diagonal: AABB Diagonal Vector Calculation

Extent Measurement for Bounding Box Dimensions

The AABB diagonal function computes the dimensional extent of an axis-aligned bounding box along each coordinate axis. This operation determines the width, height, and depth of the rectangular volume.

Given an AABB with bounds $[\vec{b_{\min}}, \vec{b_{\max}}]$ , the diagonal vector is calculated as:

$\vec{d} = |\vec{b_{\max}} - \vec{b_{\min}}|$

The absolute value ensures positive dimensions regardless of coordinate system orientation or potential bound swapping.

Dimensional Analysis

The diagonal vector provides essential geometric measurements:

X-component: Width along the X-axis
Y-component: Height along the Y-axis
Z-component: Depth along the Z-axis

Additional derived measurements include:

Volume: $V = d_x \times d_y \times d_z$
Surface Area: $S = 2(d_x d_y + d_y d_z + d_z d_x)$
Space Diagonal: $|\vec{d}| = \sqrt{d_x^2 + d_y^2 + d_z^2}$

Applications

Diagonal calculations serve multiple computational purposes:

Level of Detail: Distance-based quality adjustments using diagonal magnitude
Spatial Indexing: Grid cell sizing for spatial hash tables
Collision Detection: Broad-phase filtering using diagonal extents
Memory Allocation: Buffer sizing based on dimensional requirements

ライブエディター

const fragment = () => Scope(() => {
      const t = iTime.mul(0.3)
      const p = uv.mul(4).sub(2)
      const box = AABB({
              minBounds: vec3(t.sin().mul(0.8).sub(1.2), t.mul(1.4).cos().mul(0.6).sub(0.8), 0),
              maxBounds: vec3(t.mul(1.1).sin().mul(1.1).add(0.4), t.mul(0.8).cos().mul(0.9).add(0.6), 0)
      })
      const diag = diagonal(box)
      const center = aabbCentroid(box)
      const relPos = p.sub(center.xy)
      const normPos = relPos.div(diag.xy.mul(0.5))
      const intensity = length(normPos).saturate().oneMinus()
      const stripes = normPos.x.mul(diag.x).mul(8).sin().mul(0.5).add(0.5)
      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 wireframe = smoothstep(0.02, 0.04, edgeX.min(edgeY)).oneMinus()
      const color = intensity.mul(vec3(diag.x.mul(0.3), diag.y.mul(0.4), 0.6)).add(stripes.mul(0.2))
      return vec4(color.add(wireframe.mul(0.5)), 1)
})

Extent Measurement for Bounding Box Dimensions​

Extent Measurement for Bounding Box Dimensions