Perspective Drawing for Beginners - Introduction to Two Point Perspective

1. Trailer: Welcome to this beginner's class for two point perspective. This class is a follow up to the one point class in this series and is going to introduce to you the basic concepts associated with two point perspective. Two point is a little trickier to grasp than one point. We'll gradually figure out how to overcome its challenges as we go along. We'll start with a brief look at how perspective works in one point. Figure out how to position things correctly, and then do a series of casual and measured exercises along the way. At the end of the lesson, there will be an assignment for you to complete. If you're looking to get started with two point perspective, then this is the class for you. So let's begin. 2. 1 Point vs 2 Point: Before we do any drawing, let's first understand the difference, 1-2 point perspective. Doing a little bit of a recap from our one point class. The first thing that we have to understand is that the environment within our imaginary window is being observed from a first person point of view. You can think of this as either being an actual person or a camera. Either way, you'll often hear this referred to as the viewer or the observer. What perspective our images in relates directly to how our viewer is positioned For as long as the viewer is standing directly upright and looking dead ahead towards the horizon at a 90 degree angle. The shapes and forms in our scene are only ever going to diminish towards one single point called the vanishing point. As our objects move further back into the picture, they become smaller and more compressed, until eventually they literally vanish. Upon meeting this point, our viewer's position is not locked off entirely. However, it can still move both vertically and horizontally. We can move our camera up, down, left and right. As long as there's no rotational tilt to its position, our scene is always going to keep this one point perspective. It also means our shapes and forms in this view are always going to have one plane running flush along our imaginary picture window running parallel. We'll also find that any horizontal lines also run perfectly parallel with our horizon. And any vertical lines run perpendicular to this. True horizontals and true verticals. However, the moment our viewer turns its gaze, either left or right, or the moment we rotate an object is the moment we break that one point perspective and turn it into a two point perspective scene, we end up with not one, but two vanishing points. Even the slightest of rotational changes is enough for a second vanishing point to appear. Objects will now diminish to not one, but two points along our horizon line. Our verticals will remain true verticals, but we no longer have any true horizontals. In simplest terms, one point locks us into vertical and horizontal positions and two point adds in rotational movements. Now we are going to find that this rotational movement is going to cause us a few obstacles that we don't have to contend with in one point. So there's going to be a few more steps involved with this additional vanishing point for creating perfect squares and cubes. But before we do any drawing, let's first do a little bit of a recap for how we need to set things up. 3. Perspective Set Up: Okay, let's just briefly run over how to set things up. Again, if you haven't watched the one point perspective class, it's highly recommended that you watch that class first to really get a grasp of what we're going to cover here. But we're just going to do a brief rundown of how to set things up. Again, we start with our imaginary picture plane, which is where we're going to be placing our environment. That picture plane runs off in both directions to infinity. In essence, the picture plane is a cropped off area of a much larger environment. Across this picture plane, we have what's called the horizon line, which is literally the horizon in the distance in 1.2 point perspective, The horizon line overlaps with something called the viewer's eye line. The viewer's eye line is how far from the ground the viewer is standing. For instance, if the viewer is six feet in height, its eye line will also be equal to six feet. That horizon line intersects with a vertical line called the center of vision. If we imagine ourselves as the viewer, this is a cross section that follows us around for our entire life. Everywhere we look, this intersection comes with us in one point perspective. The center of vision is also the default vanishing point. Now overlapping the center of vision and moving down beyond the picture plane is what's called the station point. It's a little bit of a tricky concept to understand at first, but becomes clearer the more you practice. The station point is a projection of what the viewer sees, as well as how far away from the picture plane the viewer is standing. It allows us to create accurate depth from our viewer's perspective. Its station point, which sits right between its eyes, can calculate both vertical and horizontal measurements, but has no way of establishing accurate depth. That's because we have no idea how far away our viewer is standing from the picture plane, from this perspective. But if we take a look at a view from the top down, we do get an understanding of how far away the viewer is. The station point is still sitting between our viewers eyes. We're just looking at it from above in order to calculate the distance individually. These viewpoints can only calculate so much, but when we overlay them together, it means we can get accurate height, length, depth and angles. Instead of going back and forth between these two diagrams to help us out, we can use this one combined station point to do the work for us. From there, we add in what's called the Cone of Vision. The Cone of Vision is an area of approximately 60, 30 degrees each side of the station point. This circle represents the approximate boundary line for where visual distortion occurs in our images. We cannot actually see this distortion, but we can illustrate it. The further outside the cone we place an object, the more warp its shape starts to become. We don't necessarily have to draw within the cone of vision, we just have to be aware of its presence and the effect it has on the outside. Lastly is the measuring line which intersects with the picture plane and the ground plane, as the name suggests. This will be used for creating accurate measurements. So that's the general set up for perspective drawing. 