inside: Boundary Detection Function

Range Checking for Spatial Containment

The inside function checks whether a value or vector lies within specified minimum and maximum bounds. It returns true if the point is inside the boundaries, false otherwise. Useful for collision detection and spatial constraints.

Mathematical Definition: For any value $x$ and boundary parameters $\text{min}, \text{max}$:

$$\text{inside}(x, \text{min}, \text{max}) = \neg(x < \text{min} \lor x > \text{max}) \equiv (\text{min} \leq x \leq \text{max})$$

This formulation naturally extends to higher dimensions through component-wise logical operations, enabling efficient spatial queries for collision detection, procedural generation, and constraint satisfaction problems.

Nested Boundary Regions

This example shows multiple overlapping boundary regions with different visual effects for each containment level.

ライブエディター

const fragment = () => {
      const scale1 = 0.8
      const scale2 = 0.5
      const scale3 = 0.3

      const region1 = insideVec2(uv, vec2(-scale1), vec2(scale1))
      const region2 = insideVec2(uv, vec2(-scale2), vec2(scale2))
      const region3 = insideVec2(uv, vec2(-scale3), vec2(scale3))

      const time = iTime.mul(0.5)
      const rotation = time.cos()
      const rotatedUV = vec2(
              uv.x.mul(rotation).sub(uv.y.mul(time.sin())),
              uv.x.mul(time.sin()).add(uv.y.mul(rotation))
      )

      const dynamicRegion = insideVec2(rotatedUV, vec2(-0.2), vec2(0.2))

      const layerIntensity = region1.toFloat().mul(0.3)
              .add(region2.toFloat().mul(0.4))
              .add(region3.toFloat().mul(0.5))
              .add(dynamicRegion.toFloat().mul(0.8))

      const interference = uv.length().mul(8).add(time.mul(2)).sin()
      const modulated = layerIntensity.mul(interference.mul(0.3).add(0.7))

      const red = modulated.mul(region1.toFloat().mul(0.7).add(0.3))
      const green = modulated.mul(region2.toFloat().mul(0.6).add(0.4))
      const blue = modulated.mul(region3.toFloat().mul(0.2).add(0.8))

      return vec4(red, green, blue, 1)

}

Mathematical Properties and Computational Applications

Property	Mathematical Expression	Application Domain
Inclusion Logic	$\text{inside}(x, a, b) \Leftrightarrow a \leq x \leq b$	Constraint satisfaction
De Morgan's Law	$\neg(x < a \lor x > b) \equiv (x \geq a \land x \leq b)$	Boolean algebra optimization
Monotonicity	$a_1 \leq a_2, b_1 \leq b_2 \Rightarrow \text{inside}(x,a_1,b_1) \Rightarrow \text{inside}(x,a_2,b_2)$	Hierarchical containment
Dimension Extension	$\text{inside}(\mathbf{v}, \mathbf{min}, \mathbf{max}) = \bigwedge_i \text{inside}(v_i, \min_i, \max_i)$	Multidimensional queries