Incomplete

ODETLAP -- A New Surface Fitting Algorithm

W. Randolph Franklin, Metin Inanc, Zhongyi Xie

We present ODETLAP, a new algorithm for fitting a surface to an irregular set of data points (x_i_, y_i_).

ODETLAP is a generalization of a Laplacian PDE,

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The more we use ODETLAP, our overdetermined Laplacian PDE method, the more we like it. As shown in Snoqualmie, it can fit a recognizable surface to even very few points. (We showed one example where a surface fit to 36 points had some major features recognizable.) ODETLAP can also fill in missing data. It could also determine a regular grid of elevation posts from an irregular set of input data.

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   4. We tested another new representation, ODETLAP, on a 400×400 piece of the Lake Champlain W cell. After selecting every third post in each of X and Y, that is 1/9 of the points, and using ODETLAP to fit a surface to them, the error was only 0.9 meters, or 0.1% of the elevation range.

   5. We are combining TIN with ODETLAP, in order to capture the essence of a surface with very few points.

   6. We can use ODETLAP to fill in radius 40 circles of missing data, with excellent results. 

Missing data fillin

O;ne serendipitous; application of our ODETLAP representation is the ability to fill in large regions of missing data. Responding to a request at an early review meeting, the following figure shows six interpolation methods for filling in a missing hole of radius 100. The top left image, which is is ODETLAP, shows how local maxima in the missing region are inferred and realistic contours are generated. The top middle is a precursor to ODETLAP, and is slightly less realistic. The top right image is comparable to ODETLAP, but requires a higher order differential equation. The bottom three images show three Matlab techniques; all are quite unrealistic.

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