# Drawing 101: Linear Perspective

Taught by Professor David Brody

### In this lecture, you’ll learn to use linear perspective to draw an architectural landscape of two buildings on a ground plane. Construct the buildings and the space between them using the principles of one-point perspective.

Watch lecture 16 from the series How to Draw, and follow along with the transcript and video stills below.

To begin, we’ll need a clean sheet of 18 x 24″ white drawing paper.

Make sure the edges of the paper are parallel to the edges of the drawing board. We’ll be using the T-squares, triangles, and straight edges. We’ll be drawing both the exterior and the interior of the buildings. To do this, we’ll need three line weights: One for the construction lines, these should be the lightest and thinnest; one for the buildings’ exteriors, these will be the most robust; and a medium line weight, somewhat in between, for the interiors of the buildings.

We’ll be drawing with graphite. If you use pencils, sharpen them regularly to maintain similar line thickness. Many people prefer to use mechanical pencils for this type of drawing; saves on the sharpening. If you want to go with mechanical pencils, it would be useful to have both a .3mm and .5mm. The .3mm for construction lines, and the .5mm for the drawing itself. Either way, draw construction lines with a harder lead, 2H–4H, and the main lines using HB–2H leads. You’ll need your erasers; I’d suggest a pencil type, a pink pearl, and a kneaded. The last, as we’ve seen, is excellent for turning down the volume on a given section of line. Your drafting brush or a one to two inch chip brush and a kneaded erase will also be useful for all those erasure crumbs.

#### Before we get started, here are a couple tips.

We’ll be generating a lot of line, many construction lines that won’t be part of the finished drawing. Part of the craft here is managing all of this so it doesn’t turn into a jumble. Small inaccuracies in measurement become exponentially problematic as a drawing unfolds, so take time and care. If something doesn’t line up, erase and redraw; it’s going to save you time in the long run. We also need to manage the graphite. It’s easy to pick it up on the sides of your hands, on the T-square, or your other tools; so you want to check periodically. If anything’s getting dirty, give it a quick wash and a dry. There’ll be a lot of step-by-step directions here. While this lecture is about 30 minutes, it can take longer than that to complete the drawing.

We’ll be drawing an architectural landscape—two buildings on a ground plane. Then we’ll move inside the buildings and draw furniture into the interiors. You’ll also have the opportunity to take what you’ve learned and add other things to the drawing like a kitchen, or a bedroom, or even a ping pong table or swimming pool. Once you get the hang of it, you can create all kinds of things out of your imagination. We’ll be drawing two similar buildings separated by a rectangular open space. You could conceive of it as something akin to a university’s quad. Quad is, of course, short for quadrangle; literally four angles—basically a rectangular open space or courtyard surrounded or partially surrounded by one or more buildings. When you think about it, it’s a lot like Canaletto’s San Marco—a piazza flanked by buildings.

#### So let’s get started.

• Paper in the landscape position—that’s horizontal.
• First, we’ll make a 10″ line 2″ above and parallel to the bottom edge of the page.
• We’re going to center that in the 24″ width of the page.

So you should have about seven inches on either side of that line. This will be the bottom center section of the quad—the rectangular open-space.Next, very lightly, we’ll draw a horizon line 6 1/2″ above and parallel to the 10″ line. Remember, this is a diagrammatic line, so keep it light and thin. And give yourself a tiny vanishing point on this line; put it right in the center of the line at the 12″ mark. Make it as small as possible—a single pin point or a crosshair.

Vanish the two ends of your bottom line, the 10″ line, back toward the central vanishing point. Remember, don’t actually touch it; stop an inch or so away before reaching your vanishing point. If we continually touch it, it will become larger and larger—that means less precise—and that will negatively affect all of our angles.

Now, four inches above the bottom line, or six inches from the bottom of the page and parallel to both, draw a horizontal line connecting your converging diagonals. If you have some extra diagonal receding beyond this, erase what you don’t need.

You now have the quadrangle, represented by a trapezoid—same kind of shape as the piazza in the Canaletto, and the library floor in the Simpsons. Next, we’ll draw the front face of the building on the left—a rectangle to start off. Make this 10″ tall and 4″ wide. Now we’ll make a small light horizontal mark to note the height of the triangular roof that will extend above the rectangle—mine’s four inches above.

We have our roof’s height. But to draw a triangular roof, we need to locate a point centered above the rectangle at that height. Of course, we could measure with our ruler, but we want to find ways of calculating measure that don’t depend on using our rulers. That’s because we won’t be able to use our rulers to measure into the depth of the page, into the illusionistic space of the drawing. Instead, we want to use the visual information we have to find the next piece. So how can we find this point deductively?

