contain: AABB Point Containment Test

Axis-Aligned Boundary Testing for Spatial Queries

The AABB containment function determines whether a point lies within the bounds of an axis-aligned bounding box. This fundamental spatial query operation enables collision detection, spatial partitioning, and geometric filtering.

Given an AABB with bounds $[\vec{b_{\min}}, \vec{b_{\max}}]$ and test point $\vec{p}$ , the containment test evaluates:

$\text{contained} = (b_{\min,x} < p_x \leq b_{\max,x}) \land (b_{\min,y} < p_y \leq b_{\max,y}) \land (b_{\min,z} < p_z \leq b_{\max,z})$

The function uses inclusive bounds on the maximum side and exclusive bounds on the minimum side, following standard interval notation $(\text{min}, \text{max}]$ .

Boundary Conventions

The asymmetric boundary treatment prevents double-counting at shared edges when multiple AABBs tile a space:

Points exactly on minimum boundaries are considered outside
Points exactly on maximum boundaries are considered inside
This convention ensures consistent spatial partitioning behavior

Performance Characteristics

AABB containment testing provides optimal computational efficiency:

Time Complexity: $O(1)$ constant time per query
Memory Access: Sequential coordinate comparison
Branching: Minimal conditional logic suitable for SIMD processing

Live Editor

const fragment = () => Scope(() => {
      const t = iTime.mul(0.4)
      const p = uv.mul(4).sub(2)
      const box = AABB({
              minBounds: vec3(t.sin().mul(1.5).sub(0.3), t.mul(1.2).cos().mul(1.2).sub(0.4), 0),
              maxBounds: vec3(t.mul(0.9).sin().mul(1.3).add(0.5), t.mul(0.7).cos().mul(1.1).add(0.6), 0)
      })
      const testPoint = vec3(p, 0)
      const inside = aabbContain(box, testPoint)
      const distFromCenter = length(p.sub(aabbCentroid(box).xy))
      const gradient = smoothstep(0.5, 1.5, distFromCenter)
      const baseColor = vec3(0.1, 0.2, 0.4).select(vec3(0.8, 0.4, 0.1), inside)
      const edgeX = p.x.sub(box.minBounds.x).abs()
               .min(p.x.sub(box.maxBounds.x).abs())
      const edgeY = p.y.sub(box.minBounds.y).abs()
               .min(p.y.sub(box.maxBounds.y).abs())
      const edge = edgeX.min(edgeY)
      const wireframe = smoothstep(0.02, 0.05, edge).oneMinus()
      return vec4(baseColor.mul(gradient.oneMinus().add(0.3)).add(wireframe.mul(0.6)), 1)
})

Axis-Aligned Boundary Testing for Spatial Queries​

Axis-Aligned Boundary Testing for Spatial Queries