Original User: 1812
Since your points are classified/indexed by their positions in rows and columns, as shown in the image, you can try the following (requiring ArcInfo license):
Assuming the fieldname of the point classification is pointClass:
1. Run Add Field tool to add a field, rowID.
2. Run Calculate Field tool to calculate rowID by !pointClass![0]; and check Python in Parser. This should give you an "A" for all A1, A2 ... points, a "B" for all B1, B2 ... points, etc.
3. Run Add Field tool to add another field, say columnID.
4. Run Calculate Field tool to calculate columnID by a !pointClass![1:]; and check Python in Parser. This should give you a "1" for all A1, B1 ... points, a "2" for all A2, B2... points, etc.
5. Run Points To Line tool (new in ArcGIS 10) and specify the rowID as Line Field and pointClass as Sort Field. You should get rows of lines.
6. Run Points To Line tool again and specify the columnID as Line Field and pointClass as Sort Field. You should get columns of lines.
7. Run Feature To Polygon tool (requiring ArcInfo license) using both rowlines and columnlines as input. This gives you the polygons.
8. Run Feature Vertices To Points (requiring ArcInfo license) to get ALL vertices from the polygons.
9. Run Create Thiessen Polygon (requiring ArcInfo license) using the vertices as input. The output polygons go beyond the point area.
10. Run Intersect tool to intersect the Thiessen polygons with the polygons from step 7. Now you have subdivided polygons (quarters).
It's a long workaround. Does it work for you?