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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Barge-ins were handled symmetrically. When Flux detects that the user starts speaking, the agent pipeline is immediately cancelled: in-flight LLM generation is stopped, TTS is torn down, and a clear message is sent to Twilio to flush any queued audio. The agent falls silent instantly, and Flux resumes listening for the next end-of-turn.