Solve Poisson Copernicus node

Solves Poisson’s equation inside a 2D boundary.

On this page	Parameters Pre-conditioner Inputs Outputs
Since	22.0

This node solves Poisson’s equation for a Mono layer. The Boundary input is a signed distance field that defines the region to solve in. Values less than or equal to 0 are treated as inside the region, and values greater than 0 are treated as outside.

Parameters ¶

Iterations

The number of solver iterations to perform. Higher values produce a more converged solution, but take longer to compute.

Boundary Blend

Blends between the Dirichlet and Neumann boundary conditions. A value of 0 uses Dirichlet boundary values, and a value of 1 uses Neumann boundary values.

When the blend input is wired, that input overrides this parameter.

Pre-conditioner ¶

Iterations

The number of pre-conditioner iterations to perform during the solve. Higher values can improve convergence, but increase cook time.

Smoothing Iterations

The number of smoothing iterations to perform in the pre-conditioner. Higher values can improve the pre-conditioned approximation.

Coarsest Smoothing Iterations

The number of smoothing iterations to perform at the coarsest level of the pre-conditioner, in place of an exact coarse solve.

Inputs ¶

rhs

A Mono layer containing the right-hand side of Poisson’s equation.

boundary

A Mono signed distance field that defines the solve region. Values less than or equal to 0 are inside the region.

dirichlet

An optional Mono layer containing prescribed solution values on the boundary.

neumann

An optional Mono layer containing prescribed normal derivative values on the boundary.

blend

An optional Mono layer that blends between the dirichlet and neumann boundary conditions per pixel. A value of 0 uses Dirichlet, and a value of 1 uses Neumann.

initial

An optional Mono layer to use as the initial solution estimate.

Outputs ¶

solution

The solved Mono layer.

See also

Solve Poisson Multigrid

Copernicus nodes

Align

Transforms a layer to align with another layer.
Align Pixels

Shifts a layer to align pixelwise with another layer.
Attribute

Creates a detached attribute.
Attribute Extract

Extracts a detached attribute from a geometry.
Attribute Insert

Inserts a detached attribute into a geometry.
Attribute Sample with Adjacency

Creates a texture map of an attribute sampled from geometry.
Attribute from Layer

Extracts a detached attribute from a layer.
Auto Stereogram

Generates an image with a 3D illusion.
Bake Geometry Textures

Generates textures by baking between a low-resolution and high-resolution mesh at interactive speeds.
Bake Pre-Process

Sets up rays for baking, with a visualization state.
Bend

Curves images using handles or a captured region.
Blend

Blends two layers, VDBs, or attributes together.
Block Begin

Start of a block, containing its inputs.
Block End

End of a block, declaring its outputs.
Block to Geometry

Compiles a block and produces its geometry representation.
Blur

Applies a blur to a layer.
Bokeh

Creates a Bokeh effect by expanding each pixel by an aperture shape.
Bounding Rectangle

Finds the bounding rectangle of a mask.
Bright

Brightens a layer, VDB, or attribute.
Bubble Noise

Generates bubble noise.
Cable Filter

Removes empty wires from a cable.
Cable Merge

Combines two cables into one cable.
Cable Pack

Combines input layers into a cable.
Cable Rename

Renames a cable’s wires based on filters.
Cable Sort

Sorts a cable’s wires by name.
Cable Split

Splits a cable based on filtering parameters.
Cable Switch

Selects an input cable.
Cable Unpack

Extracts individual wires from a cable.
Cache

Caches the input layers for faster playback.
Camera

Creates a camera.
Camera Blend

Blends two cameras.
Camera Import

Creates a layer in a camera’s space.
Camera Properties

Adjusts the camera properties of a layer.
Cell Pattern

Generates cellular patterns.
Cellular Noise

Generates cellular noise.
Cellular Noise 3D

Generates cellular noise from 3D locations.
Channel Extract

Extracts a channel from a layer, VDB, or attribute.
Channel Join

Combines multiple Mono layers, VDBs, or attributes into one multichannel output.
Channel Split

Divides the input’s channels into Mono layers, VDBs, or attributes.
Channel Swap

Swaps channels within a multichannel layer, VDB, or attribute.
Checkerboard

Creates an alternating checker pattern.
Chladni Cymatic Patterns

Generates interference patterns that represent various vibration modes.
Chroma Key

