I just want to cover a little bit about how projections are handled inside ArcGIS Desktop. It's not necessarily as intuitive as it might be if you're coming at this for the first time. So, I just want to clarify a few things and make sure that you understand what's happening when you're adding data into ArcMap and what the projections are, how they're being set, and how that works. One thing I want to point out here is that when you're creating a new map, one of the first things that you should decide is what kind of coordinate system you're going to use. The fact that you're making a map at all, really implies that you should be using a projected coordinate system. A projected coordinate system is based on a geographic coordinate system. That's kind of to me, it's sort of the foundation. You're starting with a coordinate system that's based on an angular unit of measure, a prime meridian, and a date that specifies an ellipsoid. That's the definition of a geographic coordinate system, which is designed for three-dimensional Earth. A projection then takes that and flattens it out, and then puts a grid coordinate system on top of that, that makes it possible for you to measure things like distances and directions and so on on that flattened version of the map. So, the projected coordinate system is an add-on, or an addition, or built on top of the geographic coordinate system, just so that's clear. So, here we have a projected coordinate system, which is Canada Albers Equal Area Conic. If we look at the properties for this, you can see that it's actually listing the information for the geographic coordinate system that it's based on, which is, got a prime meridian, there's Greenwich. It's got an angular unit. It's got an ellipsoid that's listed, the semi-major axis, and so on. So, this is the grid coordinate system or a projected one that's built on top of this geographic coordinate systems. So, I just want to make sure that's clear. So, this is just a stylized version of the software just so you don't get distracted by some of the details, I just want you to get the main idea here. So, what happens is if you have a data set that's stored in a geographic coordinate system, so it has not been projected in our catalog, and then you may have another data set that's been stored with a projected coordinate system which is built on a geographic coordinate system. So, you may have added to your map, say, a Mercator projection, our data that's in the Mercator projection. When you add that data in to your map, the data frame will be set to the first coordinate system that's added in terms of that first data set. So, you have an empty map document, a new data frame. You add that first data set in, the software reads whatever the coordinate system is that it's been used for that, and that's what it sets the data frame to. It doesn't tell you that it's doing this. So, if you're new to this, it's not going to be obvious, but that's what's happening. So, then, if you add in a second data set that's stored in a different map projection, it will add that in, but then it will recalculate the positions of all of the features on that map, on that new data set, or that new data layer on the fly to match the first coordinate system that your data frame has been set to. So, I just want to make sure that's clear. So, what's happening is your data frame has been set to Mercator. That's what it's being used. That's what's you're working in. You add a second data set that's stored in a second coordinate system. In this case, it's Robinson. Then it says, "Oh, okay. Well, what would this Robinson data set look like if I added it or recalculated it into a Mercator projection?" So, then it adds that to your map, but nothing has actually changed in the data file. The data file is storing whatever coordinates were used to create that, with whatever coordinate system was used, whether it's geographic or projected. So, it's making you think that this second data set, this Robinson one, has now been converted to Mercator, but it's only been converted, what we say, on the fly, which just means done kind of a quick and dirty method to just show what it would look like in that protection, but it hasn't changed anything in the actual file itself. So, if the coordinates are being calculated on the fly and just being shown differently, and nothing is being changed in the data set, what if we do want to change something in the data set? Well, you can do that too. You can export that data. There's different ways to do it, but you can save that data set with a new coordinate system, a new projection, and that will recalculate what those values are in the actual data set itself and create a new version of that file with those new coordinates, but only if you tell it to do that. If you don't, it's only going to do it on the fly, which could be a good thing or a bad thing, but it's just something you need to be aware of when you're working with it. So, you can save data into a new file with a new projection if you want to. So, the coordinates in that data file are going to be recalculated and adjusted to match the new projection. If they're saved in that, then that's a permanent new version of that data. Something that should be kept in mind is that when that happens, you can't always transform it back exactly the same way due to rounding errors. So, what that means is, is that your computer only store so many decimal places for each number. When it does a calculation and when it's doing that to change a projection, it's a mathematical equation that it's using to do that. It's doing a calculation, it's coming up with a new number, and it's storing that number in the file. Okay, fine. But when it's doing that, it may actually be truncating that to the number of decimal places that are available for it to store that in. Even if it's six decimal places, let's say, there could still be a bit of a rounding error that's taking place that's rounding that number up or cutting it off. So, why am I telling you this? Because if you do that over and over again, if you're transforming data, your reprojecting it and resaving it a lot of different times, then every time you're doing that, there's a little rounding error that's being introduced into that calculation and being stored in the file. So, that means that if data has been projected over and over again, it's possible anyway that there's more and more errors being introduced. They may be small, but we'd like to avoid as many errors as we can if possible. So, to avoid these kinds of errors, it's kind of a guideline. It's useful to try and store data without a map projection and just to provide it, if you're providing data to somebody else, in a geographic coordinate system. So, it hasn't been projected. The idea is that you're providing data that hasn't had these calculations done to it over and over again, so that when you give it to somebody else, they can do the calculation, do the projection that they want to do knowing that there's a minimal amount of these errors that have been introduced.
