Dammit why these books have to be $60

The problem is rather, that most data structure tutorials and books don't even get the idea, to introduce a purely functional version, but merely state the imperative versions. Coming up with the functional versions of data structures can be difficult. Papers about it can be hard to understand and often require one to already know some niche language, that a researcher used for the paper. Even if you can find a functional implementation of a data structure, there is often not a good explanation and you need to, sort of, reverse engineer it and translate it to the language you are using.

In short, it seems relatively few people have the skills to implement them and even fewer have the skills to come up with functional versions of ordinary data structures. They are almost completely absent from university lectures as well, as far as I am aware. For example for AVL trees I could only find a document from ETH from a lecture, that no longer exists or is taught. The language is Isabel and I need to understand its syntax first, before being able to translate it to Scheme.

If anyone has an obscure source for implementations one can learn from and implement oneself in another language, please share.

You can even build them with basically one line of code by sorting points using Morton / Z-curve order. It's linear time if you use a counting/radix sort.

Edit: lol, downvoted for this post. Never change, HN.

I remember Arc randomly rewriting my bookmarks using some kind of summarization model or something like that, it also sometimes changed the name of downloaded files reinterpreting their names. Maybe it is related somehow.

Well, I guess it was the first AI-first browser, hence all this bs. I uninstalled it months ago...

Apologies! I think I might have a found an eager redirect on the server. I haven't been able to reproduce, but you're not the first to report it. I hope it's fixed now.

That is a cool visualization of a quad tree. I use quadtrees in geospatial applications (to partition lat longs) but this is the time I’ve seen it used to render a photo.

Quad trees are abstract until you see what they look like. It’s a clever method to partition 2D points.

(Kd trees are even better)

a whole visual identity around the quadtree concept

What does that mean?

That all sounds incredibly dystopian, ugh.

One of the reasons you mostly saw point operations and very few rectangle operations is because quadtrees aren't great for range operations.

Quadtrees might look like natural generalization of binary trees, but some things that work very efficiently in binary trees don't work for naive generalization of binary trees into quadtrees. For a full binary tree with W leaves any segment can be described using log(W) nodes. Almost every use of binary tree more interesting than maintaining sorted list of numbers depends on this property. What happens in 2d with Quadtree, how many of quadtree nodes are necessary to exactly describe arbitrary rectangular area? Turn's out you get O(W+H) nodes, not log(N), not log(W)*log(H).

If you stored a rectangle in smallest node that completely contains that avoids the W+H problem during insertion operations, but during read operations you may end up with situation where all the information is stored at the root. This is no better having no quadtree at all and storing everything in plain list that has no special order. Such worse case scenario can be created very easily if every rectangle contains centre of area described by quadtree, then all rectangles will be placed at root.

Dynamically subdividing and or allocating tree nodes on demand isn't anything particularity novel. If anything the cases where you can use fixed sized static trees outside textbook examples is somewhat a minority. Not saying there are no such cases there are enough of them, but large fraction of practical systems need to be capable of scaling for arbitrary amount of data which get's added and removed over the time and total size is not known ahead of time and the systems need to be able to deal arbitrary user data that has maliciously crafted worst case distribution. Every B-tree will split leaves into smaller nodes when necessary. Almost every self balancing binary tree can be considered of doing automatic division just with threshold of no more than 1 item per node. For 2d many uses cases of k-d tree will also subdivide on demand.

When I made a quadtree for some simple 2d games I handled AABB areas, since it was aimed at broad-phase collision detection of what were essentially sprites just rendered w/GL.

Similar to yours I split the leaf nodes when they became too full, with some simple fixed threshold defining "full". Only leaf nodes contained references to the indexed objects, and all overlapping leaf nodes would reference the objects they overlapped. Search queries were done also using an AABB, and would iteratively invoke a callback for all overlapping object AABBs found in the overlapping leaf nodes. IIRC the object references hanging off the leaf nodes had a fixed number of linked list slots to be put on a results list during a search, to deduplicate the results before iterating that list with the provided candidate-found callback. Since any given indexed object could be on many leaf nodes in the index, if they spanned a large area shared with a high density of other indexed objects for instance.

It was up to the callback to do the narrow-phase collision detection / control the results list iterating stop vs. continue via return value.

I recall one of the annoyances of sticking the search results linked list entry in the object references hanging off the leaf nodes was it set a limit to the number of simultaneous searches one could perform against the index. Basically the game would initialize the index with a fixed maximum concurrent number of searches to handle, and that set the number of results-linked-list slots the object references would be allocated to accommodate. As long as that was never exceeded it worked great.

It's been a while so I may have gotten it wrong, but that sounds right to me.

Not sure what the most common approaches are...

The C source is @ https://git.pengaru.com/cgit/libix2/.git/tree/src/ix2.c

In 3D this has to be dealt with in the form of polygons and I think it was common when people were using acceleration grids and kd-trees to split the polygons so they fit neatly.

That being said most ray tracing seems to do bounding volume hierarchies now, so maybe a bvh is the best way to deal with things that have volume.

> positions are encoded as strings over the alphabet on 2 bits

This is the most pedantic way of saying "binary 2-tuples" I've ever seen. Also for quadtrees this is inferior to base 4 because you can assume clockwise (or counter) ordering.