Master’s Thesis
Say that you have a bunch of spatial data that has been gathered at irregular, scattered locations. For example, here’s a 3D plot of 32000 elevation measurements sampled from the Bridger Mountains north of Bozeman, MT.
32,768 points randomly sampled from the Bridger Mountains.
You’ll notice that its pretty hard to get a good feel for the shape of these mountains just by looking at the points. Wouldn’t it be nice if we could construct a smooth, 3D surface from those points? If the points were regularly spaced in a nice grid, then building a surface would be easy. Unfortunately real world data is often not so co-operative. That’s where my thesis comes in. The algorithm I developed will take a mess of scattered samples and quickly estimate a smooth surface. Here’s the results after running my algorithm on the above data:
Surface reconstruction from 32,768 scattered points
The surface reconstruction gives us a much better feel for the data. There are other algorithms such as Kriging that also perform this task, but Kriging is much slower on large data sets. For more details, you can Download my Master’s Thesis which describes my algorithm and compares it to Kriging.