There's a process or workflow in vector overlay that's comes under different names, but I tend to refer to it as constraint analysis. Let's have a look at what that is, and how you might want to use it. Constraint analysis really just is built on this idea that you're applying different limitations, or criteria, or constraints, to your overlay analysis. If we have a study area like this for example, and maybe we're interested in identifying areas that might be potential sites for a landfill. There's different ways to define this, you might try to include areas or exclude areas, but for example, let's say that we're interested in areas that are not farmland, or good agricultural soil, or federal land, or archaeological sites, or endangered species. When you overlay all of these things. If you're using this as a way of excluding areas, you realize that actually, there's only one small area that meets all of the constraints, or all of the criteria, in order to be able to adequately site our landfill. So this is just a conceptual diagram to show you how this works. It can be applied in a lot of different ways, but this is the essential idea. Is that you've got these different layers, feature classes. You're applying these different criteria, it might be that you're applying some intersections and some unions, and subtractions, or all different overlay operations. But the whole point is that you're trying to see what meets all the criteria that I'm interested in for my particular purpose. This goes back to the very fundamental definition and beginning of what a GIS is. This idea of representing different themes as layers, and looking at how they relate to each other in space, and being able to model features and processes in geographic space. So, this is really how this relates to the idea of overlay analysis, and constraint analysis. There are different ways that we can approach constraint analysis, or how we can overlay things. I'm just going to show you two different ways of doing it. The first way is the simplest really. If we have an input layer here with a couple of different polygons, and then we do an intersection with a second feature class with one polygon, then we can get an intersection of those two, and so that area d, and the area e, are the only places where we have a geographic or spatial intersection between the two input feature classes. If we applied a union instead of an intersection, then we have more results. So now, you can see that we've got every combination of the a, b, and c. Some are just from a, some are a and c, some are b and c, and so on. Now, we could think of it slightly differently. If we applied numbers to these, let's say, instead of a and b, we have values of one for each of those polygons, and a zero for the background, and then we added that, literally did a sum of that with the second polygons which are also ones, and zeros. Then we can get this result where we have values that are two, that represents the intersection. We will also include the results of the union. So now, we have a quantitative or numeric way of showing that interaction between those two sets. We have areas that are zero, where there's no overlap, we have areas of one, where there's one layer, and we have areas that are two, where there's two layers. The idea here is that if you're trying to do something like constraint analysis, and you're trying to say well, maybe I have many layers that are of interest to me, maybe I'm in a stakeholder meeting, I'm talking to different groups that have different sets of priorities, or our values for whatever it is that you may be trying to discuss, or analyze. So, if you apply numbers to things, it's a way of saying, "Well, how many of these different layers add up?" Those might be areas that have a higher cost, or a lower cost, depending on how you define the problem. Let's take that a step further though. What if, instead of just adding them up like we did before, we first apply a weight to each of these feature classes? Now, those weights can be generated in lots of different ways. There's whole books that have been written about how to do this, but let's just for now say that we got together with our stakeholders, and we said that, this feature class on the left, it has a weight of two times, and the second feature class the green one, has a weight of three times. So, whatever those things are to us that are, one's a little more important than the other. We can actually multiply the values, the polygon by that. So for example, I've got a one here, so if I say the weight is two times, I'm going to say, two times one is two. Here are three times one, is three. So, when we add those together, where we have an intersections of five, that means we have an input of two here, an input of three there, that's going to give me an output of five as my result. So, that's the same idea as we did up here, except we're just applying a waiting to those values before we combine them. If we look at the rest of them, now we have a more sophisticated, or nuanced constraint analysis where when we're talking to stakeholders, when we're putting something together and saying, ''Well, where are the areas that meet our constraints.'' So, if it's something like a landfill, maybe there's no area that meets all of our constraints. Then we have to start getting into more complex conversations and saying, "'Well, if there's no area that meets all of our constraints, how do we prioritize our constraints?'' What's more important? What's less important? What would we consider to be a higher weighting, or lower weighting? If you do that, this is just a conceptual way of showing how you can do more advanced types of overlay, to do a weighted overlay, to bring more nuance or complexity to that analysis. So, the upper one here would be called a Boolean overlay. Really, actually that's even going a little far, is that if you all you had was the it's either in, or it's out, that would be Boolean. So it's either true or false. This I suppose would be a very simple form of weighting because we're actually adding things up, and then this is a more advanced form of weighting where we're applying actual weightings to the values before we do the calculations. So we have Boolean, is it either true or false. So, it's either intersects or doesn't intersect. This I suppose like I said it's a weighting and that we're saying if there's a value of two, then we know that there are two layers that overlap, and then the bottom one I would say, is a more typical type of weighting overlay where you can apply that to each of the feature classes. You may have as many of them as you want, and then when you're putting them together you're getting that weighted results.