Keys an input based on hue, saturation, and luminance ranges.
Chromatic Aberration

Adds chromatic aberration to your image.
Clamp

Clamps an input layer, VDB, or attribute.
Cloud Noise 3D

Generates a billowy cloud noise.
Color Correct

Adjusts colors in the image.
Combine Normals

Blends two normal maps together.
Compare

Creates a mask by comparing two layers, VDBs, or attributes.
Compare and Blend

Compares two pixel values on a layer, VDB, or attribute and outputs either a true or false input for that pixel.
Configure Stamps

Creates stamp/sprite attributes on points with randomization controls and inputs.
Constant

Initializes pixels to constant values.
Contact Sheet

Arranges input layers into a contact sheet.
Contrast

Applies contrast to a layer, VDB, or attribute.
Convert Depth

Converts depth layers between height, depth, and distance.
Convert Normal

Converts normal layers between signed and offset.
Convolve 3×3

Convolves a layer by a 3×3 kernel.
Convolve Filter

Convolves an image with an arbitrary kernel image using an FFT.
Copy and Transform

Copies stamps and applies transformations to the copies.
Corner Detect

Detects corners in an input layer.
Corner Pin

Pins a layer’s corners in a reference layer.
Crop

Crops a layer to a new size.
Cross Product

Performs a cross product of two RGB layers, VDBs, or attributes.
Cryptomatte

Builds a matte from cryptomatte layers.
Cryptomatte Decode

Decodes a cyrptomatte into coverage and ID.
Cryptomatte Encode

Encodes a coverage and object hash into a cryptomatte layer.
Crystal Noise

Generates a sharp and angular Worley noise type.
Crystal Noise 3D

Generates a sharp and angular Worley noise type from 3D locations.
Curl

Computes the curl of a vector field.
Curl Noise

Generate curl noise.
Curl Noise 3D

Generates 3D curl noise.
Curvature

Computes the curvature of a layer.
Curve 3D

Lets you interactively draw Bézier curves using tools similar to 2D illustration programs, as well as polylines and NURBS.
Curve Animate 3D

Lets you interactively draw and animate Bézier curves using tools similar to 2D illustration programs, as well as polylines and NURBS.
Defocus

Defocuses an input layer.
Denoise AI

Denoises an input layer.
Denoise TVD

Removes white noise from an image.
Derivative

Computes the derivative of the source layer along its width (x-axis) and height (y-axis).
Despill

Removes color spill from an input layer.
Dilate Erode

Dilates or erodes a layer.
Distort

Distorts an input layer.
Distort with Adjacency

Distorts a layer over texture seams using adjacency.
Dot Product

Performs dot product between two layers.
Drop Shadow

Composites a copy of a layer under the original to create a shadow.
Edge Detect

Detects edges in the input image.
Edge Detect by Contour

Detects varying-width silhouette lines.
Edge Detect by Depth

Detects varying-width self-occluding silhouettes.
Edge Detect by Normal

Detects varying-width crease-lines.
Eikonal

Computes distances by solving the Eikonal equation.
Equalize

Equalizes colors by stretching or shifting their range.
Error

Generates a message, warning, or error.
Extrapolate Boundaries

Fills empty areas of an image using colors at the edges of non-empty areas.
Extrapolate with Adjacency

Fills areas of a texture outside the UV islands with information from their island neighbors.
Fast Fourier Transform

Computes the Fourier transform of an image.
Feather

Smooths out sharp changes in contrast.
Fetch

Brings a COP node’s outputs into the current network.
File

Loads an image or video from disk.
Fill

Fills a layer with a constant value.
Fill Connected

Flood fills the connected regions of a layer.
Filter Frequencies

Boosts or suppresses spatial frequencies in an image.
Flip

Flips a layer horizontally, vertically, or diagonally.
Flow Block Begin

Start of a Flow simulation block.
Flow Block End

End of a Flow simulation block.
Flow Project Non-Divergent Multigrid

Removes divergent components from a 2-dimensional vector field.
Font

Rasterizes text onto a layer from Type 1, TrueType, and OpenType fonts.
Fractal Noise

Generates fractal noise.
Fractal Noise 3D

Generates fractal noise from 3D locations.
Fractal Sample

Generates a fractal of the source input that you can randomize.
Function

Applies a mathematical function to a layer.
Gamma

Applies gamma correction to a layer, VDB, or attribute.
Geometry Attribute from Layer

