Nice question. Here I just mention an interesting idea used in this [GIS StackExchange posting](https://gis.stackexchange.com/a/20831/4653) by *whuber* (William Huber): Find $n$ clusters among your $N$ points, and take the center of those clusters as your $n$ points. As he says, "You can see it's not great (but it's not too bad, either)." Below, $N=1000$ (colored points), $n=200$ (gray points): <hr /> <img src="https://i.sstatic.net/BR13y.png" width="300" /> <hr />