4. Informal 2 Point Boxes: Let's get started with some informal boxes. We're not going to worry about measurements or accuracy until later on. We're doing two point perspective, which means we'll be having two vanishing points along our horizon line. And we'll label those as vanishing point left and vanishing point right respectively. Then what we're going to do is we're going to choose somewhere completely random on the page to start things off for ourselves. That'll do nicely. We following on from the traditions that were discovered or maybe even rediscovered from the Renaissance. A little bit of debate as to when we figured out perspective drawing. Drawing up our first vertical, and this is going to be the first corner for our box. I'd like to start with the verticals first in two point. I just find it makes things a little bit easier. Starting from our left vanishing point and connecting to the bottom corner of our line. Our vertical being our true vertical. This will create our first line of depth going to the right hand side or the right vanishing point and doing the same thing there. Just remembering that any verticals in two point perspective will remain true verticals. All the horizontals that we learned in the one point class no longer apply here. Everything by the verticals is going to be diminishing to our two vanishing points connecting the top and bottom corners. And trying to be as accurate as we can as well. We can start to see quite quickly that the planes to our box are starting to take shape. Now we're just going to choose a random depth here because it's not super important that we get it super accurate right now, It's just a completely arbitrary choice that we're making for us right now. We don't care too much whether or not this is a true cube or not. We can declare it to be a cube. Not many people are going to know one way or another, that's our right plane done. And I'll get the depth for the left hand side as well. And we can start to build the rest of our box from here nicely. It's all coming together in a pretty timely fashion and it's not too difficult at all. We just get that top plane done and the bottom plane as well. We're going to draw transparently to just to make things nice and clear as well for ourselves. And all of a sudden we've got ourselves a completed box. There we go. We haven't actually done the back corner as well. We're drawing transparently, we've got to draw the back corner to our box is now officially done. That's our first two point box. We'll do a couple more and we'll change the colors as well just to make it nice and clear. Now, it's going to be super important as you take this perspective class, or any perspective class for that matter, to put down a lot of notes as you go along. There's going to be a lot of information thrown at you, even though it's intentionally presented in this class to be as easy to digest as possible. When we move on to the more measured aspects, using the station point and the measuring line, things start to get a lot more complicated. There's no point in denying that, get into the habit of taking notes as you go along, but for now we're just going to be very informal with how we draw these boxes. Starting a new one now and using a nice bright red pen for this new box. And putting it above the horizon line as well, just so we can get to see how the box looks above and below, and making it a little bit larger as well for good measure. Once again, straight lines all the way back to our vanishing point, diminishing all the way back there a nice straight vertical, ensuring everything is very upright there. And drawing another line all the way back to our right vanishing point. It doesn't actually take a long time, as mentioned, to construct the boxes in two point, it's not all that more difficult than drawing in one point perspective cylinders do become a lot trickier in two point, we're not going to worry about anything rounded or elliptical in this lesson. We'll dedicate an entire lesson to ellipses later on, but it's just one thing to two squares and cubes in depth. It's another thing to do circles. A few more challenges involved there. Back to our box, liking how this is looking so far. Again, if I wish to declare this is a cube, I can. It's not adhering to any proper measurements at the moment. The only rules that we really care about at this point in time is that these side planes are diminishing correctly to our left and right vanishing point. Now the thing that often scares us about perspective is that because there's a lot of measuring and guidelines we have to draw, we worry that it's going to rob us of our creative freedom, all of these more mathematical equations as it were starting to get in the way. But the truth is, perspective is more than capable of working for us. If we allow the straight lines and the measurements to dictate what we do, then it's never really going to be any fun. What's important though is understanding what is happening in perspective. If we know what's going on, then we can kind of pick and choose when we want to get more accurate and mathematical. Here we're doing things in a very loose and informal way and it's still producing pretty accurate results. We could craft a composition using this very rough series of guides and boxes here. But as we'll learn, if we want to take things to the extra level and map things out a lot more, be more mathematically accurate so that our objects are in specific angles and positions. Then we will have that option available to us. We want perspective to work in our favor. That's ultimately what we need. We want to weigh out third box here. We're not just going to construct accurate squares in this lesson as well. We're going to do slightly larger, more rectangular shapes. We'll do a rough rectangular box. Now this is going to be a little bit more measuring involved in this lesson compared to the one point class. There's no point in denying it. There's a little bit of a learning curve associated with two point perspective. There's probably going to be some initial frustrations as you take your notes. I promise you though, that once you get to understanding what's going on, it's going to free you up creatively. Now, this lesson is really just a broad overview of the topic. There are many other aspects like inclines and declines, and auxiliaries has mentioned things like ellipses as well that we simply can't cover in this lesson because it's just way too much information. This class is really just a broad overview of the core basics of two point perspective. But we will have enough information by the end to start constructing some rudimentary compositions. Our blue box is almost done. Just need to work out a few more things here. So let's just reiterate what we've done. We randomly chose two vanishing points along our horizon line. We randomly picked the spot on the ground. And from there we drew up a height line for the corner of our box. We then connected the top and