Calculate distance from a point to a body of water

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We have a requirement to calculate the distance between a point and the nearest body of water (or other area, e.g. a geothermic area).

I have no idea where to start but my guess would be loading a subset of some publicly available water body data in to the database (postgresql) (currently we're only concerned with New Zealand), and then querying that data somehow.

My major sticking points (due to lack of direction) would be how to get the data loaded into the database, how to query for the distance from a point to the nearest edge of the water body shape, and also how to provide a user-friendly interface where this data could be added to (e.g. to add those geothermic areas).

I guess I don't want to reinvent the wheel if there are tools already out there to do this.

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