Image: Simulation#

Reaction-diffusion, fluids, solvers and other iterative image processes.

7 nodes.

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Contents#

• COP Eikonal (PCG) — Solves the eikonal equation to give the arrival time (or geodesic distance) from seed pixels through a speed field.
• COP Flow Solve (PCG) — Projects a 2-channel velocity layer to be divergence-free, or runs a stable-fluids simulation that advects density layers.
• COP Ocean (PCG) — Evaluates an FFT ocean surface (Tessendorf) into height, displacement, normal and foam layers.
• COP Reaction Diffusion (PCG) — Runs a reaction-diffusion simulation (Gray-Scott, multi-scale Turing or Maginu) for a number of steps.
• COP Ripple (PCG) — Simulates 2D waves with a leapfrog wave-equation solver.
• COP Solve Poisson (PCG) — Solves the Poisson equation on the image.
• COP Turing Patterns (PCG) — Repeatedly blurs and sharpens a layer to grow stripes and spots while keeping the large-scale shape of the input.

Nodes#

COP Eikonal (PCG)#

PCG_COPEikonal · category PCG/cop · Houdini: Eikonal (COP)

Solves the eikonal equation to give the arrival time (or geodesic distance) from seed pixels through a speed field.

Solves |grad T| = 1/F with a Godunov upwind scheme and fast sweeping, starting from the pixels of seed_layer that are above 0.5. The speed F is the speed layer multiplied by speed; a speed of 0 is a wall. With a constant speed of 1, the result is the geodesic distance in pixels around obstacles.

Unreachable pixels are written as -1. If an id layer name is given, the id of the nearest seed region (connected component of the seed mask) is propagated and written as well.

The scheme is first order: diagonal directions close to the seeds have the largest error (around 10% within a few pixels), falling to around 1% far away.

Inputs

Outputs

Parameters

Solver

COP Flow Solve (PCG)#

PCG_COPFlowSolve · category PCG/cop · Houdini: Flow Block Begin (COP), Flow Block End (COP), Flow Project Non-Divergent Multigrid (COP)

Projects a 2-channel velocity layer to be divergence-free, or runs a stable-fluids simulation that advects density layers.

Covers Flow Block Begin/End and Flow Project Non-Divergent Multigrid. Velocity is a 2-channel layer in pixels per step (v pointing up, like the rest of COP).

project performs one Helmholtz projection, turning any vector field into an incompressible flow. simulate runs Stam's stable fluids for steps iterations, each consisting of: add force, advect velocity, project, advect the density layers, then multiply by 1 - dissipation.

Both edge modes are solved directly: Wrap uses an exact FFT projection; Clamp makes the borders walls using a mirrored extension and FFT, also exact. The velocity and density layers are written back under their original names, so the result can be fed into the next segment. The report states the maximum remaining divergence and where it was computed.

Inputs

Outputs

Parameters

Tips

• Run project on a hand-painted or noise-generated vector field to get a swirling, incompressible field, then feed it to COP Distort.

COP Ocean (PCG)#

PCG_COPOcean · category PCG/cop · Houdini: Ocean Evaluate (COP), Ocean Spectrum (COP)

Evaluates an FFT ocean surface (Tessendorf) into height, displacement, normal and foam layers.

Combines Houdini's Ocean Spectrum and Ocean Evaluate. A wave spectrum (Phillips or TMA) generates random complex amplitudes, which are advanced in time with the dispersion relation (deep water, or finite depth when Depth is above 0) and transformed with an inverse FFT. The result tiles seamlessly because the FFT is periodic. With the same seed, changing Time animates the surface; changing Amplitude only scales it (height proportional to the square root of the amplitude). With the default Amplitude the significant wave height is about 0.21*V^2/g for a fully developed sea; Grid Size should be at least an order of magnitude larger than V^2/g, or the longest waves are cut off and the sea looks low.

Output layers, in metres, named after Output Layer:

• <name>: height.
• <name>_disp: 3-channel displacement (du, height, dv): horizontal choppy displacement along the image u and v directions plus vertical displacement, to push a mesh.
• <name>_N: tangent-space normal (u, v, up).
• <name>_foam: foam, where the displacement Jacobian drops below 1 - Foam Threshold, mapped linearly to 0-1.

