aabbCentroid: Bounding Box Center Calculation

Midpoint Formula for AABB Center Determination

The AABB centroid function computes the geometric center of an axis-aligned bounding box using the midpoint formula. This operation determines the central point equidistant from all faces of the rectangular volume.

Given an AABB with minimum bounds $\vec{b_{\min}}$ and maximum bounds $\vec{b_{\max}}$, the centroid is calculated as:

$\text{Centroid} = \frac{\vec{b_{\min}} + \vec{b_{\max}}}{2}$

This simple averaging operation produces the point at the geometric center of the bounding box. The centroid represents the center of mass for uniform density distribution within the volume.

Geometric Applications

The AABB centroid serves multiple computational purposes:

• Spatial Partitioning: Center point for octree and BSP tree subdivisions
• Collision Detection: Reference point for broad-phase collision algorithms
• Level of Detail: Distance calculations for LOD switching based on viewer proximity
• Frustum Culling: Representative point for visibility testing

ライブエディター

const fragment = () => Scope(() => {
      const t = iTime.mul(0.6)
      const box = AABB({
              minBounds: vec3(t.sin().mul(1.2).sub(0.8), t.mul(1.3).cos().mul(0.9).sub(0.5), 0),
              maxBounds: vec3(t.mul(0.8).sin().mul(1.1).add(0.6), t.mul(0.7).cos().add(0.7), 0)
      })
      const center = aabbCentroid(box)
      const p = uv.mul(4).sub(2)
      const distToCenter = length(p.sub(center.xy))
      const centerGlow = smoothstep(0.15, 0.05, distToCenter)
      const boxEdge = p.x.sub(box.minBounds.x).abs()
                 .min(p.x.sub(box.maxBounds.x).abs())
                 .min(p.y.sub(box.minBounds.y).abs()
                 .min(p.y.sub(box.maxBounds.y).abs()))
      const wireframe = smoothstep(0.02, 0.04, boxEdge).oneMinus()
      return vec4(centerGlow, wireframe.add(centerGlow.mul(0.8)), centerGlow.mul(0.6).add(wireframe), 1)
})