The quadtree is the two-dimensional case of a broader family of space-partitioning data structures. Octrees extend the same idea to three dimensions (splitting cubes into eight children), KD-trees use alternating axis-aligned splits (splitting along x, then y, then x again), and R-trees group nearby objects into bounding rectangles. Each variant makes different tradeoffs between construction time, query speed, and update cost.
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It’s also possible to abandon the threshold matrix altogether and instead calculate a value for every pixel coordinate at runtime. If the function is simple enough this can be a good and efficient way to break up patterns and create interesting textures.
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