A quadtree does the same thing for two-dimensional space. It takes a rectangular region and divides it into four equal quadrants: northwest, northeast, southwest, southeast. If a quadrant has too many points in it, it subdivides again and again. Each subdivision creates smaller and smaller cells where points are densely packed.
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After OpenAI released GPT-5.3-Codex (high) which performed substantially better and faster at these types of tasks than GPT-5.2-Codex, I asked Codex to write a UMAP implementation from scratch in Rust, which at a glance seemed to work and gave reasonable results. I also instructed it to create benchmarks that test a wide variety of representative input matrix sizes. Rust has a popular benchmarking crate in criterion, which outputs the benchmark results in an easy-to-read format, which, most importantly, agents can easily parse.
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