bottom of that line to the left and right vanishing points accordingly, which created the boxes left and right planes. We then randomly chose landmarks for the depth for both of those planes, and then aligned those planes to our vanishing points to finish off constructing our box, that's our first lesson done, Let's move on to creating a two point grid. 5. Informal 2 Point Grid: Okay, so an informal grid or a casual grid, whichever you prefer. What does that mean exactly? Well, first, it's similar to what we just did with our boxes. So again, we want two random vanishing points along our horizon line. And again, labeling them as left and right accordingly. But what is an informal grid? Well, it simply means the squares on the ground plane aren't actually squares, they're just an estimated square. So we're just going to arbitrarily call them squares though, for the moment. And we're going to use something called a 45 degree reference point to help build out the rest of our grid. Once again, we are going to find a random spot on the ground plane to begin with. And just like that, drawing it all the way up to our two vanishing points, you could label that as point A or 0.1 or any other name that you like, really if you want. Then again, criss crossing things over like so. And that's going to give us the foundational corner for our first square. Once again, we are going to just estimate the depth of this square, similar to what we did with our box, just a random place along the right that we can then align to our left vanishing point. Now as mentioned, this is an informal grid. These squares are just an educated guess, which means it's great if we're not too concerned with doing things 100% accurately, maybe we're just doing a quick concept sketch or just taking some notes down to put down a quick idea. So we've got the depth for one side and we've got the depth for the other, and we're going to declare this as a square. Where to from here? Well, as mentioned, we need to create a 45 degree reference point. If we split a square diagonally, we get two triangles with a 45 degree angle. What we'll find in two point perspective is that all the diagonals to our squares will converge to the same point along the horizon line. So let's first draw a guide here from our first square, splitting it in half, going all the way down the middle corner to corner diagonally until we meet the horizon line. And that's going to give us the reference point for constructing the rest of our grid. So I'll label that as our 45 degree reference point. Now how do we construct the rest of our grid? Well, we went diagonally from corner to corner, so it makes sense that we need to do something similar. Again, we need another corner to create another diagonal. And sure enough, we have two corners to choose from here on the left and the right. And I'll just make that a little bit more obvious here. If we align our ruler to one of these outside corners, to our 45 degree measuring point and draw up, and we'll do the other side as well. So we'll go over here and do the exact same thing. Suddenly we have created for ourselves another diagonal to make things nice and clear. We're using a nice bright red marker. In this instance, what you're going to find is that these new intersections that are taking place, well, they're going to be the landmarks for what we need to start creating the rest of our grid. Our 45 is crossing over with our initial diminishment lines at the back and the front here. With these new landmarks, you might be one step ahead of me already about what exactly we can do with these now. But let's just make things 100% clear and I'll change the opacity down and use a bright blue color in this instance. These new landmarks we can now align to our vanishing points. I'll just draw that in. Just align that right and put that all the way back there. And come all the way to the front as well. And do the exact same thing. We'll go over the original lines as well in blue. Just so we make things nice and clear, we can start to see the grid is slowly coming together. Now as mentioned again, these are not actual squares, But because we've used that first tile as a means to find our 45 degree reference point, it means that these tiles on the ground are going to be the exact same size and shape, only diminishing off into the distance. That's our left hand side done. Let's move over to the right hand side now and start doing the exact same thing. Again, aligning up to our new landmarks, to our right vanishing point. And we'll strike a line all the way through this back landmark, just like so. And then we'll rotate things to this front landmark as well and strike all the way through that. And then all of a sudden we've got for ourselves a nice nine paddle grid on the floor. Just to reiterate, we created a random square on the ground. We use that square to find a 45 degree reference point via its diagonal corners. And then use that reference point to intersect with our original diminishment lines to find new landmarks to construct our grid. But can we make this a little bit bigger? Well, of course we can. We simply need to follow on from what we started with, that initial tile. And the first thing we need to do is find a new corner for us. So we've got a couple of corners here on the left and the right that we can use from this nine panel grid that we've just done. And we can just simply follow on from exactly what we've done, taking another diagonal from our reference point here, and then striking it down to this corner. And then doing the exact same thing on the other side as well. Now we've got a whole new bunch of intersections that are taking place. Two additional diagonal lines has produced for us a whole series of new points. We've got one there on the one there on the left hand side, we've got a bunch more on the other side as well. More landmarks that we can continue with and build out an even larger grid. And we're not going to be limited to just moving backwards into space as well. We could drag our 45 degree lines out further and create more squares that are coming towards the viewer. So we've got two directions where we can take our grid. So let's start to crisscross things over once again with this new set of landmarks going further back this time. Now there's going to be a lot of software applications out there that have perspective tools built into them. But you do want to learn how to do this type of grid manually. Because if you're out and about and all you have with you as a sketch pad, then those digital tools aren't exactly going to come in handy. So even if you're working digitally in Photoshop or Clip Studio or art rage, whatever it is, get into the habit of drawing perspective manually. It will end up making you a