Let’s take a detour. If I gave you a rectangle and asked you how to locate its center without measuring, I’m guessing you’d have no problem. You’d cross diagonal and say, “Voilà, center found.” So, you’re probably beginning to see how this applies here.

Our building’s bottom section is a rectangle. If you guessed that we could cross our diagonals to find the center and then extend this up vertically to the roof’s height, you’d be right. And here’s a point to remember: Crossing diagonals of rectangular shapes to find a center point is a common starting point to finding an answer to a problem having to do with measure in linear perspective; this will apply to trapezoids and parallelograms, too.

On another note, here’s a tip on minimizing construction lines. Often we don’t need to draw the whole line to get the information we need.

In this case, we can just line up the straight edge with a rectangle’s corners and draw two small crossing line segments near the center. Similarly, when we extend the center line up vertically, we only need position our straight edge on the center point; then draw a bit of line intersecting the horizontal associated with the roof’s height. Once we have this point, we can extend diagonals from the upper corners of the rectangle to the center point to create the front face of the building’s roof. We can get rid of our construction lines at this point, and brush away any erasure crumbs.

Now, let’s shift to the building on the right. Using our straight edge or T-square, we can carry over a measure horizontally for the height of the building’s rectangular section. Then intersect this point with a line from the bottom right corner of the trapezoid. This gives us the height of the first section of the building. We want the building on the right to be equal in width to the one on the left. Now here’s a puzzle: How could we find the far right extension of our second building without measuring? Is there a way to figure this out deductively? I’m going to leave you to think about it a bit, but I’ll give you a hint: It will involve intersecting diagonals.

So, let’s move back to the building on the left and give it dimension. Just as we did with the blocks, we’ll do this using our vanishing point. We already have the receding bottom edge of our building; it’s synonymous with the receding left edge of the trapezoid of the quadrangle. We can complete the receding face of the building in two steps.

First, we’ll make a line from the top of the vertical representing the height of the building’s base and take this back towards the vanishing point. Again, don’t touch the vanishing point itself. Second, we’ll extend a vertical line upward from the back corner of the quadrangle to meet the receding diagonal, and we’ll erase any line segments that extend beyond their intersection.

Our next step’s to complete the roof. We’ll start by taking a line from the top of our triangle back toward the vanishing point. But where do we stop? We know we have to connect the back upper corner of the building’s base to the roof, but to what point exactly? Now, the back face of the building is exactly the same as the front face except that it’s zoomed back in space, so we should be able to apply the same set of procedures we used to construct the front to construct the back.

Think back to what we did earlier. We found the center of the bottom rectangle, then extended a vertical straight up to find the location of the center of the roof’s apex. While we don’t have the back rectangle or wall, we can certainly construct it. We’ll draw the building as if we had x-ray vision, as if it were a building made of glass; like we drew the blocks in the last lecture. We call this drawing-through, and this is central to drawing itself. Imagining the three-dimensional form of things on a two-dimensional surface, making ourselves believe wholeheartedly in the illusion; that’s part of the magic.

If you have a take on drawing the interior of the building, take it as far as you can. Find the floor, ceiling, back wall; find the center of the back wall, and all the pieces will fall into place. Once you begin to get a sense of how this works, it unfolds like the solution to a puzzle—each subsequent move naturally suggested naturally by the prior one, and it begins to be a good deal of fun. But I also know this can get confusing, so I’m going to take you through this step-by-step as well.

Let’s start with that floor. The back edge of the floor is located along the same horizontal as the back edge of the quad, so we’ll pull this line over into our building.

And remember, we’re now in the interior, so we want to modify our line weight relative to what we used on the exterior. It should be a bit lighter and/or a bit thinner, but not as light and thin as our horizon or other construction lines. To finish the floor, we’ll take a line from the building’s lower left corner and recede toward the vanishing point, stopping where we intersect the horizontal line representing the bottom edge of the back wall. Then, erase any extra line.

Here’s a tip to make the exterior/interior illusion a bit stronger. There’ll be places where the external lines overlap the internal lines; I often make the internal lines discontinuous at these junctures. If you’ve already drawn these as continuous lines, experiment with erasing a bit of the internal line at the point of intersection. It can often heighten the sense of overlap and depth of that space. We’ll draw the ceiling following a similar set of steps.

We’ll start at the back of the building at the upper right corner of the building’s base, and draw a horizontal into the interior of the building.

Next, we’ll jump to the front to the top left corner of the building’s base and draw a line receding toward the vanishing point, but we’ll stop where we intersect the horizontal line we just made.

We now have an interior floor and ceiling. We’ll add one more line—a vertical connecting the left corners of the floor and ceiling. That will complete the interior of the base.

