Surfaces and Interpolation!

MOHAMED_ABDALLAALKAMEL_ABASS1

In this lecture, you'll learn how those are made. And I'll introduce a new data format that handles it. While some rasters are created using sensors, like cameras that sense continuously across an area, others are created from discrete observations, such as those taken at GPS points.

0:48

If I have a handful of point observations, let's say of elevation, to keep it simple, I, as a human, might be able to guess values that I didn't capture in my data. If I have three points arranged approximately in a triangle, where we captured elevation values and one's value is 10m, the other is 9m, and the other is 6m. I can guess that the value in the middle of the triangle is somewhere around 7-8m. If we want to be more precise, or perform this process with a larger sampling of points across a landscape, then we need to perform what's called interpolation.

1:23

For those of you who've worked with photography and image manipulation on computers before, interpolation might be a familiar word to you. It is the process inferring additional information where you don't have any. With photos, this comes if you try to increase the resolution on a photo in software. There isn't any additional information, but we can try to add some, based on what is already there. It's not new factual information, but a guess instead. This process applies to rasters too, since photos are a type of raster data, and resampling is just the type of interpolation.

1:56

As I said before, we're not truly creating new data. I can't just make up new data, however good an algorithm I have. But I can make new predictions. That's what interpolation's good at. That may seem like semantics, but it does matter. Remember the lessons from the previous course on sources of error. This is one of those times where we're inserting a not completely known amount of error into our data. But it's still useful to do anyway, because it allows us to look at the complete picture, rather than just the pieces we were able to collect data on.

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In our elevation example, it's the difference between having a few surveyed locations and having a terrain model capable of simulating solar influx, water flow, suitability for human needs, slope, and more.

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To interpolate, we need to specify an attribute to build our interpolated data source on. We can think of this almost like a Z value. If the location of our points specifies the X and Y locations, this attribute becomes our Z value or height that makes it 3D.

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In your minds, you can take those points and extrude them so that their height matches the value. With terrain data, this makes sense, since that attribute truly is a height value, but we can do it with other sensors. Maybe it's the number of people living at a location, or the amount of a toxic material measured there, or stations used in air quality monitoring.

3:15

If we conceptualize those values as heights, we can then build the surface or raster that connects them. Just like GIS isn't one technology though, interpolation isn't one single tool or method. There are many different ways to develop that surface between our points, or in other words, to interpolate our data to develop a raster from points. One that's easy to conceptualize is the TIN, which stands for triangular irregular network. We'll cover TINs in more depth in the rest of this lesson. But for now, think of drawing a line or an edge that connects each point to all of its neighbors. In the process, we get triangular surfaces in between the points. These surfaces have area, slope and direction associated with them. One of these triangles exists between each set of neighboring points, which is where the name triangular irregular network comes from. It's a network, or set of connected edges, that forms triangles, but without a defined pattern that lays out where each triangle is, it's irregular. Once we create that network and associate its surfaces, if we want to infer the unknown value of a location from the values we have, we can just find the height of the surface at the X and Y coordinates we're interested in.

4:27

Now, the TIN is an inherently three-dimensional structure. Some of you might be familiar with similar structures from 3D graphics or sculpture. Well, rasters are sort of a 2.5 dimensional surface. The exist in two dimensions but the values at each location represent the third dimension. We might think of TINs as a separate data type, akin to rasters and features, but mostly they aren't. We often use TINs for 3D rendering, but in interpolation they're mostly an analysis tool we use to generate a raster. So when we're done generating the TIN, we can run a tool to turn the TIN into a new raster. Completing the interpolation process of going from points with values to a continuous inferred surface of observations that we can use to do a full landscape analysis of a variable of interest. Maybe in the example of air quality monitoring stations, we want to know what each neighborhood's potential exposure to pollutants from cars is. This method allows us to turn air quality measurements that aren't in those neighborhoods into a data source we can use for that analysis. As I said before, there are other methods to interpolation but we'll stick to the TIN for now to not make this more confusing. That's it for this lecture. In this lecture, you learned what interpolation is and then how we can conceptually create TINs in order to perform that interpolation. In the rest of this lesson, we'll pick it up from here and discuss the mechanics of TINs. See you there.