quatSub: Quaternion Subtraction Operations

Component-wise Difference for Quaternion Analysis

The quatSub function implements component-wise quaternion subtraction, computing the algebraic difference between two quaternions. This operation provides essential arithmetic for quaternion error analysis, deviation measurement, and relative orientation calculations in 4-dimensional quaternion space.

Mathematical Definition:

For quaternions $q_a = (x_a, y_a, z_a, w_a)$ and $q_b = (x_b, y_b, z_b, w_b)$:

$$\text{quatSub}(q_a, q_b) = (x_a - x_b, y_a - y_b, z_a - z_b, w_a - w_b)$$

Properties:

• Component-wise arithmetic operation without geometric meaning
• Non-commutative: $q_a - q_b \neq q_b - q_a$
• Preserves quaternion structure but may not preserve rotation validity
• Useful for error analysis and deviation measurement

ライブエディター

const fragment = () => {
      const coords = uv.sub(0.5).mul(8)
      const gridPos = coords.floor()
      const local = coords.fract().sub(0.5)

      const hash1 = gridPos.x.mul(127.1).add(gridPos.y.mul(311.7)).sin().mul(43758.5).fract()
      const hash2 = gridPos.x.mul(269.5).add(gridPos.y.mul(183.3)).sin().mul(43758.5).fract()

      const t = iTime.mul(0.3)
      const q1 = vec4(t.add(hash1.mul(6.28)).sin(), t.add(hash1.mul(4.15)).cos(), t.mul(0.7).sin(), t.cos()).normalize()
      const q2 = vec4(t.add(hash2.mul(3.14)).cos(), t.add(hash2.mul(5.67)).sin(), t.mul(0.9).cos(), t.mul(0.8).sin()).normalize()

      const difference = quatSub(q1, q2)
      const deviation = difference.length()

      const transform = quat2mat3(q1)
      const rotated = transform.mul(vec3(local, hash1.sub(0.5)))

      const field = rotated.x.mul(rotated.y).mul(8).sin()
      const intensity = field.abs().mul(deviation.mul(2))
      const color = vec3(intensity, intensity.mul(0.7).add(deviation.mul(0.3)), intensity.mul(0.5).add(deviation))

      return vec4(color, 1)

}