I'm Karl Ulrich, and this video explains how to draw, using a technique called two point perspective. I want to start by explaining a few of the theoretical foundations for using two dimensional drawings to represent three dimensional objects. We can use a few basic properties of how our brains process images to give the perception of three dimensionality using lines on a two dimensional drawing. These are visual properties that we take for granted, because they're so ingrained in the way our visual system works. Look at this image of a cafe. It's pretty obvious that this image represents a three dimensional space and that the tables in the cafe extend out away from us. There are three main reason our brains know this, the first reason is occlusion, objects in the foreground occlude our ability to see what's behind the object. We can use that trick in a drawing to communicate that an object is in front of another and therefore to represent three dimensional information. The second reason is relative size. See how the flowers in the foreground are much larger than the flowers in the background as displayed on that two dimensional image that indicates that the smaller flowers are farther away. The third reason is shading and shadow, the way light interacts with three dimensional objects creates shade and shadows that our brain uses to interpret three dimensional shapes. In product design, we'll use all three properties to communicate geometry. Perspective drawing exploits the relative size property of images, particularly as exhibited by parallel edges. Here's what I mean. Consider a pair of parallel edges, say, any parallel features in this street scape. We know these edges are parallel in reality, but if the edges extend away from us, they appear to our eye to converge. That's because the distance between the edges will appear to be smaller if those edges are farther away from us. The visual trick in perspective illustration is to show edges that are parallel in reality as converging on the page. That gives the brain visual cues as to the three dimensional arrangement of the edges. For many kinds of sketch and visualization, and particularly for product design we make a simplification we call two point perspective. We assume that the objects we're drawing are relatively flat, that the horizontal dimensions are longer than the vertical dimensions. And that we are essentially looking at the front corner of the object, and that the horizontal edges will converge off to the sides of that front corner. In two point perspective, all parallel edges that are in the horizontal plane, will converge, like the edges along the side of the bus. But in two point perspective, vertical edges stay parallel, there is no convergence. So anything that is vertical in reality is shown exactly vertical on the page. All vertical edges are parallel and vertical in two point perspective, always. This clearly would be a terrible simplification. If we were trying to create the impression of looking up, for instance, at a skyscraper, in which case the vertical edges would have to converge because the vertical distance is so great. But it works pretty well, for a more horizontal object as shown here, with the famous Falling Water house designed by Frank Lloyd Wright. So in two point perspective, vertical edges are always vertical, but all horizontal edges converge. And in two point perspective, they converge at two points on the horizon called the vanishing points. Again, the assumption we make here is that the object we're trying to visualize or represent is block like with two orthogonal faces meeting at a front corner. Here's another way to think about it. Imagine you're facing the corner of a big fenced field out on a flat landscape. And the two fence sides are orthogonal to each other. Consider a corner post which we draw perfectly vertical. A rule of two point perspective. But the fence lines, think of this as the top and bottom edges of a fence wall, converge at two vanishing points on the horizon. Again, in two point perspective all vertical lines remain vertical. So if we were to imagine some additional fence post for instance, they would all be vertical. But the horizontal edges converge at two vanishing points on the horizon. Before we get into the details of how to actually draw these converging lines, I want to tell you another trick. Most objects can be thought of as combinations of blocks and cylinders. Some objects are clearly blocky, some are clearly more cylindrical, and of course, some are complex combinations of blocks, cylinders, and other forms. But if you can master drawing blocks and cylinders in two point perspective, then you can pretty much draw anything. So let's use these ideas to draw a block in two point perspective. Let's go back to the fence and imagine that there's a block at the corner. The basic idea is that the edges of the sides and the top of the block will converge at the appropriate vanishing point. You already see how the sides follow the fence and converge at the two points on the horizon. Now imagine the top of the block, the parallel edges of the top will also converge at those same two vanishing points as shown here. See how the edges defining the sides converged at the horizon, so did the edges define in the top phase. Now let's consider how perspective changes with the location of the object relative to the horizon and the vanishing points. First consider a block below the horizon, and centered. We draw it by first drawing the front corner, like the fence post. And then drawing the sides and top. Now, see how the apparent position of the block changes if we locate the front corner of that block in different places relative to the horizon and the vanishing points. Remember the rule. All vertical lines remain vertical. Horizontal lines always converge at one of the two vanishing points. Now let's turn to drawing cylinders. The first insight as at the top and bottom faces of a cylinder appear as ovals or ellipses when viewed from an angle. So we can get something that looks pretty close by just drawing an oval freehand and connecting up the sides. But let me show you how to draw a cylinder with a more technically correct shape. First draw an enclosing block, that is the block that would enclose the cylinder. Then put some guidelines on the end faces. In this case, just draw two diagonals and two bisecting lines that cross at the center. Now draw an ellipse on the end faces. Now it's technically not a perfect ellipse because of the foreshortening of the image. But you know where the tangents must be located, there at the intersection of the bisecting guidelines with the top and bottom of the enclosing block. Then you draw the sides and then you ink and erase. So in most sketching, you will rarely go to the trouble to actually draw that enclosing block. With practice, you'll be able to just draw a credible cylinder freehand. All right, now, let's put all this together. Here's a simple, very blocky object, not much different from just drawing a block. It's shown here as a pencil case and it's basically just a block with some additional features on it. Here's a simple object with a circle as its defining feature. But it's a circle with a slab stuck to it to represent the handle. To draw this spoon, you block out the handle and the box that would enclose the spoon itself, and then you sketch in the curved edges. Here's some more complex object. This is actually the stapler my grandfather used in the general store he owned. It's composed of a slab like object, a block, and a few cylinders. Here's a really quick sketch that in real time took about 90 seconds to draw. And then here's a much more careful version of the same object that took about 15 minutes to draw. But they're both drawn by thinking about the object as a composition of blocks and of cylinders. Well that's basically it. But let me add a few additional points for those who want to get into more details about how to make the drawings both more dimensionally accurate and also to use shading and shadow to better communicate three dimensionality. You may have noticed heavy inking of some edges. What's going on here? Well, a trick used in drawing for product design is to use a very thick line for all the outer edges of an object. These are the edges that have nothing behind them but empty space. By making those outer edges thick and dark you suggest a shadow, giving the object a three dimensional feel. Note that the lines that do not represent outer edges are drawn quite thin to establish contrast with those thick outer edges. You can also add shading and shadows. Consider what kind of shading and shadow would be created if your object were illuminated from a single source. Here I show some faces darker than others because they're not directly illuminated. And I also show a shadow cast by the object. The last technique I want to show is Is how to create proper proportion along the horizontal feature of the object. You can work out proportion by dividing the faces of an object using diagonals to find the midpoint. Pick a face, draw two diagonals from the corners. You know the intersection of those diagonals must be the center of the face. Then draw a vertical line at that intersection and you've now bisected the face into two rectangles. Note that visually the back half is smaller than the front half on the image. Even though in the object you're representing, those will be of equal size. You can bisect again and again to further divide the face, and therefore to give yourself a reference for establishing locations and proportions of features on the object. Well that's pretty much it for the tricks and techniques. Now you just need lots of practice. Practicing your perspective illustration is a really good thing to do in boring meetings. And I'm pretty sure we can all find a few minutes in a boring meeting every day to practice our drawing.