more valuable artist in the long term, It's a valuable skill to have. Now we can see already here, there's already a new set of intersections that are taking place on the left hand side. I'll just finish the right side first. We'll see if we need to keep going with that further back into space. In practice, you could actually take this type of diminishment all the way back to the horizon line. You'd probably need a pretty sharp pencil to do it though. We'll continue on with this new set of intersections. We can see here now we've got all these new intersections that are taking place along the back here. A couple more on the left, a bunch more on the right. So let's continue on with this. You probably wouldn't need to put that much grid in anyway. The closer you get to the horizon line, the more compressed and cumbersome the grid becomes to draw. You'll probably find is that eventually you won't end up needing that much information on your ground plane to start your illustration. The more you draw perspective, the more intuitive it become, and the less grid you're likely to need. Many perspective artists don't even put in full grids. They just throw in a couple of really rough diminishment guides. And that's all they'll need to create the scenes. We only need a couple of landmarks here and there to start putting together a composition. Our grid is pretty much done here. We could, of course, keep going back further and further, or we could bring it forward as well, just finding new corners that we can align to our 45 degree reference point and keep going from there. But we'll leave this here for now and we'll move on to doing something a bit more measured. 6. Vanishing Points at 90 Degrees: So let's talk about how we use the Station Point to create accurate two point measurement. Again, the station point is a combination of two viewpoints. A top down view representing the distance the viewer is standing from the picture plane, overlaid with what the viewer's first person perspective is or what the viewer is looking at. This means that a measurement in one viewpoint directly relates to a measurement in another. How do we use this to create perfect flat squares on the ground? Well, we know that a square has to be made up of 90 degree corners. And we know that we have to have two vanishing points, which means we need to create guides that are 90 degrees from each other. We can't get that specific calculation from our viewers first person station point, but we can get it from our top down station point. If we draw two lines, 90 degrees from each other out from this station point, they are going to end up at two specific places along the horizon. Because these landmarks are truly 90 degrees from each other, it means that it's going to give us the ability to build true squares and cubes. Now, the beauty of this is that as long as we keep those guides at a true 90 degrees from each other, it means that we can rotate them to any area that we want and still produce perfect squares and cubes. We're not limited to this one position. Our station point suddenly starts to double as a bit of a pivot point. If our guides go beyond or before the 90 degrees, then our vanishing points are going to be off, and we will never have true squares and cubes. The key to creating squares and cubes in two point perspective is to lock our vanishing points to be 90 degrees from each other. 7. Formal 2 Point Cube: All right, measured cubes. And we've got our formal set up here. We've got our horizon line, we've got our A vision which is spreading out 60 degrees either side of our station point. Which of course is the two dimensional representation of how far away our viewer is standing from the picture plane. Measured cubes means we are creating vanishing points that are exactly 90 degrees from each other. But first, we need to find a random spot to begin with here. And that's going to be the corner of our cube, and we'll readily choose a place for vanishing point left. These are both random choices at this stage, but because we know the location of vanishing point left, it means that if we want that true 90 degree corner in our two point perspective, vanishing point right has to be a very specific location and we get to that location via the station point. A true 90 degree corner from the view of our station point. That top down perspective of our viewer is equal to a 90 degree from the viewer's perspective. So I'll line the ruler up here to be exactly 90 degrees, nice and flush up against. Then all of a sudden we've got the exact location of where vanishing point right needs to be. So we are 100% committed. The moment we choose the position of vanishing point left means we are committed to this position for vanishing point, right, because of that true 90 degree corner through the station point. So where to from here then. Well, in order for us to make things accurate, we first have to put down a measuring line. And that's going to help us ensure that our cube is nice and even all the way around. So I'll just go back to our original spot here and I'll measure out two units of measurement either side. And we'll just say one a half inches. Either side here should be fine. And this horizontal measurement is going to represent the length of our right and left planes for our box. And of course, if this is the length of our cube, it also means that our height needs to be the exact same measurement as well. Because a cube is equal all the way around, what we're going to do is lift that up 90 degrees and get the exact same measurement. Then that's going to give us the exact height that we need for our cube. I'll just draw that up right now. This height measurement is also going to double as the first corner to our cube, similar to what we did with our casual set up. We've got our height and we've got our length here. What we can start to do then, and we're going to use different colors just to make things nice and clear, is that we'll criss cross things over. So this is the bottom of our cube. And we'll use a nice blue color for this side, for our left hand side. And we'll change it over to a green here, I think, for our right hand side. And we're not going to worry about doing the top just yet, because we need to figure out a way to swing these horizontal measurements that we've just drawn in. So they strike these left and right planes in the exact position that we need. Because we can't guess here if we want that even cube all the way around. These need to be in very specific positions. So we're not just going to randomly guess this time. So how do we go about getting the exact depth measurements? Well, luckily it's not too difficult. All we need to do is take the length between our vanishing point and our station point and swing it up