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I'm looking for a way to store and edit spatial data that preserves topological information.

In my concrete application, I need to represent triangular meshes, which consist of unique nodes and triangular polygons. So far, I have been working with two separate shapefiles, one for the nodes and one for the triangles. This has the drawback that the two aren't topologically connected: If I move a node, the affected polygons in the other shapefile can't be updated accordingly.

Is there a standard open format for storing and editing spatial data of different types (points and polygons) that are connected topologically, similar to what I understand ESRI Coverages to be?

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GRASS's native vector format has topology, and topology is a major feature of PostGIS 2.0.

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TopoJSON is a GeoJSON-like format that stores topology.It has an API and a command line tool that helps the integration with other applications. Check the wiki:

https://github.com/mbostock/topojson/wiki

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