You can describe a projection based on its aspect, and really all that does it relate to how the developable surface touches the globe or where it touches. If we have our reference globe here and our cylindrical, developable surface, when it's in this vertical configuration like this, we call that a normal aspect. And that's a typical one you see for things like a Mercator projection. And the standard line would be at the equator. So that's why there's no distortion, and so the scale factor is increasing away from the equator. With the transverse aspect, all that's happened is that we've taken the cylinder and turned it on its side so that now the standard line is along the meridian. And so our scale factor still increases away from the standard line. But now it's increasing away from the meridian in an east-west direction instead of a north-south direction. You can also have the cylinder at any other angle. And if we do that, it's called oblique. So if it's vertical, it's normal, if it's horizontal, it's transverse, and anything else is referred to as oblique. Same thing still applies though. You still have a standard line, you still have no distortion at that line, and then skill factor increasing away from it. So these are just some options that you can use when you're choosing your projection or if you were designing your own. In relation to other factors or things you could do with projection, in terms of whether it's tangent or secant and so on. But this is a way of being able to determine how you want the surface to touch the globe and where that distortion is going to take place. And that helps us if we want to customize a map for a particular purpose or a particular location. With our azimuthal or planar projection or developable surface, you can see that we can have the sheet of paper touching at the globe or, sorry, at the pole. And that's a common way to do it, but you could just as easily have it touching here along a point at the equator or any point in between. And so if it's at the pole, it's called a polar aspect, if it's at the equator, surprisingly enough, it's called the equatorial aspect, and if it's at any other angle, it's called an oblique aspect. So this is in relation to the planar or azimuthal class of projections. Here is an example of the map that's using a planar or azimuthal projection for the North Pole, this is from the government of Canada. And so you can see this kind of the circular pattern to the map, that the lines, the meridians, are radiating out from pole, okay? And so this is a common type of projection that's used for mapping areas like the North Pole or the South Pole. So that's a standard way of using it. So you can see here that it's an azimuthal projection, which is another way of saying a planar projection. It's equidistant, which means that distances are maintained in directions from the center, or the standard point, or a standard line, outwards, radiating outwards from there. So I just wanted to show this as an example of an azimuthal or planar projection, and how it's applied with a polar aspect. This is a conic projection for Canada, and you can see here there's this, if you look at the meridians, there's definitely a conic shape to it. So that's the lines of latitude and longitude, if I just kind of draw them in here roughly. And so this can help you to visualize, when you're looking at a map like this, what developable surface was used. There, I'm guessing, would be two standard lines. One about here, and another one there, to minimize distortion on that. And if we look at the detailed information for this map, it turns out that yes, it is a conformal, conic projection. That means that it's a conic projection, so it's using the developable surface that we thought. It's conformal, meaning that the shapes are being maintained, they're not being distorted for this particular map, which is nice. You'll see too that it has standard parallels at 60 degrees north and 75 degrees north. So that's the strategy that they've used in order to minimize distortion at those two standard parallels. Then the fact that there's two of them tell us that it's a secant case projection as well. This is a fun example of how you can use an oblique aspect to customize a map using GIS software. So I was contacted out of the blue by this guy named Rob Spence who was making a movie called Let's All Hate Toronto. It's kind of a tongue-in-cheek, fun movie about people's attitudes in Canada about people that live in Toronto, there's this kind of pervasive thing about everybody hating Toronto. So he was trying to make fun of that, and went around the country interviewing people and asking them why they hate Toronto. It's kind of a fun movie. Anyway, so he called me up and he said, I've never met him before, I've never heard of him, and he said, can you make a map that makes it look like Toronto is the center of the universe? because that's often what it gets called, people kind of roll their eyes. And I said, yeah, sure, I'd love to do that, that'd be fun. And I hung up the phone and thought to myself, how am I going to do that exactly? Hm, so I thought about it and I thought, I know what I could do. I'll do a planar or azimuthal projection using a oblique aspect where Toronto is, where the sheet of paper or developable surface is touching the globe. And that will make it look like everything is radiating out around Toronto. So this is what it ended up looking like. So you can see that there's Toronto there on the map. And if you're visualizing this, if that was Toronto and that's the sheet of paper, It doesn't have to touch at the North Pole, even though that's the most common place that you see, or the South Pole. You can make it touch wherever you want as an oblique aspect. And so this is the resulting map that you get, it definitely looks like everything is kind of wrapped around the point of contact, which in this case was Toronto. So that's a little screenshot from the movie. I spent not a huge amount of time, but a bit of time on this, and it ended up lasting in the movie for maybe one or two seconds or something like that. But that's okay, I was happy with that. What I didn't know at the time was that he actually included me in the credits. Yes, [LAUGH] there I am, in the credits for this movie. And not only that, that means that I am listed in the Internet movie data base, yay! So [LAUGH], if you ever look me up in the IMDB, there I am with my one film credit for Let's All Hate Toronto. Okay, so you never know where map making may take you. It may end up making you famous someday, or in my own mind famous, and listed in the IMDB, so that's kind of fun.
