com.wallstop-studios.unity-helpers

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wallstop.github.io/unity-helpers

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<!doctype html><html lang=en class=no-js> <head><meta charset=utf-8><meta name=viewport content="width=device-width,initial-scale=1"><meta name=description content="Production-ready Unity utilities: 10-15x faster PRNGs, O(log n) spatial queries, zero-allocation pooling, Odin-level inspector tooling, and data-driven effects."><meta name=author content="Wallstop Studios"><link href=https://wallstop.github.io/unity-helpers/features/spatial/spatial-tree-semantics/ rel=canonical><link href=../hulls/ rel=prev><link href=../../effects/effects-system/ rel=next><link rel=icon href=../../../assets/images/favicon.png><meta name=generator content="mkdocs-1.6.1, mkdocs-material-9.7.3"><title>Spatial Tree Semantics - Unity Helpers</title><link rel=stylesheet href=../../../assets/stylesheets/main.484c7ddc.min.css><link rel=stylesheet 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<span class=md-ellipsis> Structures At A Glance </span> </a> </li> <li class=md-nav__item> <a href=#2d-consistent-results-across-quadtree2d-and-kdtree2d class=md-nav__link> <span class=md-ellipsis> 2D: Consistent Results Across QuadTree2D and KdTree2D </span> </a> <nav class=md-nav aria-label="2D: Consistent Results Across QuadTree2D and KdTree2D"> <ul class=md-nav__list> <li class=md-nav__item> <a href=#when-to-use-2d class=md-nav__link> <span class=md-ellipsis> When To Use (2D) </span> </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=#3d-why-kdtree3d-and-octtree3d-can-differ class=md-nav__link> <span class=md-ellipsis> 3D: Why KdTree3D and OctTree3D Can Differ </span> </a> </li> <li class=md-nav__item> <a href=#3d-rtree3d-semantics class=md-nav__link> <span class=md-ellipsis> 3D: RTree3D Semantics </span> </a> </li> <li class=md-nav__item> <a href=#guidance class=md-nav__link> <span class=md-ellipsis> Guidance </span> </a> </li> <li class=md-nav__item> <a 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<div class=md-content data-md-component=content> <nav class=md-path aria-label=Navigation> <ol class=md-path__list> <li class=md-path__item> <a href=../../.. class=md-path__link> <span class=md-ellipsis> Home </span> </a> </li> <li class=md-path__item> <a href=../../inspector/inspector-overview/ class=md-path__link> <span class=md-ellipsis> Features </span> </a> </li> <li class=md-path__item> <a href=../spatial-trees-2d-guide/ class=md-path__link> <span class=md-ellipsis> Spatial Data Structures </span> </a> </li> </ol> </nav> <article class="md-content__inner md-typeset"> <a href=https://github.com/wallstop/unity-helpers/edit/main/docs/features/spatial/spatial-tree-semantics.md title="Edit this page" class="md-content__button md-icon" rel=edit> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75z"/></svg> </a> <a href=https://github.com/wallstop/unity-helpers/raw/main/docs/features/spatial/spatial-tree-semantics.md title="View source of this page" class="md-content__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M12 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0 8a5 5 0 0 1-5-5 5 5 0 0 1 5-5 5 5 0 0 1 5 5 5 5 0 0 1-5 5m0-12.5C7 4.5 2.73 7.61 1 12c1.73 4.39 6 7.5 11 7.5s9.27-3.11 11-7.5c-1.73-4.39-6-7.5-11-7.5"/></svg> </a> <h1 id=spatial-tree-semantics>Spatial Tree Semantics<a class=headerlink href=#spatial-tree-semantics title="Permanent link">¶</a></h1> <h2 id=tldr-why-semantics-matter>TL;DR — Why Semantics Matter<a class=headerlink href=#tldr-why-semantics-matter title="Permanent link">¶</a></h2> <ul> <li>Different structures make different promises about boundaries and tie‑breaks.</li> <li>2D point trees (QuadTree2D, KdTree2D) agree on results; RTree differs by design (bounds‑based).</li> <li>In 3D, KdTree3D vs. OctTree3D can diverge at exact boundaries; add small epsilons if edge‑cases matter.</li> </ul> <p>This page explains how the 2D and 3D spatial structures compare in terms of correctness, when to use each structure, and why some 3D variants may produce different results for identical inputs and queries.</p> <h2 id=result-buffers>Result Buffers<a class=headerlink href=#result-buffers title="Permanent link">¶</a></h2> <ul> <li>Every range/bounds/nearest-neighbor API accepts an output <code>List<T></code> and <strong>clears it before</strong> appending results. Reuse the same buffer between calls to avoid garbage and do not expect prior contents to survive a query.</li> <li>This pattern is consistent across <code>QuadTree2D</code>, <code>KdTree2D/3D</code>, <code>OctTree3D</code>, and the RTree variants, matching the log-friendly “provide your own buffer” approach used throughout the helpers.</li> </ul> <h2 id=structures-at-a-glance>Structures At A Glance<a class=headerlink href=#structures-at-a-glance title="Permanent link">¶</a></h2> <ul> <li>QuadTree2D — Recursive 4-way partitioning of space. Good general-purpose point queries.