You now know how to find the center of the back wall intersecting diagonals. Using your straight edge, carry this measure up vertically to intersect the line representing the roof’s peak, and you’ve found where the roof ends.

Last, connect the upper left and right corners of the back of the building’s base to this point and you’ll have completed the basic form of the building. At this point, you might want to get rid of any unnecessary construction lines, any bits of diagonals or vertical extension lines; but make sure you leave the internal structure—the glass building view—because we’re going to use it later.

There are a couple things worth noting here. The front face of the building is made of two simple shapes: a rectangle, and a triangle. The building itself is made of two simple volumes: a block for the base, and a prism for the roof. We constructed all this starting with line, turning line into shape, and then shape into volume. While a goal may be to draw things that feel convincingly real, we make it out of abstract elements—lines and shapes. We can’t actually make a building, all we can draw are lines. It’s like the novelist who arranges abstract elements, letters, into words and sentences on a page. And yet, we as readers come away feeling like we’ve experienced real three-dimensional people in actual places. So, it’s time to return to the puzzle of the second building. How can we find its width? How can we predict this using diagonals? I’m sure many of you guessed right. Here’s the thinking underlying the solution:

The shape formed by the interior vertical walls of the two buildings is a rectangle.

The shape which will be formed by the external vertical walls will also be a rectangle, and it will be centered on the internal rectangle—you’re seeing where this is going. Both rectangles will share the same center point. If I find the center of the internal rectangle by crossing diagonals, I can use that center point to construct the external rectangle. I can do this by lining up my straight edge with the upper left corner of the left building’s base, and following this through the rectangle’s center point to the place where it intersects an extension of my ground line.

Then draw a vertical line up from that point, and then a horizontal across the top to complete the rectangular front face of my second building.

If you’re working along with me, this would be a great place to pause the lecture and work through the construction of the second building on your own. Just repeat the steps we took in drawing the first building; this will help cement what we’ve just done. It’s by doing these things repeatedly that they become second nature; instinctual; part of what becomes automatic in our seeing, thinking, and drawing. For your reference, here’s what you should end up with, and then we can take it the next couple steps.

So, we’ve got two see-through buildings. Our next step will be to add three equally-spaced floors above the ground floor. We’ll start with the building on the left and put a floor in the center of the structure. Remember to control the line weights; we’re going to end up with lots of lines crossing one another. Controlling the relative weights will really help you see it all clearly. Once again, to find the center we’ll use diagonals, and then draw a horizontal line.

Now we’ll draw the lines representing the long dimension of the floor receding into space. We’ll start at both right and left sides of the horizontal, and draw lines back toward the vanishing point. We’ll stop at the intersection with the vertical lines representing the back of the building. Connect the ends of the two receding diagonals to complete this part of the floor.

Now, let’s add some thickness to the floor. I’m going to make it about an eighth of an inch on the front face of the building, then vanish back. We’ll repeat this set of steps to create a floor below this one.

• Find the center
• Make a horizontal
• Vanish it back
• And add the same thickness.

Now for an upper floor.

• Once again we’ll find the center and draw a horizontal.
• This time we’ll draw the thickness first and vanish both horizontal lines back toward the vanishing point.
• Then draw the underside of this plane.

You’ll note, the three lower floors are seen below the horizon and we see their top planes. This last floor’s above the horizon, so we see its underplane.

Once you’ve done this, add identical floors to the building on the right.

Now we’re just about ready to add windows to the receding plane of our building. But before we do, and since we’re talking about space, let’s do a little more work on managing line weights to make the drawing more compelling; more clearly readable. As we’ve seen before, the kneaded eraser will do a good job of incrementally diminishing a line’s weight. We can drag it over certain lines, or sections of lines, varying the pressure to control how much graphite we remove. The twin keys are thinking spatially and hierarchically at the same time; balancing the two is where a lot of the art comes in. Thinking spatially, thinking in terms of atmospheric perspective, and applying this to line, tells us to adjust the things farthest away so they have the least contrast.

The contrast here is that of the line relative to the white of the paper. The lighter the line, the more similar to the paper, the less contrast; this equals farther away. The darker the line relative to the paper, the closer. We have to integrate this way of thinking with thinking hierarchically. The higher the contrast of line to paper, all else being equal, the more it will attract the viewer’s eye; higher contrast gets more attention. Part of the question here is what should be more prominent and what less so based on spatial and hierarchical considerations? So take a look at your drawing. Ask yourself are any of the lines too prominent? Are any not prominent enough? And you can make adjustments back and forth.

The higher the contrast of line to paper, all else being equal, the more it will attract the viewer’s eye; higher contrast gets more attention.

