 These are three-dimensional pictures laid out in another kind of view. And there's two kinds of views that I want to sort of discuss here. So I'm going to go, here's a picture of a three-dimensional system, kind of like we were sketching before. This is a three-dimensional system in space. And in this case, I might say, hey, let's call this the x-axis. And we might call this the z-axis. And we might call this, if I keep going in this direction, maybe the y-axis goes into the page. I've sort of been sketching things like that before. But notice there's different angles here. This angle here is a right angle, 90 degrees. If that's a right angle, what are these two angles? Well, together they will add up to 270. And since this seems to divide them right in half, what's half a 270? 135 degrees. The other way we can sort of think about that is if we divide it up into 90 and 90, then this is 45 and 45. And 45 plus 90 is 135. So this is what we call a diametric projection. The reason why it's called diametric is because we have two of our angles are the same. Or the other way of thinking about that is two of our lines are lined up so the space along these lines is the same. And usually, this diagonal one is a little bit longer. This kind of corresponds, if I take my picture in net logo, you'll notice that's more or less when it starts. Let me hit reset perspective again. When it starts, you'll see that we have a nice right angle right here. And that this angle here kind of runs almost to 45. I probably have to move it just a little bit, but pretty much at a 45 degree angle off there. Maybe if I zoom in, it looks a little more like a 45 degree angle. This is called a diametric progression where two of my angles are equal to another. But if I take that and I spin it around, let's see if I can orbit this the way I want to orbit it. Yeah, let's go. I'm going to spin it around and look right down the middle at that point in the middle. So now I have a vertical and an angle here and an angle here. And it's looking right down the middle. It creates a different perspective. And this is the one we're going to use today where all my angles are the same where I have a whole bunch of equilateral triangles. This is called an iso. Iso meaning the same metric projection. Iso meaning everything's the same. So with that, I might draw my x-axis. My z-axis is the one that's up. And then the y-axis goes into the page. But now instead of these being 45 and 90 degree angles, they're 60 degree angles. So we're going to practice taking an isometric projection and turning it into orthographic, that picture looking at it from each side. So I'm going to go back to this page here. Here I have a bunch of little figures. You're going to draw some of these figures on your own. But today we're going to practice in looking at number one, this kind of L shape. OK? To do that, first I want to go ahead and set up a coordinate system or a basis. So I'm going to identify my basis like this. Let's start. I'm going to draw an origin here. And I'm going to say up and down is going to be my z-axis. There's my z-axis. Side to side on my little piece here, this looks like it's side to side. So I'm going to go ahead and make side to side from that upper left to lower right. Anything that runs from upper left to lower right on that angle is going to be along an x-axis. And then anything that runs front to back will represent by moving from the lower left to upper right. There's my y-axis. So there's x, y, and z are defined. So I'm going to kind of sketch here. Here are lines that are running along the x-axis. Here are lines that are running along the z-axis. And here are lines that are running along the y-axis. People sort of see those. OK? I'm going to use my color coding for something else here. I'm going to go ahead and erase those right now. But that's the idea is that's how isometric views are drawn, that we orient things so that their axes are at these 60, 60, or the 120, 120, 120 lines. So now that I've established my basis in the picture, I need a piece of graph paper. And you'll want to take out a piece of normal graph paper. And I'm going to start by creating my front view. And to create my front view, I'm going to need to go ahead and create here's an x-axis. And I'll go ahead and create a z-axis. And I'm going to put a point right here. We'll call this point number one, which is going to be the lower corner of my picture. Hey, there's one in the lower corner of my picture, the beginning of the x-axis. There's the x-axis, and there's the z-axis. So let me go ahead and travel along the x-axis. One, and a unit's going to be one of these bases of a triangle. Two, three units. Three units along the x-axis. OK, here I go. One, two, three units along the x-axis. From there, I go one unit up the z-axis. And on the other side, I go one, two, three, four units up along the z-axis. One, two, three, four. One unit up here on this side, and one, two, three, four units on that side. I'm beginning to see that sort of shape of that L shape. From that top point, I go one along the x, down three along the z, and then two along the x. And now I've finished creating this sort of front view. One along the x, down three along the z, and then two along the x. And there is my front view. And notice I've grabbed all of the things that haven't had any motion when I start here. If this is my origin, if point one is my origin, none of the places I went to, I got by going backwards along the y-axis. So they're all in that same front plane. All right, what do we want to do next, Makayla? You want to do the top view or the side view? Let's do the top view. OK, so if I'm looking here, I got to figure out which things are going to be the top. Well, those are going to be things that I'm looking down on. And it looks like if I'm looking down, I'm going to land on these things here. So I'm going to go ahead and color those in purple. Or there's that one of them, and there's the other one. So let's start with that one that's up on the top there. But I'm going to have to identify some points that I already know. Hey, here's a point. Let's go ahead and call that point two. And the thing about point two is it's directly above point one. OK? So one and two are directly above each other. They have the same x and the same y coordinates. But really, all I care about is that they have the same x-coordinate. Because now I'm