How do I convert from points to raster making the point the lower left corner of the cell?
I'm using ArcGIS 10.1.
The default for the "Convert Point to Raster" tool is to make the point the centroid of the resulting raster cell.
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You can use the Shift tool to shift the raster by the desired increment in X and Y so that the point is now in the LL corner.
Moves (slides) the raster to a new geographic location, based on x and y shift values. This tool is helpful if your raster dataset needs to be shifted to align with another data file.
I would suggest you create the points at the centres as the tool does by default, then shift the resulting points as required. This gives you relatively easy ability to modify your displacement from cell centre and analyze the results.
Or are you hoping to interpolate values at non cell-centred points based on neighboring values?
Open table, right click on field Shape, Field calculator, Python
arcpy.Point( !Shape!.firstPoint.X+5, !Shape!.firstPoint.Y+5)
Solution assumes your cell size is 10 m and you'd like to move point to upper right corner of the cell. You might use extended version at Moving a shapefile point 500 m west