If cop is connected, layers are added to it and its resolution is used; otherwise Resolution applies. report lists the maximum wave height and the imaginary residual of the inverse FFT (should be 0).

Inputs

Outputs

Parameters

Wind

Waves

Compared with Houdini

One node replaces Houdini's Ocean Spectrum and Ocean Evaluate pair. The TMA directional spread is Hasselmann with Horvath's swell term; the sign handling of Swell (negative adds against-wind waves) is chosen by the plugin because the documentation is not specific.

COP Reaction Diffusion (PCG)#

PCG_COPReactionDiffusion · category PCG/cop · Houdini: Reaction-Diffusion Block Begin (COP), Reaction-Diffusion Block End (COP)

Runs a reaction-diffusion simulation (Gray-Scott, multi-scale Turing or Maginu) for a number of steps.

One node advances the simulation by Steps iterations. The state is stored in extra layers next to the output: <Output Layer>_u and _v for Gray-Scott, _g for Turing and _a / _b for Maginu. Feeding the output back into the input continues the run from that state (the seed layer is then ignored).

Gray-Scott presets are common feed/kill pairs; Feed Layer and Kill Layer allow per-pixel values. Maginu solves A' = Da*lap(A) + alpha*(A - A^3) - B and B' = Db*lap(B) + beta*(A - gamma*B). Turing uses the listed activator radii. An optional boundary SDF restricts where the reaction takes place.

The second output is a text report of the run.

Inputs

Outputs

Parameters

Gray-Scott

Initial State

Spatial Variation

Turing

Kenjiro Maginu

Reaction

Boundary

Output Correction

Tips

• Chain several nodes, wiring each output into the next input, to continue a long simulation across runs.

COP Ripple (PCG)#

PCG_COPRipple · category PCG/cop · Houdini: Ripple Block Begin (COP), Ripple Block End (COP)

Simulates 2D waves with a leapfrog wave-equation solver.

Solves the 2D wave equation for Steps iterations. The Source Layer gives the initial displacement on the first run, or with a Drive Frequency keeps driving the source continuously with a sine. The Obstacle Layer defines walls. State is stored in <Output Layer>, <Output Layer>_prev and <Output Layer>_t; wire the output back in to continue the run.

Wave Speed is limited to 0.707 pixels per step, the CFL stability limit. The second output is a text report.

Inputs

Outputs

Parameters

Wave

Drive

Boundary

COP Solve Poisson (PCG)#

PCG_COPSolvePoisson · category PCG/cop · Houdini: Solve Poisson (COP)

Solves the Poisson equation on the image.

Solves lap(u) = f with the five-point stencil and a pixel spacing of 1. With Input Type Gradient it solves lap(u) = div(g) instead, which reconstructs a height from a gradient field (for example slopes derived from normals), and enables gradient-domain editing and Poisson blending.

Periodic and Neumann boundaries are solved directly with an FFT (Neumann via mirror extension). Dirichlet uses conjugate gradients, preconditioned with the direct Neumann solve. The second output is a text report.

Inputs

Outputs

Parameters

Dirichlet

COP Turing Patterns (PCG)#

PCG_COPTuringPatterns · category PCG/cop · Houdini: Turing Patterns (COP)

Repeatedly blurs and sharpens a layer to grow stripes and spots while keeping the large-scale shape of the input.

Each iteration blurs the current state x with the chosen filter and radius, then sharpens it with an unsharp mask of the same radius, and clamps to 0-1:

b = Blur(x), x = clip(b + Power * (b - Blur(b)), 0, 1)

The start value is Gain * source. The unsharp step acts as a difference of Gaussians (activator minus inhibitor), which amplifies features with wavelength near Radius, and the clamp saturates them into two phases; larger Power gives more solid patterns. Because the iteration begins from the source, the large shapes of the input remain visible. The input is clamped to 0-1 during iteration, so HDR values are compressed.

The result is blended with the original by Mask (multiplied by the optional mask layer).

Inputs

Outputs

Parameters

Compared with Houdini

The exact formula is the plugin's own interpretation of Houdini's blur-then-sharpen description. There is no per-pixel radius input layer and no per-channel RGBA toggles. This is distinct from the Turing option of Reaction Diffusion, which uses McCabe's multi-scale algorithm.