I will build a GIS system based on polygons, not just points. I wanted to use mongodb or postgis.
how do this in mongodb?
Query A - get the center of a polygon
Query B - distance between two polygons
Query C - list of polygons that are part of a third that I specify
Query D - near distance of the polygon
support SRID?
Currently MongoDB does not support these spatial operations - only Geospatial Indexing of 2d points is supported with some basic accompanying queries (near, within). If you need them you would need to develop support from scratch. Hopefully in the future this will be included.
However if you are interested in storing spatial data in a NoSQL database (instead of a standard relational database, such as PostGIS) you could try CouchDB with the geocouch extension. Geocouch uses GeoJSON to store geometry so polygons can be stored. However as far as I can see only boundnig box queries are supported so far - which you could use to narrow your search - with hopefully polygon and radius search, and srs support coming soon. (Also, a tutorial that I found from Todd Jackson gives a good run-through on getting started. And see this question on GIS SE.).
I think postgis will be a better bet at this stage.
Query A: use ST_Centroid
Query B: use ST_Distance
Query C: not sure what logic you are applying, but probably something like ST_Intersects. Read up on the 9 intersection model if this doesn't do what you were expecting.
Query D: I think you want ST_Distance again. Please explain further if that doesn't do what you were expecting.