going to go and create my top view. And on my top view, I have the same x-coordinate. But now I have y here. So point two is directly above point one. But it has the same x-coordinate. So we're going to put both of those points, point one and two, are on top of each other. They're sitting on top of each other. Now that I've established where that is, let's go and see how we can trace it out on our picture. Well, point two here looks like it goes along the y-axis, one, two, three units. And then from point two along the x-axis, it goes out one unit. And from there, I make a nice rectangle. Let's see if I can make that same rectangle back here. I started at point two, and I went three units in the y-direction and one unit in the x-direction to make my rectangle. Well, that was easy enough. Notice that corresponds with what would be sitting right there. What other surface do I see? Well, let's take a look. I think it's this surface down here. Let me make this one in green. There is a surface right there. OK, so I'm going to identify a point that I start with. I'm going to go ahead and look for this point here. We're going to call that point three. Let me identify point three in a couple places, because we're going to use it to work from. Here is point three on my front face. Now that I've located it on my front face, let me go ahead and figure out where it is up there. Well, I know where it is vertically there, but I don't know where it is exactly on the y-axis. Let me go and take a look and figure out where it is on the y-axis. Oh, it's in the same location. It's directly above this other point down here, and it doesn't go back at all from number one. It went over and up from number one, but it doesn't go back. And it looks like it's on the same plane. Since it's on this blue plane, it must have a y-axis or y-coordinate of zero. So I'm going to go ahead and put it right here. There's point three. If I'm not sure about that, it'll hopefully we'll confirm it a little bit when we draw the other view. But let's see what point three looks like. Point three goes three units along the y, and then three units in the backwards direction along the x. Oh, no, sorry, two units, one, two. So three units along the y and two units backwards, three units along the y and two units. So there's a rectangle there. I know it doesn't look like a rectangle on that page, but here I go three units in the y direction and two units in the negative x direction. And then I fill out that rectangle. That's the rectangle that's sitting right here. And now we've completed the plan view. Well, now I need a miter line. Kind of wanted that in a different color. Let's try it in a different color. There's my miter line. And now I'll make my right side view. To do the right side, I'm going to need a z-axis. Here's a z-axis that lines up with this other z-axis. And here's a y-axis that lines up with the other y-axis off of the miter line. Well, now I'm going to identify some points. The nice thing is point three is all ready to go. Let me bounce point three off here and bounce, create the rectangle for point three. Maybe I'll do that in yellow to sort of see it. Here's the rectangle for point three when I use the miter line. So here is point three. Let's go see what it looks like from the right side view. Now I'm looking here. Oh, yeah, there's point three. Let's go ahead and trace out point three. Three units along the y and one unit down along the z. Three units along the y and one unit along the z. I think I can create that. So here's my three units, three units along the y-axis, and one unit down on the z-axis. Notice that corresponds to this face right here. And let's see what happens here. Let me go ahead and look. I'm going to identify another point, see if things match up. We're going to call this point over here point four. Notice point four is along the y-axis for both that green side and that yellow side. Let's see. Here's point three. And if I go along the y-axis three steps, I get to point four. Over here, here's point three. And if I go along the y-axis, it's vertical here. I end up at point four. Hey, what do you know? Point four bounces correctly off of my miter line. So I'm almost done. I got one more face to look for here. This one, let's do it in what color of red. I haven't done red yet. So we don't have any points here quite yet for this. So let me go and identify some points. I'm going to go and identify a point five right here in this upper corner, point five in that upper corner. So that's where the blue and the purple meet coming along the x-axis from number two. So let's see here. Coming along the x-axis from number two, coming along the x-axis from number two, there's point five. I've now identified point five in both places. Let me go and identify point five on my side view. Here's point five on my side view. And now I can follow my rectangle for point five. I'm going to start here and go along the y-axis three units, down the z-axis three units, and then come back three units y, three units down z, starting at point five. Three units along the y, three units down z, and then come back negative y and positive z. And there is the last face. And that represents the thing that you see right here, or that you see sort of right there. The yellow would be something we would see there. And the blue, hopefully that color coding makes it a little easier to see what the faces are as they match up. So it's a little messy because I got all those other parts there. But basically, we have something that looks like one, two, three, boom, boom, boom. And we have something that looks like, of course, I'm going to make it just as messy. Here's the L shape. And then the last piece looks like, and I've got to make sure it's lined up. I've got to make some sort of miter line here. Let's go ahead and line it up one, two, three. There we go. Line it up like that and shape like this. And notice whatever I use there, yeah, that miter line works, so I don't need to worry about those pieces. So that's the more simplified version of what we just drew with all the colors. Whoops, forgot a part for our race to buy accident. So your assignment for this section, this segment, is going to be to choose five of these, OK? And draw their orthographic projections. Folks, this is Dr. Garrett Love with Honors Aerospace Engineering at the North Carolina School of Science and Math. Have a good day.