Now we’re ready to construct our windows. We’ll create four vertical bays for windows in the long foreshortened and receding plane facing the quadrangle. And we’ll make a brief detour to learn how to draw regularly repeating shapes that appear to diminish in size as they become more distant from the viewer—things like the tiles on the ground in the Raphael, or the windows in Canaletto’s painting of San Marco.

Here’s the basic principle; hold off drawing here. We know that we can locate the center of a rectangle by finding the intersection of the rectangle’s diagonals. What really helps us in linear perspective is that this will also work in a foreshortened shape, like the side plane of our building.

Crossing diagonals will yield the perspectival center of the shape. So to create four vertical bays of windows, we could draw a vertical through the center point and repeat on either side to create quarters; and voilà, four bays for windows. But there’s a more sophisticated way of doing this, which will open up a range of further possibilities. Let’s come back to our front view again. If we have a rectangle divided along the horizontal half and traverse it with the rectangle’s diagonal, the point of intersection will similarly be the center point of the rectangle. And this will also work in foreshortened shapes like trapezoids; it will locate the perspectival center.

Now, back to the rectangle. If it were divided into four vertical sections or stripes, the rectangle’s diagonal would traverse these lines at four quarters—the half included.

And this will work in perspective, too, if the trapezoid’s divided into regular horizontal intervals. They’re diagonals, of course, receding into a vanishing point, but they represent what would be horizontals seen face-on. So all we need to do is draw a diagonal from corner to corner, and the points of intersection will indicate where our divisions should be.

Now, let’s return to our building and apply this. The side plane is already divided in quarters, so we’ll draw the diagonal. In the example, I drew the diagonal all the way across, but all you need in your drawing are the bits where it traverses the floor lines. Then extend verticals through the intersections, and erase any extra construction line to reveal the four bays for windows.

It’s a good idea to check your drawing at this point. Ask yourself if the four vertical bays are getting predictably smaller as they move back in space. If the third bay’s the same size or larger than the second you’ll want to retrace your steps. It’s easy to get confused and draw the wrong diagonal; take care to extend it across the whole trapezoid. Another common error is to draw the vertical in the wrong place. We have lots of intersecting lines to choose from, it’s easy to make an error.

Now some of you are probably thinking, “But what if I wanted five bays of windows or, like Canaletto, 14 bays of windows? How do I do this?” No problem, it’s all about how we divide the vertical axis. It’s a function of how many stripes we start out with. Four initial divisions of stripes give us four vertical columns, five divisions or five stripes would give us five bays of windows, and 14 stripes would yield 14 columns.

So let’s play with this a bit. We have a second building to experiment with. In the building on the right we’ll create five bays for windows. First, you’ll need your ruler. We want to divide the vertical axis—that’s the front vertical of the building on the right—into five equal units. It’s 10″, so make small marks at 2″ intervals. Lightly vanish these back, just line up the tick marks with the vanishing point to make five receding stripes. Place the straight edge on the diagonal, corner to corner over the receding plane, then make tick marks where this diagonal traverses the receding lines.

At the points of intersection, draw your verticals. Get rid of some of your construction lines and you’ll have five bays or columns for windows. Again, check to make sure that each receding bay is smaller than the preceding one.

We can apply what we’ve learned, and further cement the idea, to draw windows of a specific size within the bays. Let’s say I wanted the window itself to be centered in the bay and framed by an amount equal to one-fifth of the total height and width. Start by dividing the vertical edge of the bay into five equal measures.

Next, I’ll vanish my divisions back toward the vanishing point, and position my straight edge across the diagonal. Now, I could draw five vertical divisions in each bay, but all I need are two to show where each window will begin and end—front and back. So I’ll make two tick marks, then two verticals.

I now have the placement for my windows, and I can erase my construction lines.

Now, we’ll give the windows dimension. Let’s start with the window closest to us in space. You can decide for yourself what kind of thickness you want here and draw a vertical to indicate the amount. Next, we’ll draw a horizontal from the window’s bottom corner to intersect that vertical. Some people have a tendency to want to draw a diagonal here; make sure you stick with a horizontal. Remember, most of our lines will be horizontal, vertical, or diagonals going back to our vanishing point.

This point of intersection between the horizontal and vertical’s important; it will let us carry the measure to the other windows. We’ll line this point up with our vanishing point and draw a construction line forward and back across all four windows. We now know where the interior edge of the window recess is, and we can erase any extra diagonal line—we only need it where the windows will be. To get the same measure in the rest of the windows, we draw a horizontal from the corner to the receding diagonal and a vertical up from their intersection; and we’ll draw a horizontal from the corner at the top of each window to intersect the vertical, then a diagonal related to the vanishing point.

You can finish the remaining windows at your own speed.