Samples layers with a geometry’s attribute to create attributes from those layers.
Geometry to Adjacency

Rasterizes geometry to generate an adjacency cable.
Geometry to Layer

Converts a volume, VDB, or camera primitive into a layer or VDB.
Glow

Adds glow to an image based on its luminance.
Grunge Aurora

Generates a pattern resembling an aurora display.
Grunge Bark Strips

Generates a pattern resembling bark strips.
Grunge Birch Bark

Generates a pattern resembling the bark of a birch tree.
Grunge Drips

Generates a pattern resembling drips.
Grunge Galvanized Steel

Generates a pattern resembling galvanized steel.
Grunge Layered Noise

Generates a higher-level noise pattern by layering simple noises.
Grunge Leaking Streaks

Generates a pattern resembling leaking streaks.
Grunge Moisture

Generates a pattern resembling sponge-like moisture.
Grunge Mold Spots

Generates a pattern resembling mold spots.
Grunge Pine Bark

Generates a pattern resembling the bark of a pine tree.
Grunge Rust

Generates a pattern resembling rust on a surface.
Grunge Rusty Surface

Generates a pattern resembling a rusty surface.
Grunge Sheets

Generates a pattern resembling sheets.
Grunge Wipe Trails

Generates a pattern resembling circular wipe trails.
HSV Adjust

Converts between RGB and HSV color spaces, or modifies HSV.
Heat Distort

Distorts the input layer to simulate heat around fire and other mirage effects.
Heat Distort by Layer

Distorts the input layer using another layer to simulate heat around fire and other mirage effects.
Height to Ambient Occlusion

Imagines a sphere for each pixel and determines how occluded that sphere is based on its surroundings.
Height to Caustics

Creates caustic patterns on the ground from a refractive height layer.
Height to Normal

Converts a height layer to a normal layer.
Height to Shadow

Creates shadows using a virtual light source.
HeightField Clip

Clamps height values to a minimum and/or maximum value.
HeightField Erode

Simulates hydraulic and thermal erosion at a specific scale to create more realistic terrain.
HeightField Mask by Feature

Creates a mask based on different features of the heightfield.
HeightField Project

Projects 3D geometry onto a heightfield.
HeightField Slump

Simulates loose material sliding down inclines and piling at the bottom.
HeightField Strata

Adds sedimentary layering patterns to a HeightField.
HeightField Terrace

Creates stepped plains from the slopes of a HeightField.
HeightField Transform 2D

Transforms a height layer in 2D.
HeightField Transform 3D

Transforms a height layer in 3D.
HeightField Visualize

Visualizes layers as a colored heightfield by converting them into geometry
HeightField to Mono

Converts a heightfield into a grayscale mono layer.
Hex Tile

Randomly tiles texture.
Histogram

Builds a histogram from a layer.
Hyperbolic Tile

Generates hyperbolic polygon tiles for texture patterns.
ID to Mask

Creates a mask from an ID layer based on filtering parameters.
ID to Mono

Converts an ID layer, VDB, or attribute into a float.
ID to RGB

Converts an ID layer, VDB, or attribute into an RGB layer, VDB, or attribute.
ID to SDF

Computes a signed distance field from changes in ID values.
Illegal Pixel

Detects and then fixes or highlights illegal pixels in images.
Input

Fetches the input to a subnetwork.
Integrate Volume

Integrates a VDB along camera rays.
Invert

Inverts a layer, VDB, or attribute.
Invoke Block

Runs a block using inputs plugged into this node.
Invoke Geometry

Runs a program saved into geometry using inputs plugged into this node.
Julia Fractal

Computes the Julia set to create a fractal.
Knit

Generates a grid of knitted fabric stitches.
Kuwahara Filter

Applies the Kuwahara filter, which creates painterly effects.
Labs UV Grid Texture

Generates procedural UV grid textures.
Laplacian

Computes the Laplacian of the source layer.
Lattice Deform

Applies grid-based deformation to a layer.
Layer

Generates a layer.
Layer Merge

Combines all inputs.
Layer Properties

Edits basic layer metadata.
Layer Property Copy

Transfers layer properties from one layer, VDB, or attribute to another.
Layer Property Create

