# create grid cells of fixed dimension around a point acting as a centroid

I've been trying to solve a problem for the last few days but not having much luck. I'm hoping someone here can point me in the right direction. I'm new to ArcGIS so I hope my explanation makes sense.

Here's my problem. I have a layer of points with x,y co-ordinates. They are laid out in a mecrator projection. What I need to do is create another layer with a grid. Each grid cell needs to be 2 degrees high, by 2 degrees wide, with the point acting as a centroid (so the boundaries are at a distance of 1 degree above the point, 1 degree below, 1 degree left and 1 degree right of the point). The grid cells cannot overlap. Because of the mecrator projection, I would expect the height of each cell (latitude) to remain the same, but the width (longitude) to expand the further away from the equator they are.

I've tried the thiessen polygon tool, creating buffers, the fishnet, and the minimum bounding geometry tool but its not quite what I'm after.

Any ideas? Any help is greatly appreciated!

Thanks very much

PS: I've popped a (badly drawn) image up on to G+ of what I want. See here. Figure 1 is what I have, and Figure 2 is what i need to create

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Your expectation is curious: because the cells are specified in terms of degrees, and because the Mercator projection is cylindrical, then necessarily (1) all cells will have identical widths (2 degrees of longitude) but (2) their heights must vary with latitude. In the Mercator projection the extreme example occurs for points near 89 degrees latitude: their cells extend almost infinitely far from the map's center, but still have widths of just 2 degrees. Nevertheless, in any (pseudo-)cylindrical projection all those cells will be mapped to perfect rectangles. – whuber May 19 '13 at 15:15

These are the steps that I would use:

1. Create Fishnet to create a 2 x 2 grid
2. Define Projection on your fishnet as a Geographic Coordinate System (in lat/long)
3. Project your GCS fishnet into Transverse Mercator

You should now see the expected broadening of cells at the equator.

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I would also suggesting Densifying your 2 x 2 grid since the actual resultant polygons will not be a true representation of the grid cell once projected. They will be flat in the East West direction rather than having the appropriate curvature which would be expected when following a parallel. See resources.arcgis.com/gallery/file/geoprocessing/… and experiment with various densifications (eg start with a 0.1 or 0.2 degree densification) – Dan Patterson May 19 '13 at 12:24
Definitely use ArcGIS Densify tool if you have access to Standard or Advanced license level. Or @DanPatterson Densify tool that looks like it may be designed for Basic too. – PolyGeo May 19 '13 at 12:36
Yes PolyGeo, originally this designed to run in 10.0 ArcView and it should run at all license levels in 10.0 and 10.1. It also allows you to produce a point file showing the locations of the densified points if they are needed for other analyses. – Dan Patterson May 19 '13 at 13:00
@Dan Patterson Concerning the need for densification, please see my comment to the original question. The four corner points will suffice to define these cells perfectly in either a GCS or in the Mercator projection. – whuber May 19 '13 at 15:17
Whuber, Perhaps I was thinking of what happens when using a UTM projection, then trying to perform a select by location (within) which produces erroneous results if the selection grids are not densified prior to projection. – Dan Patterson May 19 '13 at 18:06