube extends over the edge of that triangle: it behaves like a box in one or twopoint perspective that crosses the horizon. Instead of seeing three faces of the cube, you can now only see two.
This is more easily understood if you think about what is going on back on the surface of the earth. Think of a rectangular building from a streetlevel perspective. You can’t see the floor of the building because the walls are in the way; you also can’t see the ceiling because the walls are in the way. From some locations you would only be able to see a single wall!
C. Lastly, and most importantly, think about what is going on when all of these boxes share the same vanishing points. This means the boxes are all orthogonal to oneanother.

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October 13th, 2007 #6
ThreePoint Perspective, Continued
If you want to draw boxes in threepoint perspective that aren’t parallel to oneanother, then each box will need to have its own three vanishing points.
Watch out! Things will start to get confusing here with all the lines flying about. Make sure you aren’t using the wrong perspective point.
Line management starts to become more necessary when you’ve got such a tangle of scaffolding. You might want to start selectively erasing some of the lines to keep yourself sane. Don’t obliterate all of it, however. You will need at lest two lines from each vanishing point so that you can tell at a glance which vanishing point goes with which box.
Assignment: More Rectangular Volumes in ThreePoint Perspective
Try it!

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October 13th, 2007 #7
How Many Vanishing Points Do I Need?
In any given scene, the position of the rectangular objects will dictate whether you will need to use one, two or threepoint perspective, and whether any of those objects share vanishing points with each other.
It is entirely possible for different objects in a scene to require different numbers of perspective points. For example, a scene with buildings that sit at a thirtydegree angle to oneanother. Those two buildings might each be best drawn with twopoint perspective, but one or both of their vanishing points would be at different places along the horizon. If a flying car were zipping around the corner between them at a dramatically tilted angle, then that flying car would require three entirely different points of perspective, none of which would be on the horizon.
Assignment: Rectangles with Different Numbers of Vanishing Points
Try drawing rectangular volumes with one, two, and three points of perspective all in the same image.

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October 13th, 2007 #8
Drawing From Observation Using Perspective
Rectangular blocks are fun for a while, but ultimately they need to be combined with drawing from life or imagination if they are going to do you any good.
This is a sample of how perspective can be applied to a drawing made from direct observation. On the left I scribbled down my impression of a cardboard box. For every line I drew, I was asking myself two things: where is the vanishing point that this group of parallel lines points to? And compared to a horizontal or vertical line, what angle is this edge on the 2D plain of my paper?
On the right side, I scribbled out the same loose drawing a second time, and then used a straight edge over top of that sketch to correct and adjust the drawing in perspective.
A, B, and C are the locations of the box’s vanishing points. A is the only one that happens to be on the page. B is close enough that the lines visibly converge towards it. C is far enough away that this drawing could just as well be considered twopoint perspective.
So what can be done about a vanishing point that is off the edge of the page? One method is to attach another piece of paper. In this case, I’ve just eyeballed my lines carefully. As long as the lines appear to be converging at the same rate, that might be all the precision I need for a drawing of a simple cardboard box.
The drawing itself will tell me if I have improvised poorly, because the more incorrect my improvisations are, the more errors will spring up. The biggest telling point will usually be the far, hidden points of any rectangular volume. If only two of the three lines meet properly there, then a mistake has been made. (Which is why it is important to draw the hidden sides of objects.)
There are, of course, more precise ways of dealing with this sort of problem, because architectural draftsmen can’t rely on any sort of guesswork in their drawings. But that stuff can come later.
Assignment: Apply Perspective to a Drawing from Observation
Find a tissue box, cereal box, brick, or other simple rectangular volume, and draw it from multiple angles by first sketching, and then correcting with a ruler. Identify the locations of all three vanishing points.

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October 13th, 2007 #9
Drawing Shadows in Perspective
If you take the time to draw an object properly in perspective, you can spoil it by guessing where its shadow will fall. Hard light falling on hardedged objects create hardedged, precise shadows. All the same rules that apply to boxes apply to rays of light, too.
The sun, a light bulb, and the flame of a candle all have one thing in common: under certain conditions each behaves like a vanishing point. Rays of light extend in straight lines in all directions from such a lightsource.
The first drawing below is a diagram of how to think of light when drawing in perspective. A rectangle sits on the ground, and above is a lightsource. A ray of light drawn from the light source to the corner of the rectangle and then to the ground shows where the shadow of that object would end.
From the light I have also extended a line straight down to the ground. Where that line meets the ground is just as important as the lightsource. Look at the next drawing to see why. Lines drawn from that point through the lower corners of the boxes then intersecting with the rays drawn from the light to show where the shadow ends.
Basically, when a light is in a scene, you have to draw several rightangled triangles to calculate where the shadow will fall.
The third drawing shows the sun. The only difference between the sun and a nearer point of light is that the point below the sun goes on the horizon.
If the sun is behind you then it will behave differently, but this method works if the sun is in the picture or just beyond the edges of the picture.
The edges of shadows cast by a box will be parallel to the edges of the box. This means that if you do this correctly, the edges of your box’s shadows will point to the same vanishing points as your box.
Assignment: Draw Boxes with Shadows
Try drawing boxes with one and twopoint perspective lit by points of light in different locations. Try drawing a box with a light directly above it. Try drawing a box that is lit with two lightsources.
One thing to note: for now, use one shade of gray for everything that falls in shadow, and leave the rest white. This is because a common mistake that people make when shading cubes is to use gradients. In reality, reflected light may cause some gradients, but reflected light is small potatoes compared to direct light. Keep it simple for now by using only flat gray.

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October 13th, 2007 #10
Finding the Center
Here is an easy trick that you will use over and over. To find the centerpoint of a rectangle in perspective, draw lines connecting the opposite corners. Where those lines meet is the center.
Connect the center to a vanishingpoint to cut your rectangle in half.
This trick can be used to subdivide rectangles over and over and over.
Assignment: Mess Around with Centerpoints
Use this trick to make checkerboards or other patterns on rectangles in perspective. Or, for more of a challenge, use this trick to make a rectangular donut, or other 3D shape.

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October 13th, 2007 #11Ellingsworth Guest
Beautiful, Michelle. Great work on the thread and very thought out, I'm going to go over all this again. Five stars from me.

October 13th, 2007 #12
Wow, Seedling, this is fantastic.
Very detailed and easy to understand, five stars.
Thank you so much.

October 14th, 2007 #13
So wonderful and helpful! Thank you very much, Seedling. Sums up a good chunk of my illustration class

October 14th, 2007 #14
I have one doubt, how can I draw a perfect cube in perspective
thanks for your efforts, its great

October 14th, 2007 #15
Seedling will you be also covering the human body in perspective, with foreshortening as well?
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