Adds or edits user-defined properties on a layer.
Layer Property Delete

Removes user-defined properties from a layer.
Layer from Attribute

Fills a layer from a detached attribute.
Layer from Curves

Render Curves into a Layer.
Layer from VDB

Sets a layer’s values from a VDB.
Layer to Geometry

Converts a layer or VDB into geometry.
Layer to Points

Creates points based on a layer.
Layer to VDB Leaf Points

Creates a point for each leaf of a VDB that would be in an envelope.
Lens Distort

Adds radial and tangential distortion to a layer based on OpenCV coefficients.
Light

Lights a layer given a light direction and normals.
Live Video

Captures images from a live video source.
Logic

Applies logic operations to ID layers.
ML Computer Vision Inference

Apply a model trained using the ML Train Computer Vision TOP.
Mask Combine

Combines several mask layers from an input cable into a single mask.
Mask from Curves

Creates a mask from 2D curves.
Match Camera

Transforms a layer to match a reference camera.
Match UDIM

Reframes pixels of a layer to match a particular UDIM tile.
Median

Applies a median filter to an image.
Mirror

Mirrors an image based on an arbitrary number of planes.
Mono

Converts a layer, VDB, or attribute into a mono, VDB, or attribute.
Mono to HeightField

Converts a mono layer into a heightfield.
Mono to ID

Converts a mono layer, VDB, or attribute into an integer.
Mono to RGB

Converts a mono layer, VDB, or attribute into an RGB layer, VDB, or attribute.
Mono to RGBA

Converts a mono layer into an RGBA layer.
Mono to SDF

Computes a signed distance field from an iso-level of a mono layer.
Neural Cellular Automata Core

Runs a neural cellular automata model to evolve cell states.
Neural Cellular Automata Decode

Decodes a cell state from the Neural Cellular Automata Core into a visible pattern.
Neural Layer to Depth (MoGe-2)

Estimates metric-scale depth, normal, and position maps from an input image.
Neural Layer to Mask (SAM2)

Creates a mask based on coordinates set through prompts.
Normal to Height

Reconstructs a height layer from a normal layer.
Null

Passes inputs to the outputs.
OCIO Transform

Converts color spaces using OCIO transforms.
ONNX Inference

Applies inference from an ONNX Machine Learning model.
Ocean Evaluate

Converts the layers of an ocean spectrum into an animated ocean surface.
Ocean Spectrum

Generates layers containing information for simulating ocean waves.
OpenCL

Executes an OpenCL kernel on layers, attributes, volumes, and VDBs.
Output

Collects the outputs of a subnetwork.
Paint 3D

Paint on a COP layer or UV-mapped geometry.
Phasor Noise

Generates phasor noise, which resembles a wave pattern.
Pixelate

Increases the size of pixels to pixelate an input layer.
Planar Inflate

Inflates a 2D SDF into a height layer.
Point Delete

Deletes points from a point cloud geometry.
Point Generate

Adds points to a point cloud geometry.
Point Merge

Merges point cloud geometries.
Points from Blobs

Creates points from blobs in an input layer.
Polar to UV

Converts polar coordinate pixels to Cartesian pixels.
Position Map

Generates a position map.
Position Sample

Samples an input texture by position.
Prefix Sum

Computes the prefix sum of a layer.
Premultiply

Premultiplies or un-premultiplies an RGBA layer.
Preview Material

Applies the preview material to geometry.
Project on Layer

Projects a layer onto a target layer.
Pyro Activate

Changes the activation of VDBs in a Pyro simulation.
Pyro Advect

Advects VDBs by Velocity.
Pyro Advect by Map

Advects a VDB by a flow map.
Pyro Axis Force

Applies a force around an axis to a velocity VDB.
Pyro Block Begin

Start of a Pyro simulation block.
Pyro Block End

End of a Pyro simulation block.
Pyro Build Advection Map

Constructs a flow map from a velocity VDB.
Pyro Buoyancy Force

Applies a Buoyancy force.
Pyro Collision Shape

Creates points representing implicit surfaces to add collision objects into a Pyro simulation.
Pyro Collision from Shape

Adds collision from pyro collision points representing implicit surfaces, into a VDB.
Pyro Configure