till it meets the horizon line. Alternatively, we can use a ruler and get the exact measurement distance here. In this instance, it's about 21.5 centimeters according to this rule. I'll just jot that down, 21.5 and we'll take that distance and mark it across from our left vanishing point, like so 21.5 And that's going to give us the first landmark we'll need to get our depth. And we're going to be calling this our measurement point. So I'll label this as measurement point left. And I'll also change this to blue as well just to make things nice and clear. So just jot this down as well as left plane as well just to make things a little bit clear as well. So we've got measurement point left that we've created. It's the exact same distance between our vanishing point and our station point. What we've essentially done here, and it's a little bit of a tricky concept to wrap our head around. We've taken this distance here, and we've taken it from a flattened two D space and essentially swung it up into a three dimensional space. So we've done it for our left hand side, but we also need to do this for our right hand side as well. So switching to green again, and I'll just write that down as right plane just so we're 100% clear about what's going on. Again, the distance between our right vanishing point and our station point. And swing that up, I'll just grab the distance here just to align that up. It's about 19. A nice easy number to remember. Again, I'll align that up to our right vanishing points. If I could just get the ruler to work, I'm measuring that up to be 19 centimeters across from our right vanishing point. And that's our second measuring point. And that's going to be measuring point, right? And that's going to relate to vanishing point, right? Which again, just to make things 100% clear, is this length between our station point and our vanishing point being swung up into three dimensional space right here. These landmarks, these measuring points are going to be used to construct our true depth for our cubes. We're going to do that by connecting them to our measurement line, our horizontal measurement line here. Normally, what we think we have to do here in this situation is that we connect our vanishing points to the measuring line to get our correct depth. That's never going to give us true depth. Instead we want to connect these new measuring point landmarks to our measuring line on the ground here. If we strike all the way through here, that's going to give us the actual depth. So let's get our ruler out and align things up again. Perfectly again, like so. And just criss cross things over again. Connecting measuring point left to our measuring line on the ground plane. That intersection that we now have that we've created here on our left plane. That is the true depth of our cube. We've previously just done a bunch of random guessing about the depth for our cubes. But now, because we've done all these measurements, we know for certain here that we've essentially swung back this measurement line back into three dimensional space. So if we do a little bit of a top down view of what this actually kind of looks like, that's our left plane, that's our measurement line. And essentially we're swinging at the door shut as it were. We know 100% with certainty that because we align that measuring point to that measuring line, this is the exact depth for our cube. And we can do the exact same thing to the other side as well. If we take our right point and we align that up to our measuring line on the right hand side here. Twist that round, get that aligned up, and try to get that all the way right. It seems better if we strike that all the way through, we're going to get the exact depth for the right plane of our cube. We've taken measuring point left and connected to our measuring line and got the depth for our left plane. We also did the same thing for the right hand side as well. These are the foundations that we can start to use to actually build up the rest of our cube. Knowing that for certain that because we've done all these measurements, that this is actually a genuine cube in two point perspective. What we can then do is take this new landmark, take it up to our right vanishing point, Strike that all the way across. If we get the alignment right, strike that across and do the exact same thing for the other side. Going back to the left vanishing point, align it to that brand new landmark, that depth landmark, just like we'll strike that all the way through, That gives us a perfect square tile in depth. Now it has to be pointed out that this intersection here is where we start to build from for the rest of our box, rest of our cube rather, and not the intersection where our measuring points cross over. We just want to do those very lightly, those measuring point guidelines. From there, you might be one step ahead of me already. Here we can start to build the rest of our cube, aligning to our left vanishing points, going all the way across there. Getting that correct, then what we can do is take things over to the other side as well. Just making that clear, that's going off in that direction. Now moving over to the right vanishing point. Do the exact same thing that we just did here. Strike it all the way through. Striking it through just like. So once again we'll be drawing transparently to, just to make things abundantly clear. We've got the top and bottom of our box done now, because we've got the exact depth that we need, we can flip things vertically and start to put in our corners. This is looking good so far. So let's start to get the verticals in now to our true cube. Get that in like line that up nice and straight, just like that. True verticals as mentioned, go to the other side as well. Get that in. All of a sudden our cube is coming together and you can see how we can start to put things together pretty quickly. Just to reiterate what we've done, we started with a random choice for the position of our cube. We randomly chose a location for vanishing point left, which subsequently committed us to the position of vanishing point. Right? We located vanishing point right, by creating a 90 degree corner from our station point to the horizon line. We then created a measuring line on the ground to establish the length and height of our cube. We then had to work out the true depth of our cube by taking the distance between each vanishing point and the station point, and creating measurement points along the horizon line for both sides. We then connected both of these measurement points to our measuring line, which created landmarks to establish the true depth for our cube. And then finally, we used those landmarks to construct the rest of our cube into two point perspective. There's a lot going on there. And I really encourage you to take these concepts and go over them several times to really try to memorize it for yourself. Because there's a lot of information that's just been thrown at you here. Just take it at your own pace and take it one step at a time and construct the cubes as best you can. All right, let's move on to the next video. 