Wicked Cool Stuff

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posted 09/10/06 by Anthony Governanti What the heck is Kriging?

So a lot of the tips and tricks out there right now are for things that most users may run into on a day to day basis, and that's all well and good - but what about the stuff that you don't even know is there? Well I thought there isn't a better candidate for my first wicked cool tip then to talk about a little known surface editing tool called Smooth Surface.

So basically, smoothing a surface allows for two things. One, quite obviously, you can smooth out the data in an area of a surface to help create a more pleasing set of contours, and I recommend this for all you LDT users who are used to the Contour Smoothing option for contour styles.

The second and less obvious use is that you can interpolate for and fill gaps or holes in a surface where data doesn't exist using something called the Kriging method. The Kriging method enables you to extrapolate data beyond the extents of a surface based on statistical trends in the existing data across the surface. Now I'm not going to pretend that I understand any of the theory or mathematics behind the Kriging method, I don't have the IQ or the time to get into that much detail. I have however played around with the settings and tried it on several different surface conditions, and I must say that I'm quite impressed with what it can do.

So, with that said, let's give it a try on a surface I have and see what kind of output we can get. The scenario with this example is that the Surface I'm working with has a large U-shaped gap in the middle of it, and the road I wish to design will run close to the edge of this gap. In order to be sure I have enough room for daylighting my corridor design, I want to add some data to the left side of the U, as seen here:


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So the first thing I'm going to do is establish two areas of interest with closed polylines. The first one is the area I wish to fill with extrapolated data, shown here as the red polyline:


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The second polyline is the area I want to sample the data from to use for the extrapolation, shown here in yellow:


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With these two areas defined, I can now run the Smooth Surface command. Its important to note that I don't have to have these polylines done ahead of time, as the routine allows me to define the areas from either polygons, rectangles or just drawing a shape while running the command.

From the Prospector tab of the Toolspace, I expand the Surfaces collection, then expand the surface I am working with. I then right click on the Edits collections under Definition, and select Smooth Surface. We get this dialog:


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There are two methods for smoothing as I mentioned above, and they are specifically called Natural Neighbor Interpolation and Kriging. I'll select Kriging, since its the one that will fill gaps or holes in a surface. The Natural Neighbor option is used for simply smoothing an existing area of the surface. Once selected, the options for the Kriging method are now editable. I'll activate the value column for the Select Points row, and pick the button with the three dots which prompts me to select the sample region. This is the area that it will use to extrapolate data points from, so I select the yellow polyline shown above. As the dialog comes back, I can see that the bottom view is filled with a picture containing a series of dots which represent the extrapolated points from that area of the surface.


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This is the cool part; as we select different semivariogram (Ok I can't even pronounce that word, much less explain what it is, so check out the link to get an idea of what it means, if you're into that sort of thing) methods, we'll see different best-fit lines projected on those points. Simply pick the method that gives the best best-fit line, in this case I'm using the Gaussian method. (See we don't have to be geniuses, we can just look at a pretty picture and choose the one we like!) Ok, now we setup how the extrapolated points are added to the surface to fill in the gap using the rest of this dialog. I choose to use a grid of points, and set the output region using the red polyline I defined earlier. One thing to note, the smaller the grid you define, the more points that are added and the more processing the command will need. I used a 10 unit grid, which for this surface is probably too tight, but let's see what it gives us. Once the output region and grid is setup, I select Ok and let it run the calcs. It may take some time, but I can use this opportunity to have a snack or something.

Here are the results.

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Not too shabby huh?

Now before you go off and say 'but that's not real data, how can you have more surface where you don't have data?!' I want you to realize that this is an extrapolation of trends across a given area, and not a replacement for real data. So keeping that in mind, let's realize that this isn't as accurate as sampling real field data, but in those situations where you can't get good field data, this is a great tool to help fill in areas of need that will be pretty dan close.

I'll leave it up for discussion as to the merit of its use, but for me, this is Wicked Cool Stuff!


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Till next time,
Cheers,
AG

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