Configures a Pyro simulation.
Pyro Dissipate

Dissipates a VDB’s values over time.
Pyro Disturbance

Applies disturbance to a velocity VDB to break up still air.
Pyro Emit from Flame

Burns up the flame field.
Pyro Light Ambient

Builds a light field of ambient illumination of a VDB.
Pyro Light Scatter

Builds a light field of internal glow of a VDB.
Pyro Light from Points

Builds a light field of points lighting a VDB.
Pyro Packed MipMap

Builds an in-place MipMap of a VDB.
Pyro Project Non-Divergent Electro Static

Removes divergence from a velocity VDB.
Pyro Source Shape

Creates points representing implicit surfaces to source into a Pyro simulation.
Pyro Source from Layer

Sources from a layer’s envelope into a VDB.
Pyro Source from Points

Sources points into a VDB.
Pyro Source from Shape

Sources from pyro source points representing implicit surfaces, into a VDB.
Pyro Source from Volume

Sources from a VDB into another VDB.
Pyro Turbulence

Apply turbulence to a velocity VDB.
Pyro Uniform Force

Applies a uniform force.
Pyro Velocity Scale Force

Scales fluid velocity based on the fluid’s current speed.
Pyro Vortex Confinement Force

Applies a vortex confinement force to a velocity field.
Python Snippet

Runs a snippet of Python on layers.
Quantize

Quantizes input data into discrete steps.
RGB to RGBA

Converts RGB layers or attributes to RGBA.
RGB to UV

Splits an RGB layer or attribute into UV and mono layers or attributes.
RGBA to RGB

Converts RGBA layers or attributes to RGB.
RGBA to UV

Splits an RGBA layer or attribute into two UV layers or attributes.
ROP Image

Writes the output of a COP network to disk.
Ramp

Generates linear and radial ramps.
Random Mono

Creates a mono layer, VDB, or attribute with random values.
Random RGB

Creates an RGB layer, VDB, or attribute with random colors.
Rasterize Curves

Rasterizes curves onto a layer.
Rasterize GSplats

Rasterizes Gaussian Splats onto layers.
Rasterize Geometry

Rasterizes geometry onto a layer.
Rasterize Implicit Surface

Rasterizes an implicit surface onto a layer.
Rasterize Layer

Rasterizes a layer onto another layer’s camera.
Rasterize Setup

Prepares geometry for the Rasterize Geometry COP.
Rasterize Volume

Renders a volume viewed through a camera.
Ray Trace

Performs ray tracing on an input mesh based on an origins and directions map.
Reaction-Diffusion Block Begin

Start of a Reaction-Diffusion simulation block.
Reaction-Diffusion Block End

Creates unique patterns by solving the reaction and diffusion of multiple chemicals as described by its inputs and parameters.
Refract from Height

Refracts an image through a height layer.
Remap

Remaps a layer, VDB, or attribute.
Resample

Performs image scaling by changing the width, height, and pixel sizes.
Ripple Block Begin

Start of a Ripple simulation block.
Ripple Block End

End of a Ripple simulation block
SDF Adjust

Modifies the values for a Mono SDF layer.
SDF Blend

Combines two Mono SDF layers.
SDF Shape

Builds a 2D signed distance field of a selected shape.
SDF to Mono

Converts an SDF field to a mono image layer.
SDF to RGB

Converts an SDF field to an RGB color layer.
SOP Import

Imports SOP geometry into Copernicus.
SOP Invoke

Invokes a compiled SOP block on the inputs.
SOP Invoke Graph

Invokes a geometry SOP graph on the inputs.
Scatter Shapes

Scatters input stamps across the image using randomization controls.
Scatter on Curves

Scatters input stamps along an input curve using randomization controls.
Segment by Connectivity

Segment a layer into connected components.
Segment by Value

Segment a mono layer into bands of similar value.
Sequence

Sequences parts of one or more inputs temporally.
Sequence Blend

Blends multiple layers together.
Sharpen

Sharpens an input layer to increase the definition of its edges.
Slap Comp Import

Import live layers from the Solaris Viewport.
Slope Direction

Converts a height layer into a direction layer.
Smooth Fill

Smoothly fills a region of a layer.
Solve Poisson

Solves Poisson’s equation inside a 2D boundary.
Solve Poisson Multigrid

Solves Poisson’s equation in a rectangular region using geometric multigrid.
Space Transform