8. Formal Grid Part 1: Okay, we're going to do a formal set up for a grid now, which is going to be very similar to what we just did with our cube. So that's our center of vision line in place. The station points down below there. We've got our horizon line as well. And we also need to establish the cone division, which is 30 degrees either side of our station 0.60 degrees in total. There's going to be a lot of similarities to what we just did with the cube, with the measuring point and the measurement line. But this is going to be a few additional steps here. So we're going to break this part of the lesson up into a couple of videos just to make sure things are abundantly clear. Because there's going to be a lot of line work that we're going to have to put down. And it's going to take a little bit more work and it can get a little bit more confusing as well. So we'll just take it one step at a time. So that's the code division in place now. We've got our random choice for vanishing point left. And because we have a random choice, we know precisely now where vanishing point right has to go. And that's 90 degrees from this station point. So I'll just line this up here, try to get as perfect as possible. Nice. And 90 flush against the line there. And measure that up. And that's going to give us vanishing point, right? And it is also going to mean we're going to get a true 90 degree corner when we start to construct our grid. If we're repeating things a couple of times here, it's entirely by design because these are some difficult concepts to understand Sometimes the more repetition we do here, the easier it starts to become for us long term. So I'll start to criss cross this over. Now we've got our random vanishing point left here, which is created our committed vanishing point on the right. So I'll crisscross that over. That's going to be the starting point for our grid, a nice 90 degree corner in two point perspective. Let's just do a recap. We've chosen a random spot for the start of our grid that's 100% random. And then we've gone to choose a random spot for our first vanishing point, vanishing point left. And because we made that decision, we automatically committed ourselves to a specific place for vanishing point. Right? We got that position by creating that 90 degree corner via the station point. We are 100% committed to that second vanishing point, the moment we chose the first one. That's the breakdown for the first part of our grid. Let's move on to the second part. 9. Formal Grid Part 2: All right, we're continuing on from part one, where we're going to be doing something very similar to what we did with our cube and draw out our measurement line. But this time we're going to extend it out with our cube. We needed only one unit of measurement either side of our starting point to help calculate its true depth and two point perspective. But our grid has got many tiles on the ground. So we need to increase the number of increments in our measurement line. First things first, let's put down some units of measurement here. And I'm going to be using just 1 " increments this time. And we're going to put down as many as we can here across the page of our starting point, all the way to the right, and of course all the way to the left as well. Our goal here is just like the cube to swing these 1 " increments back into this three dimensional space that we are creating. I'll make a couple of those landmarks I think, just a little bit clearer, A little bit bolder, so we can see exactly what we're connecting to. I'll mark this down, as well as our measuring line, just to be clear. We just want to reiterate from earlier in the video as well that this is also overlapping with the ground line which is the intersection between the picture plane and the ground plane. So there's a lot of intersecting and overlaying going on with perspective. Again, I'll just make sure that these initial diminishment lines are labeled as left and right accordingly. All right, our measurement line is done and our goal is to apply these increments to our left and right planes, accurately getting their position in depth correct. What's the next step? Well, we need to figure out our measurement points again. What do we need to do? Well, we need to take the distance line between our vanishing points and our station points, and then swing them up to our horizon line. Again, we're starting with vanishing point left. We're going all the way down here to the station point. We're going to swing that measurement all the way up until it meets our horizon line. Or alternatively, as I prefer to do, I'd like to just get the distance here, which if I align this ruler correctly, looks to be, I'd say that's about 19.1 centimeters to my eye. I'll just say that's the measurement in this case. And I'll jot that down and then I'll take that same distance from our vanishing point left along the horizon line to get the position of our left measuring point. So I'll mark that down as left measuring point, or measuring point left, whichever you'd prefer. Just to reiterate again and forgive the repetition. In essence, we are taking this distance from our flat two dimensional perspective and we're translating it into a three dimensional first person perspective by swinging it up to the horizon line. And of course, we need to do the exact same thing for our right hand side as well. So getting our right measuring point, which in this case is about 22.6 centimeters. Again, just measuring across here to get that exact same length. As I said, forgive me for repeating things a few times. There's a lot of concepts that we're going to have to remember here, and sometimes just having a little bit of repetition is going to help us out. Again, we've got these measuring points which are linking over to their respective vanishing points. You might be one step ahead of me here, but we'll go over it. Just to be clear with our cube, we created a guideline between our measurement line and our measurement point left. And the intersection with our left plane created the depth landmark for that unit. We're swinging that unit of measurement back onto that left plane. But now we've got multiple units of measurement along the left and right measuring line. Because we're trying to create a grid here. And we have to find landmarks that run along the left and right planes respectively. So how do we do that? Well, luckily we