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I don't understand how this is related to the article. The article has to do with searching spatial data structures, such as you would make for partitioning the space of a large scene in a graphics or mapping application (or game, etc.). Maybe I'm wrong and someone could enlighten me....

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It doesn't have to be for spatial data, that's just the easiest way to get N-dimensional data.

Basically, every variable in your problem becomes a dimension. You could think of grocery shopping as a 10-dimensional problem involving cost, dietary restrictions, nutritional value (we'll say there are 7 for this example) and brand preference. You could potentially use a VP tree to search for all products that fall within a 10-D sphere that encodes your product tolerance.

3D spatial problems are just three dimensions. True you can do that with VP but you can do that with octtree too.

Imagine beyond 3D like clustering of friends or likes or recommendations or all those other N-dimensional data-points and you'll see the overlap.

Right. There are plenty of cases where you ONLY have the distance (or similarity) between two points and don't actually have an n-dimensional point in space.

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