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What happens behind a single mouse click

When you click an object in a 3D viewer, a process called "Raycasting" runs. A virtual ray is shot from the mouse position into the scene, and the system checks which object it hits.

The limitation of the default approach​

The default approach checks every triangle in a mesh, one by one. 100,000 triangles means 100,000 intersection tests. Every time the mouse moves.

What is BVH?​

BVH (Bounding Volume Hierarchy) is a tree data structure designed for efficient spatial queries in 3D space.

How it works​

A 3D model is made up of tens or hundreds of thousands of triangles. To find which triangle a ray hits, you'd normally have to check every single one.

BVH wraps these triangles in bounding boxes (AABBs — Axis-Aligned Bounding Boxes) and groups them hierarchically.

          [Entire Model]            ← Root bounding box
          /            \
   [Left Half]    [Right Half]      ← Space split in two
    /      \        /      \
 [△△△]  [△△△]   [△△△]  [△△△]      ← Leaf nodes (actual triangles)

If the ray doesn't hit the root box → done, skip the entire model. If the ray only hits the left half → skip the entire right half. At each step, the search space is cut in half.

Split strategy: SAH (Surface Area Heuristic)​

The performance of a BVH tree depends on where the space is divided. Voxel3D uses the SAH (Surface Area Heuristic) strategy.

SAH is based on the principle that "the smaller a child node's surface area, the lower the probability a ray will hit it." It evaluates all possible split positions and picks the one that minimizes the overall traversal cost.

Cost = left surface area / parent surface area × left triangle count
     + right surface area / parent surface area × right triangle count

It takes longer to build, but produces the fastest tree for ray traversal. This makes it ideal for 3D viewers where real-time interaction matters.

Other split strategies​

StrategyMethodBuild speedQuery performance
SAHOptimal split based on surface areaSlowBest
CENTERSplit at triangle centroidFastAverage
AVERAGESplit at mean positionFastAverage

Where BVH is used​

BVH is a fundamental algorithm used across the 3D industry.

  • Game engines (Unreal, Unity): Collision detection, occlusion culling
  • Ray tracing renderers (NVIDIA RTX): GPU-accelerated BVH for real-time ray tracing
  • Physics simulations: Fast collision candidate pair search
  • 3D viewers (Voxel3D): Raycasting, cross-section computation, distance measurement

Solving it with BVH​

Voxel3D applies this BVH to Raycasting. It divides space into a tree structure, skipping entire regions the ray doesn't pass through.

Default: 100K triangles → 100K tests (O(n))
BVH:     100K triangles → ~17 tests (O(log n))

How it's implemented​

  • Built on three-mesh-bvh, wrapped in a BVHManager for control
  • All mesh raycasting is accelerated automatically, no code changes needed
  • Meshes over 500K triangles are auto-filtered for memory protection
  • Helper objects like Grid and Gizmo are excluded from BVH generation

Features that run on top of BVH​

The real value of BVH goes beyond faster clicks.

Selection (object picking)​

BVH tree traversal narrows down candidate triangles, and stops as soon as the first intersection is found. Even on large models, mouse clicks respond instantly.

Clipping Edge (cross-section outlines)​

All scene models are merged into a single geometry, and a unified BVH is built. This BVH computes plane-triangle intersections in real time to visualize cross-section outlines.

Measurement (distance calculation)​

BVH-based geometric analysis calculates precise distances between two meshes.

BVH (foundation)
 ├── Selection - firstHitOnly + BVH acceleration
 ├── Clipping Edge - merged BVH + shapecast
 └── Measurement - BVH-based geometric analysis

Without BVH, none of these features could work in real time on large models. Every bit of responsiveness you feel in Voxel3D starts with BVH.