just have to move our measurement point over to the next unit. Let's first draw in the landmark for unit one. And we'll just strike a line straight through there. And that's going to be our first intersection on our left plane. Then move over to unit two and do the exact same thing. We don't have to draw lines all the way back just where the intersection is taking place. Unit three done over to unit four, over to unit five, and so on and so forth. We can keep going along, ensuring that we are creating landmarks all along our left plane. We're just about to run out of units here. This will be our last one. Just like that, we've created our first set of grid landmarks along our left plane. So for as long as these units of measurement along our measurement line are diminishing off and to our left measurement point here, we're going to get their correct position relative to each other in two point perspective. But we can also bring this out towards the viewer as well. We've got a bunch of landmarks that we can do here because not only is our left plane extending out well beyond where we put our initial center point down here, but our measurement line is also extending out here and giving us new increments that we can strike through Just going through unit one on the right hand side of our starting point. And we're striking it through to our left plane, which is extending quite a long way out here. Now we'll start to see that things are going well outside the cone of vision right now. Our vision is where we have a bit of a boundary line before things get distorted and things are getting really distorted out here. Now those are our landmarks for our left plane, and these are all equal to each other. What we need to do next is the exact same thing for our right plane. We are aligning our right measuring point up and we're just aligning it with the corner first and moving over to unit one on the right hand side and striking through the right plane. Unit two, unit three, and then again, so on and so forth. Going all the way back probably about five or six units on this side. That's our landmarks. Moving towards the horizon line there as well. Again, we've taken measuring point, right? And we are aligning with the units of measurement along our measurement line, crossing it over, striking it over until it hits our right plane to get us the landmarks that we need. Now, if all of this is feeling a little bit overwhelming, just try to take it a step at a time. And I know there's a lot of lines on the page right now. There's a lot of landmarks as well. And you're probably saying to yourself, well, this is getting a bit too much for me and all that, but I really recommend just going slowly through these concepts and going over them again and again, and to take notes as you go along. I promise As convoluted as this looks at this stage, it does become a lot easier. Eventually you'll eventually get it and you won't think twice about how to set these up. You'll be able to do it in a matter of minutes. So just to reiterate, we've done something very similar that we did with our cube. We aligned our measuring points to our measuring line and we figured out how to craft these units of measurement along our measurement line into their correct depth along their respective planes. So let's finish this off here and we'll move on to now, constructing the actual grid. 10. Formal Grid Part 3: Okay, we're finally onto the home stretch now where we finally get to put our grid together. So, we just want to be a little bit careful here because it's actually very easy to start putting down lines and connecting them to the wrong marking. So we just want to be a little bit cautious as we do this out. So we'll use a nice thick black marker here to make things nice and clear. And we'll just go over our first original diminishment lines, our left and right planes that we originally put down and criss cross those over. And we'll start to criss cross things over to our landmarks in a second. As soon as I get this lined up and it looks about right, again, criss crossing that over our original markings there. And that once again gives us that nice 90 degree corner. What we're going to be doing now is that we're going to be going from our vanishing points to these landmarks along our left and right plane, our right vanishing point to the left plane landmark. Let's do this one at a time and align that up just like this. And move over to unit one. Strike that all the way through, we'll go pretty long here as well. Go to unit two, strike that all the way through as well. And just keep going backwards until we've hit all of those landmarks. Make this nice and clear again, I just want to take your time a little bit here because there's a lot of markings on the ground, even though we've done things pretty lightly for the most part. And it's only now that we're really making things nice and dark and clear, it's very easy to still hit the wrong mark. I know I've done it more than once in my life. That's our first side done. Let's move over to our left vanishing point now and we'll do the exact same thing. We'll align that up, go to our right plane and strike to our next landmark. That's going to be going all the way back here. All these landmarks. And now aligning to vanishing point left. And we'll strike that all the way through. Go to the next one. This is unit two. Now onto unit three as well, and so on. Or actually this one is not looking too good. Let's try that again. Go all the way back there. Want to double check your measurements and make sure everything is nice and aligned in that you haven't accidentally missed a marking somewhere along the line as well. It's good to double check your stuff all the time. Again, going all the way back here. As you can start to see, our grid is finally starting to form. Now after a lot of work and a lot of measurement, we're starting to get our actual grid in space. So all of these tiles in the ground here, they are actual squares. Now we'll just bring this forward too, coming towards the viewer now and going well outside the cone of vision as well. Things are getting very stretched and more extreme outside the cone of vision. These squares are actually going to look like rectangles. And it's going to be super tempting for us to actually try to fix that. But we know, because we've done all these measurements, that our vanishing points are exactly 90 degrees from each other through the station point. These are actual squares. Avoid the temptation to try to fix these. As it were. Our grid still coming together nicely. We'll just bring these diminishment lines out the front. Now strike that all the way back again, making sure we hit the right landmarks and not accidentally hitting our measurement line, which is