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I'm performing a fairly routine task, which is to add height information (from a 50m DEM) to survey polygons to work out mean height, as well as max and min.

I've noticed that zonal statistics (Spatial Analyst) is very slow, and depending on the raster analysis settings, can miss out polygons due to raster sampling size. For example, in the image below, the red polygon is missed out of zonal statistics because it's too thin to adequately intersect enough (or indeed any) raster cells.

missing polygons

Interpolate shape -> Add surface information, by contrast, seems much much faster. But I don't understand what's being interpolated here for a polygon feature. Is it just the vertices, or is the interior of the polygon also being compared with my underlying DEM? At what resolution?

Which method would provide more accurate results? And, are there any other solutions. I often find that terrain operations work equally well with rasters containing non-height information, and vice versa.

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Interpolate shape is used to create a 3D image of a 2D shape containing Z values.

http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//00q900000038000000

To capture values for your red shape resample the raster to a finer scale. You can use either the bilinear or majority interpolation.

http://help.arcgis.com/EN/arcgisdesktop/10.0/help/index.html#//00170000009t000000

Furthermore, if you have having difficulty running tools while working on a network you can transfer to the local hard drive to hopefully speed up the process. Setting a computational mask is also a way to speed up raster calculations.

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