Mapping

UV Map

2D Coordinate Remapping

This component provides a flexible way to remap pixel positions using a two‐dimensional coordinate system. The input image texture is re‐projected according to U and V coordinates, where U corresponds to the horizontal axis and V corresponds to the vertical axis.

This approach allows for controlled warping, shifting, and reorientation of images — making it a fundamental tool in both image processing and rendering workflows. Whether used for texture projection, procedural pattern design, or creative distortion effects, UV mapping enables a structured method of reshaping how pixels are distributed across the output image.

By defining how input coordinates are mapped to the output space, this UV Map Component acts as a versatile foundation for more complex mapping operations, such as tiling, layering, or non‐linear remapping.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling,
Texture Coordinates by FME,
UV Mapping on Wikipedia

UVW Map

3D Coordinate Remapping

This component extends traditional UV mapping into three dimensions, generating a UVW coordinate field where U corresponds to the horizontal axis, V to the vertical axis, and W to depth. Instead of working in only two axes, the UVW Map allows you to define and manipulate a full three‐dimensional coordinate space for texture projection and spatial mapping.

By incorporating a W axis, this component enables more complex remapping operations such as volumetric textures, layered projections, and triplanar blending. The UVW coordinate field can be rotated along all three axes and stretched or compressed independently, making it a versatile tool for procedural patterning and advanced mapping techniques.

As with UV mapping, the UVW Map operates by re‐projecting the input image into a new coordinate space, but with the additional flexibility of depth‐aware manipulation. This allows for effects and workflows that go beyond simple 2D warping, including pseudo‐3D pattern generation and multi-axis distortions.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling,
Texture Coordinates by FME,
UVW Mapping on Wikipedia

Hex Grid

Hexagonal Tiling UV

This component generates a hexagonal coordinate grid, producing a continuous tiling pattern that can be used for procedural mapping, pattern generation, or texture sampling. Unlike a square or rectangular UV layout, the hexagonal grid introduces six‐way symmetry.

Each hexagonal cell is defined within the UV coordinate space, and the number of cells is determined by the Repeat parameter, which controls tiling density along the X and Y axes. The Margin parameter adjusts the spacing between neighboring hexagons, enabling everything from tightly packed honeycomb structures to spaced, modular layouts.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling

UV to Hex Grid

Hexagonal Remapping of UV Space

This component extends the functionality of the standard Hex Grid by allowing any UV Map input to be segmented and restructured into a hexagonal coordinate layout. Rather than generating a tiling pattern from scratch, it adapts an existing UV space — regardless of how warped, scaled, or distorted it may be — and subdivides it into a field of hexagonal cells.

Each hexagon acts as a localized sampling region within the input UV space, providing a way to reinterpret complex or procedural mappings through a structured, six‐way symmetric grid. The result is a UV representation that preserves the original mapping’s topology while imposing a consistent hexagonal tessellation, ideal for generative pattern design, geometric quantization, or stylized image remapping.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling

UV Transform

2D Coordinate Transformation

Instead of remapping from scratch, the UV Transform component modifies existing UV maps by applying pivot‐based transformations within the UV coordinate space. This provides precise post‐control over how textures or procedural images are projected.

This component is particularly useful in workflows involving chained mappings or layered projections, where incremental adjustments to UV coordinates are needed to align, tile, or animate textures across multiple surfaces. Used in combination with the UV Map or UVW Map components, the UV Transform serves as a flexible intermediary step for refining complex coordinate manipulations.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling

UV Corrector

Local UV Linearization

This component corrects distorted UV maps by restoring local linearity within the UV coordinate field. Rather than globally reprojecting or re‐mapping coordinates, the UV Corrector operates locally — allowing repeated or tiled UV structures to be corrected independently within each repetition.

When UV maps are warped, stretched, or procedurally modified, their red and green gradient fields often lose linear consistency. This loss of structure results in visible artifacts during image remapping, such as warped geometry, bent textures, or uneven scaling. The UV Corrector addresses these issues by re‐linearizing the UV gradients while preserving the original spatial placement and character of the distortion.

The mathematical approach behind this component was shared by Andrei Zelenco, who defined the locally correcting UV gradients via differential analysis as:

Let the input UV map be treated as a vector‐valued function over image space:

$ƒ\left(\iota \right)=\left[\begin{array}{c}u\left(\iota \right)\\ v\left(\iota \right)\end{array}\right]$

Where $\iota$ denotes a pixel position in the image, and $u$ and $v$ correspond to the red and green channels of the UV map respectively.

The local deformation of this UV field is described by its Jacobian matrix:

$J\left(\iota \right)=\left[\begin{array}{cc}\frac{\partial u}{\partial x}& \frac{\partial u}{\partial y}\\ \frac{\partial v}{\partial x}& \frac{\partial v}{\partial y}\end{array}\right]$

This matrix captures how the UV coordinates stretch, shear, or rotate locally with respect to image space.

To correct the distortion, the UV Corrector computes the inverse of the transposed Jacobian and applies it to the original UV vector:

${ƒ}_{\mathrm{Corrected}}\left(\iota \right)=\left(J\right(\iota {)}^T{)}^{-1}·ƒ\left(\iota \right)$

This ability to restore linearity to input UV Maps while preserving the positional intent of the original UV transformation proves to be a powerful differential tool for repairing distorted UV fields rather than replacing them, enabling reversible, high‐fidelity UV workflows in complex procedural mapping pipelines.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling,
Andrei Zelenco’s YouTube Channel

UV Inverse Map

Inverse Coordinate Reconstruction

This component computes the inverse of a UV mapping: given any forward UV map that remaps pixel positions, this operator generates the complementary UV field that reverses that transformation.

Formerly, if the original UV map defines a function:

$ƒ:(x,y)\to (u,v)$

The UV Inverse Map reconstructs the inverse mapping:

${ƒ}^{-1}:(u,v)\to (x,y)$

Such that:

${ƒ}^{-1}\left(ƒ\right(x,y\left)\right)=(x,y)$

In other words, the inverse UV map returns each displaced pixel to the location from which it originated.

When applied to an image that was previously distorted via the original UV map, the resulting inverse map restores the image back to its undistorted state, minus any information that was lost in the forward transformation.

This makes the UV Inverse Map a powerful tool for workflows involving reversible warping, bidirectional mapping, UV‐based lenses, and procedural distortions that require a mathematically exact undo.

As the white color of the component suggests, this is an experimental operator and becomes unreliable with UV map inputs larger than 1024×1024.

Resources:

Download the .tox files,
Texture Coordinates and Texture Sampling