Using polylines with gstat

(This chapter was written by Konstantin Malakhanov. Names and addresses of contributors to the code are found in the source code file polygon.c)

Often during interpolation one has to take into account boundaries (edges) between data and/or interpolation points. These boundaries can be natural, like rivers or geological faults, or man-made, like legal boundaries. The boundaries should be used at the selection of candidate data points, so only appropriate ones will be used for estimation.

For open boundaries, selected data points and the estimation point have to be at the same side of each boundary. For closed boundaries, data points and the estimation point all have to be either inside or outside of each boundary.

Figure B.1: Most often cases of open and closed boundaries (  estimation point, $\circ$ data point). Selected data points are connected.

Certainly one can imagine cases of more complicated topology, with open and closed boundaries mixed, or with connected boundaries etc. To see an example how boundaries can be used in estimation process, see [14]. For general computational geometry questions, see a book of O'Rourke [19] (with software available at http://cs.smith.edu/~orourke/books/ftp.html) and Computational Geometry FAQ [18].

To handle the ``interpolation with boundaries'' in gstat, a new keyword (edges) and a new method (point-in-polygon) are introduced. edges allows to take boundaries into account during estimation. point-in-polygon calculates which data points are inside of given polygons. The point-in-polygon test is useful, if you want to exclude some data points outside of given boundaries.