quite easy to do. Again, striking that all the way back there. Do a couple more here. We've just got enough room for one more, I think. Just strike that all the way back there. All of a sudden, this is our measured grid in two point perspective. I'll just turn off all these other lines for a second and take a look at it. This is looking pretty good to me. We've done a lot of work here to try to get this right. Actually, I think there's one that's missing at the back there. I think I've accidentally missed one. There you go. It pays to double check your work then. Yes, I've definitely missed a landmark along that left plane. Let's fix that up, shall we? We'll align that up there and strike it all the way through. That's officially our grid done. That's everything that is now measured and we know for certain now because we've adhered to all of those measurements that we've done. This is actually a grid with true squares on the ground. But we could expand upon this as well because we ran out of room for our measurement line and we've got a whole lot of space out the back here that hasn't got any actual grid to it. What we can do is what we did with our casual grid is that if we connect our diagonals here, in theory, all of these diagonals should connect and go all the way corner to corner to find our 45 degree reference point. What we can do then, the same thing that we did with our casual grid, is then find ourselves a corner, which I'll use on the left hand side here. Strike a guideline through that, just like so. All of a sudden that's going to give us a new set of landmarks to continue our grid on from. I'll just align up to our vanishing point here and I'll just start to strike these through and that's a little bit thick, we might choose a slightly thinner pen going backwards here because it's going to be a little bit too convoluted trying to use that thickness. So yeah, we can just continue on with this all the way back to the horizon. So that's how we do a measured grid in two point perspective. There's a little bit of work involved, no doubt. But if you do a little bit of practice with it, eventually it starts to become second nature. And it means then that you can pick and choose when you want to do something more mathematical and accurate in your illustrations. 11. Measured Rectangular Box: All right, so onto our last video. Now, we're not going to bother setting things up from scratch now. We're just going to overlay from what we've done previously. We've got our cube here, but we're going to expand upon this. And I mean that quite literally, we're going to turn our cube into a rectangular box. So we look at this from the top down view. Obviously that's the top of our cube and we want to make something now that is a little bit more rectangular. Like luckily this is just another extension from what we've just gone over. So we've got our measuring line here, of course, on the ground. And I'll just label that there as such. Now instead of doing what we did with our grid and marking each individual increment along our respective planes, we're going to count across to a specific unit of measurement now and draw our box in that way. So this is our corner, of course, for our box. And we're going to make things a little bit easier for our measurement line in a moment by actually numbering each of these so that it's a lot clearer for us. But like the other times that we've already gone through this, we're going to go from our measuring points to our measuring line left and right here accordingly. Instead of counting to the next unit, we're going to go to a specific unit. Let's start to write our numbers in. So this is obviously 0.0 We've got 1,234.5 along the right hand side. We've also got 12,345.6 on the left. We've got extra space on the left hand side there. We probably won't use it. Now We need to figure out what is going to be the size of our rectangular box. Let's just try something not too difficult. Let's try, actually you know what? Let's make it a little bit longer. Let's go crazy and make it three, shall we? So three on one side, on our left hand side, and our right plane is going to be four units in length. Let's grab our ruler and align it to measuring point right first this time. And we'll count 1234. We're going, of course, along our right plane there, making sure that we are intersecting that plane and no other lines here. 1234. And there is our unit of measurement now in depth, we'll label that as four, it's four units deep for the start of our box. And we're going to measuring point left now, and we're counting across our third unit over here. 123 of course. Going across to our left plane here, making sure the intersection is taking place. There. Just getting the ruler in right here. There we go. There's our landmark for three units going towards the left plane. That's the start for our box. That's the depth that we need for both sides here. Let's once again align things up to our vanishing points. Start to criss, cross things over. And I'll just build on top of our original cube here and a nice bright pink color to make it obvious to see, taking that vertical all the way up. And that is the depth for our box and it's right plane, so it's four units deep in that direction. Now we want to go over to the other side now, aligning up to vanishing point left here and taking this across to our three unit length on the right. Take it from the top here as well, so it's looking pretty good. Align our vertical here, straight up from there. So we've got our three units deep on the left hand plane here. We're three units on the left hand side, four units on the right. Let's finish this box off this rectangular box again, over to our right vanishing point, criss crossing that over for the top of our box. There we are. We've got a little bit of a loose end here, we might erase that out. I think just to make it look a little bit better. Again, we've measured across from our measuring points to a specific location along our measuring line. Now we'll just finish off the box. Again, we're working transparently here. I'll just do a little bit more of a lighter color for the back side of our box here, just so we finish it off properly. That's pretty much going to do it for this lesson here. It's been a lot of information, no doubt. Take your time when learning this stuff because it's going to take a little while it to really sync in. If you want to play around with more complex shapes and start creating your own little more complex compositions from this, then by all means give it a real good go. But just take it one step at a time here, because it has been a lot of information. It really does take a little while to master this stuff out. We'll consider this done and we'll move on to the assignment.