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4 months ago
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The 3D Tree Traversal Problem
Spatial data structures are everywhere — from game engines to robotics and scientific simulations. But while traditional trees like quadtrees, octrees, and BSP trees do well in axis-aligned or position-based contexts, they begin to falter when direction and orientation become the dominant parameters. How do you traverse a hierarchy not by going "left" or "down," but by rotating your point of view?
Enter SpinStep
SpinStep is intended to be a lightweight traversal framework based on quaternions — mathematical structures that represent 3D rotations. Rather than following nodes based on positional distance, SpinStep selects branches according to their angular proximity to the current orientation. This creates a new traversal metaphor: not stepping from point A to B, but rotating into the next part of the tree.
At its core, SpinStep implements a directional depth-first iterator. It uses quaternions to determine whether a child node is reachable from a parent within a configurable angular threshold.
Why Quaternions? Why Now?
Quaternions offer several advantages over Euler angles or rotation matrices: they avoid gimbal lock, interpolate smoothly (slerp), and compactly represent rotation in SO(3) space. Many fields already rely on them — 3D animation, aerospace, robotics, and VR — but their use in tree traversal and data filtering remains largely unexplored.
SpinStep proposes that when data is inherently orientation-based, a rotation-driven tree may be more natural, compact, and flexible than its positional counterparts.
Challenges and Trade-offs
This paradigm isn’t without complications. Quaternion math, though elegant, is computationally heavier than simple vector comparisons. Tree traversal in orientation space also requires new heuristics — especially for pruning or estimating traversal depth.
Some technical challenges faced so far:
• Defining intuitive thresholds for “angle closeness” in noisy or imprecise data.
• Ensuring traversal stability across small floating-point errors.
• Visualizing traversal paths in 3D for debugging and understanding.
Despite these, the clarity it offers in domains where orientation is king outweighs the cost in many cases.
When Does It Make Sense?
SpinStep shines in niche but growing areas where rotational context matters more than position. Examples include:
• Robot joint planning where each node encodes an actuator state.
• VR/AR scene graphs where transitions are viewpoint-based.
• Game AI that reasons about field-of-view or camera orientation.
• Astrophysical simulations where celestial mechanics follow rotational paths.
• Procedural generation for spherical or planet-like worlds.
Even in performance-sensitive environments, SpinStep can serve as a filter, narrowing large sets of directional options before falling back on standard methods.
The Path Ahead
SpinStep is a prototype — lean, flexible, and ready to grow. Key improvements on the roadmap include:
• A performance pass using Cython or Numba to accelerate quaternion math.
• Visual debugging tools to display tree structure and traversal paths in 3D.
• Integration with physics engines or robotics APIs for live use cases.
• Alternate traversal strategies (e.g. weighted branching, path scoring).
It’s an open invitation: SpinStep isn’t the final answer to rotational data traversal — it’s a first sketch of what a rotation-native structure might look like.
Final Thoughts
In a world increasingly shaped by spatial computing — from drones to digital twins — the way we traverse data matters. SpinStep asks: what if we stop thinking in terms of X, Y, Z, and instead start rotating through our problems?
Give it a try, and if it sparks ideas, let’s collaborate.
GitHub: https://github.com/VoxLeone/SpinStep/tree/main/spinstep
License: MIT