Transforms positions and UV values between spaces.
Space Transform with Adjacency

Transforms a vector from world space into tangent space.
Sphere Sample

Samples a layer onto a sphere.
Stamp Points

Stamps layers from point positions.
Star Glow

Streaks the layer multiple times in different directions to create a star effect.
Stash

Stashes the input of the node on command and uses it as the node’s output.
Statistics

Outputs the average, minimum and maximum values of the input layer
Statistics by ID

Compute statistics for each ID island.
Streak Blur

Streaks an image, adding a motion blur effect.
Subnetwork

Used to organize a collection of COPs into one node.
Surface Dither

Applies a halftone dithering pattern relative to UVs.
Swirl

Twists an image layer into a spiral shape.
Switch

Selects an input layer.
Switch If Wired

Selects an input based on what is connected.
Switch by Type

Selects an output layer by the type of the inputs.
Test Geometry: Capybara

Creates a capybara, which can be used as test geometry.
Test Geometry: Otto

Creates Otto, a production quality test character.
Test Geometry: Pig Head

Creates a pig head, which can be used as test geometry.
Test Geometry: Rubber Toy

Creates a rubber toy, which can be used as test geometry.
Test Geometry: Shader Ball

Creates a shader ball, which can be used to test shaders.
Test Geometry: Squab

Creates a squab, which can be used as test geometry.
Test Geometry: Tommy

Creates a soldier, which can be used as test geometry.
Tile Pattern

Generates rectangular tiles for texture patterns.
Time Blend

Blends intraframe values for layers and VDBs.
Time Loop

Repeats input frame range to form a looping animation.
Time Pack

Combines its input at multiple times into a cable.
Time Shift

Cooks its input at a different time.
Tone Map

Applies a filmic tone mapping curve to compress a high dynamic range input into a displayable range.
Transform 2D

Transforms a layer in 2D.
Transform 3D

Transforms a layer in 3D.
Triplanar

Generates a texture by projecting X, Y, and Z textures onto the position layer.
Triplanar Hex Tile

Seamless texturing and normal mapping of triplanar projections without visible repetitions.
Triplanar UV

Generates UVs in three orthogonal projections.
Turing Patterns

Applies a filter to create Turing patterns.
Two Way Switch If Wired

Selects between two inputs based on if you wire in another input.
UDIM Pack

Combines its input at multiple UDIMs into a cable.
USD Material

Represents a USD material referenced from disk.
UV Inverse

Computes the inverse of a UV distortion map.
UV Map

Generates a UV Map.
UV Map by ID

Creates a UV Map for each connected ID island.
UV Sample

Samples an input layer using a UV layer or attribute.
UV Shape

Generates UV coordinates for common 2D shapes.
UV Transform

Transforms the values of a UV layer in 2d space.
UV to Polar

Converts Cartesian coordinate pixels to polar coordinate pixels.
UV to RGB

Combines a UV and mono layer or two attributes to create an RGB layer or attribute.
UV to RGBA

Joins two UV layers or attributes into an RGBA layer or attribute.
VDB Activate from Points

Activates leaves on a VDB according to a point cloud.
VDB Leaf Points

Creates a point for each active leaf in a VDB.
VDB Position Map

Stores in each voxel that voxel’s position.
VDB Reshape

Rebuilds a VDB to match another VDB’s topology.
VDB Visualize

Creates multi-volume visualization.
VDB Visualize Slice

Extracts a slice from a VDB as Geometry for visualization.
VDB Visualize Tree

Builds a geometry visualizing the topology of a VDB.
VDB Visualize Velocity

Traces streamers through a velocity VDB.
VDB from Layer

Sets VDB values from the closest values in a layer.
Vector Transform

Transforms values of an RGB layer, attribute, or Vector VDB in 3D space.
Vector Transform 2D

Transforms the values of a UV layer or attribute in 2D space.
Vignette

Darkens the corners of an input layer.
Visualize Velocity

Creates an RGBA Layer visualizing a 2d velocity field.
Weave

Generates a woven fabric pattern of interlacing fibers.
Wipe

Performs a wipe transition between two images.
Worley Noise

Generates Worley noise.
Worley Noise 3D

Generates Worley noise from 3D locations.
Wrangle

Runs a VEX snippet to modify layer values.
Z Composite

Composites two layers by depth.