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Domain Warping Formulas

Mathematical formulas showing how each warp mode transforms coordinates.

Simple Warp​

Single-pass domain warping using the warp noise layer.

W(p) = N_warp((p + O) × S)

p' = p + W(p) × strength

result = N_base(p')

Where:

  • p = input position (uv coordinates)
  • O = (offset_x, offset_y)
  • S = scale
  • N_warp = warp noise function
  • N_base = base noise function
  • strength = warp_strength

Effect: The warp noise pushes and pulls the base noise sampling coordinates, creating smooth flowing distortions.

Dual Warp​

Two sequential warp passes applied one after another.

W₁(p) = N_warp((p + O₁) × S₁)

p' = p + W₁(p) × strength

W₂(p') = N_warp((p' + O₂) × S₂)

p'' = p' + W₂(p') × n_strength

result = N_base(p'')

Where:

  • O₁ = (offset_x, offset_y)
  • S₁ = scale
  • O₂ = (n_offset_x, n_offset_y)
  • S₂ = n_scale
  • n_strength = secondary warp strength

Effect: Compound distortions where the second warp adds detail within the first warp's flow. Use different scales for primary (large flows) and secondary (fine detail).

Chained Warp​

The warp noise itself is warped before being used to distort the base noise.

W_pre(p) = N_warp((p + O₁) × S₁)

p_warp = (p + O₂) + W_pre(p) × n_strength

W(p) = N_warp(p_warp × S₂)

p' = p + W(p) × strength

result = N_base(p')

Where:

  • O₁ = (offset_x, offset_y) - pre-warp offset
  • S₁ = scale - pre-warp scale
  • O₂ = (n_offset_x, n_offset_y) - main warp offset
  • S₂ = n_scale - main warp scale
  • n_strength = how much pre-warp distorts main warp

Effect: Creates extremely organic patterns where the warp itself has internal structure. The warp varies across space, producing natural marble veining and flowing liquid effects.

Parameter Summary​

Common to all modes:

  • warp_strength - Overall warp intensity
  • offset_x, offset_y - Primary warp offset
  • scale - Primary warp scale/frequency

Dual & Chained modes:

  • n_offset_x, n_offset_y - Secondary warp offset
  • n_scale - Secondary warp scale/frequency
  • n_strength - Secondary warp intensity

Key Difference:

  • Dual: Warps are applied sequentially to the base noise coordinates

    base_noise(warp1(warp2(uv)))

  • Chained: First warp distorts the second warp, then result distorts base noise

    base_noise(warp2(uv + warp1(uv)))