</li> <li>KDTree2D — Alternating axis splits. Strong for nearest neighbor and range queries on points.</li> <li>RTree2D — Groups rectangles (AABBs) by minimum bounding rectangles (MBRs). Best when items have size.</li> </ul> <p>Illustrations:</p> <p><img alt=QuadTree2D src=../../../images/spatial/quadtree-2d.svg></p> <p><img alt=KDTree2D src=../../../images/spatial/kd-tree-2d.svg></p> <p><img alt=RTree2D src=../../../images/spatial/r-tree-2d.svg></p> <p>3D Variants</p> <p><img alt=Octree3D src=../../../images/spatial/octree-3d.svg></p> <p><img alt=KDTree3D src=../../../images/spatial/kd-tree-3d.svg></p> <p><img alt=RTree3D src=../../../images/spatial/r-tree-3d.svg></p> <p>Diagram notes</p> <ul> <li>Octree splits are centered along each axis, evenly dividing space into eight octants.</li> <li>KDTree3D splits are data‑dependent and may be off‑center; the diagram shows an off‑center y‑split to emphasize this difference.</li> </ul> <h2 id=2d-consistent-results-across-quadtree2d-and-kdtree2d>2D: Consistent Results Across QuadTree2D and KdTree2D<a class=headerlink href=#2d-consistent-results-across-quadtree2d-and-kdtree2d title="Permanent link">¶</a></h2> <ul> <li>QuadTree2D and KdTree2D (balanced and unbalanced) index points and use equivalent per‑point checks for range and bounds queries. For the same input data and the same queries, they return the same results. Differences are limited to construction/query performance and memory layout.</li> <li>RTree2D differs by design: it indexes rectangles (AABBs). If your elements have size, intersection/containment semantics involve those sizes, so results will differ from point‑based trees.</li> </ul> <h3 id=when-to-use-2d>When To Use (2D)<a class=headerlink href=#when-to-use-2d title="Permanent link">¶</a></h3> <ul> <li>QuadTree2D</li> <li>Use for broad-phase neighbor checks, visibility, and general spatial buckets where balanced performance and simplicity help.</li> <li>Pros: Simple mental model, predictable, easy to rebuild or update.</li> <li> <p>Cons: Hotspots can create deeper trees; nearest-neighbor not optimal vs KDTree.</p> </li> <li> <p>KDTree2D</p> </li> <li>Use for nearest-neighbor and precise point range queries at scale.</li> <li>Pros: Excellent for NN queries, balanced variant gives consistent query time.</li> <li> <p>Cons: Balanced build costs; dynamic updates more expensive than QuadTree.</p> </li> <li> <p>RTree2D</p> </li> <li>Use for geometry with area (AABBs), e.g., sprites, colliders, map tiles.</li> <li>Pros: Querying by bounds is very fast; items with size are first-class.</li> <li>Cons: Overlap between MBRs may increase query visits; tuned for bounds, not points.</li> </ul> <h2 id=3d-why-kdtree3d-and-octtree3d-can-differ>3D: Why KdTree3D and OctTree3D Can Differ<a class=headerlink href=#3d-why-kdtree3d-and-octtree3d-can-differ title="Permanent link">¶</a></h2> <p>While KdTree3D and OctTree3D are both point‑based and target equivalent use cases, algorithmic choices can yield different edge‑case behavior for identical inputs/queries.</p> <p>Key reasons and scenarios:</p> <ul> <li>Split planes and child assignment</li> <li>KdTree3D splits by alternating axes (x, y, z); balanced builds use median selection, unbalanced builds split at node‑center. Points lying exactly on a split plane are deterministically assigned but may end up in different leaves between balanced vs unbalanced trees.</li> <li> <p>OctTree3D partitions space into eight octants at each node. Points on plane boundaries are classified using octant rules; borderline points may be grouped differently than in KdTree3D.</p> </li> <li> <p>Bounds queries: half‑open vs closed edges</p> </li> <li>KdTree3D constructs an inclusive half‑open query box for per‑point checks and uses Unity <code>Bounds</code> for traversal. OctTree3D uses <code>BoundingBox3D</code> with inclusive‑max conversion and additional node‑level fast paths when a node is fully contained.</li> <li>Minimum node size enforcement keeps node bounds non‑degenerate. Near boundary edges this can expand a node just enough to flip a fully‑contained check, changing whether the algorithm fast‑adds all points in a node or checks them individually.</li> <li> <p>Result impact: points exactly on max edges or at floating‑point limits can be included by one structure and excluded by the other in rare cases.</p> </li> <li> <p>Range (sphere) queries</p> </li> <li> <p>Both trees use exact per‑point distance checks. However, their traversal pruning and “node fully contained in sphere” checks differ (sphere vs AABB overlap/containment and different numeric guards). For points close to the query radius, minor numeric differences can alter inclusion.</p> </li> <li> <p>Balanced vs unbalanced KdTree3D</p> </li> <li>Balanced uses median selection; unba