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I believe this answer: How to calculate a percentage of an area covered by polygons ArcGIS 10.1 will help you get a table showing the distribution of land cover types (or whatever your thematic dataset is) for each fishnet square. Essentially, it's Union followed by some Summary Statistics to get one row for each square, with a column for each land cover ...


This could be a comment to MikeT's excellent answer, if it wasn't too long and too complex. I've played with it a lot and made a QGIS plugin named FFT Convolution Filters (in "experimental" stage yet) based on his function. Besides smoothing, the plugin can also sharpen edges by subtracting the smoothed raster from the original one. I've upgraded Mike's ...

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