So, is it possible to maintain both distance and direction properties on a map projection? Kind of. Not everywhere, sometimes maybe. So, let's have a look at how this works. Okay. So, here we have the Mercator projection and we can ask these questions, where can we have a straight line and shortest distance? In other words. remember the shortest distance between two points on the globe is a great circle. The great circle is the line that passes along a plane that cuts through the center of the earth. Okay. Try to remember that because I do think it helps you in terms of visualizing this. So, if we have a line from A to B, is that a great circle route? If it is, is the direction correct? Well, the direction is correct because it's following a North-South path. So, there's no distortion taking place there and you can see how if it's following a Meridian or a line that's parallel to Meridian or along a Meridian, then you don't have any distortion and the direction will be correct and the distance will be correct. So, that is a great circle route and that's going to work. So, there's our Mercator version here. So, the distance along and the direction along that line from North-South is the same as it is along the meridian. So, that works, that's okay. So, we could measure distances along that, we could navigate along that and everything would be okay. So, that gets a check mark. What about this one though? Is this a great circle route? No, it's not. Because it's run line. Remember, a run line is where you have lines of constant bearing which you have here. So, these angles are equal. So, if it's a run line, it can't be a great circle route. That's true because you're getting distortion or another way of thinking of this is you have distortion in the East-West direction because the meridians are being stretched apart. So, it would not be possible for any line that has any kind of horizontal part to it or dimension to it. That can't be a true line or a great circle route or have their directions be correct as they would be on the globe because of that east-west distortion. So, that gets an X. So, that's a run line not a great circle. What about with this projection? This is a planar also known as azimuthal projection and we'll see why it's called an azimuthal projection here. Okay. So, the idea is that we have our sheet of paper touching the globe at one point. So, it's a plane that's touching. That's where the planar comes from. But, what's interesting about this is that if you draw a line from the standard point where it's touching which is this point here at A, if you draw a line from there to any other location, then that is automatically a great circle route. Because it's following these meridian. So, all of these meridians are correct and they're all great circle routes. So, those directions will be accurate. So, if I said you go along this bearing from A to B, that will get you where you want to go. What about this one? Is that okay? Yes it is. Because it's going through the North Pole. So, if you extend that line down through the center of the earth, that would be a plane that cuts through the center. So, that's a great circle route. So, that would also count as being correct in terms of direction. What about this one? Yes, that's fine too. It doesn't cut through the North Pole but if you extended the line, it would and so that's fine. What about this one? No. No good. Because as we've said before, we're getting distortion in the East-West direction. So, we've got this component to it that's making it so that there's no possible way that this can be a great circle route or that the directions will be accurate or maintained if you're not following along a meridian. So, this is why it's known as azimuthal projection because if you're navigating from the center of the projection to any other point, that azimuth will be correct. So, that's why it's known as a planar or also as an azimuthal projection. So, I wanted to finish off this section by showing you a compromise projection. We've talked about projection properties such as area, shape, distance, and direction. Depending on which projects you're using, you might be able to maintain one or more of these things. But a compromise projection doesn't maintain any of those things. You might say, "Well, doesn't that make it kind of allows you projection?" Well no because it's not meant to be used for measuring areas or measuring distances. What it's meant to do is compromise in a way that all of those things are distorted as little as possible in a way that makes for an overall kind of pleasing map. So, nothing is distorted way too much. You're not getting green and looking completely squashed. You don't have it being way too big. So, the relative sizes of things are generally correct and you get this look like, well, it's like a globe. Obviously it's not exactly like one. But it's a pleasing overall effect in terms of making a map of the world. So, you're not making measurements off of this, it's just for display. But it's a common type of projection that's used by agencies like the United Nations and the National Geographic and organizations like that.
