10.6. Apply Transformation to Geometry

Group (Subgroup)

Rotation, Scale & Transformation

Description

This Filter applies a spatial transformation – rotation, translation, scaling, or an arbitrary 4x4 matrix – to a Geometry. Both Image Geometries and node-based geometries (Vertex, Edge, Triangle, Quadrilateral, Tetrahedral, Hexahedral) are supported.

Node Geometries

For node-based geometries, the transformation modifies vertex positions only. No interpolation occurs. Multiple transformations can be applied in succession without artifacts.

Image Geometry

For Image Geometries, transformation requires re-gridding because cell positions are implicit in the grid spacing and origin. After transformation, a new grid is generated and cell data is interpolated onto it. This is governed by two extra parameters:

• Interpolation Method – how cell data values are sampled from the old grid (see below).

• Cell Attribute Matrix – which attribute matrix holds the cell data to transform.

Image Geometry Caveat: Successive Transformations

Applying multiple transformations one-at-a-time to an Image Geometry produces visible re-gridding artifacts because each intermediate step re-samples the data. The following example shows a 90-degree rotation done as a single step versus as two 45-degree steps:

Description	Image
Input Image
After single 90-degree rotation around <001>
After first 45-degree rotation
After second 45-degree rotation (artifacts visible)

The problem is that after the first 45-degree rotation, the cell centers no longer align with the new grid cells – the re-gridding has shifted them. On the second rotation, those misalignments compound.

Description	Image
Input Image
After 1st 45-degree rotation (cell centers in green)

To avoid these artifacts, combine all transformations into a single 4x4 matrix first using Combine Transformation Matrices, then apply that combined matrix as a single transformation:

Description	Image
Combined 90-degree rotation applied once

This caveat only applies to Image Geometries. Node-based geometries can have any number of transformations chained without issue.

Example Transformations (Image Geometry)

Description	Example Output Image
Input Image
45-degree rotation around <001>
2x scale in X and Y

Transformation Type

The Transformation Type parameter selects how the transformation is specified:

Value	Type	Description
0	No Transform	Identity (geometry unchanged).
1	Pre-Computed Transformation Matrix (4x4)	A 4x4 matrix supplied as a 16-element float32 Attribute Array in row-major order.
2	Manual Transformation Matrix	A 4x4 matrix typed in directly.
3	Rotation	Axis-angle: a unit vector (x, y, z) and an angle in degrees.
4	Translation	A (dx, dy, dz) translation vector in the geometry’s physical units.
5	Scale	A (sx, sy, sz) scaling vector (dimensionless multipliers).

The linear / bi-linear / tri-linear interpolation math is adapted from Purdue CS530 slides, page 36.

If Translate Geometry To Global Origin Before Transformation is enabled, the geometry is shifted so its centroid sits at (0, 0, 0) before the transformation is applied, then translated back. Use this to rotate about the geometry’s center rather than the world origin.

Interpolation Method (Image Geometry Only)

• Nearest Neighbor [0] – each output cell takes the value of the nearest input cell. Fast; preserves sharp boundaries; blocky.

• Linear (trilinear in 3D) [1] – each output cell value is interpolated from surrounding input cells. Smoother; may blur sharp features.

• No Interpolation [2] – no resampling. Use only when the transformation does not change the grid topology (e.g., integer translations that align exactly with the existing grid).

Saving the Final Transformation Matrix

Optionally, the final 4x4 transformation matrix can be saved as an Attribute Array. The output is a 16-element float32 array in row-major order:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

represents the 4x4 matrix:

1   2   3   4
5   6   7   8
9   10  11  12
13  14  15  16

Required Input Sources

• Geometry – any supported geometry; for Image Geometry workflows, typically produced by Create Image Geometry, ITK Import Image Stack, or an EBSD reader.

• Pre-Computed Transformation Matrix (only for Transformation Type 1) – typically produced by Combine Transformation Matrices.

• Cell Attribute Matrix (Image Geometry only) – the cell-level data to be re-gridded.

Input Parameter(s)

Parameter Name	Parameter Type	Parameter Notes	Description
Transformation Type	Choices		The type of transformation to perform.
Transformation Matrix	DynamicTable		The 4x4 Transformation Matrix
Rotation Axis-Angle	Vector of Float32 Values	Order=x,y,z,w (Deg)	w (w in degrees)
Translation	Vector of Float32 Values	Order=X,Y,Z	A pure translation vector
Scale	Vector of Float32 Values	Order=X,Y,Z	0>= value < 1: Shrink, value = 1: No transform, value > 1.0 enlarge
Precomputed Transformation Matrix Path	Array Selection	Allowed Types: float32	A precomputed 4x4 transformation matrix
Translate Geometry To Global Origin Before Transformation	Bool		Specifies whether to translate the geometry to (0, 0, 0), apply the transformation, and then translate the geometry back to its original origin.

Input Geometry

Parameter Name	Parameter Type	Parameter Notes	Description
Selected Geometry	Geometry Selection	Image, Rectilinear Grid, Vertex, Edge, Triangle, Quadrilateral, Tetrahedral, Hexahedral	The target geometry on which to perform the transformation

Image Geometry Resampling/Interpolation

Parameter Name	Parameter Type	Parameter Notes	Description
Resampling or Interpolation (Image Geometry Only)	Choices		Select the type of interpolation algorithm. (0)Nearest Neighbor, (1)Linear Interpolation, (3)No Interpolation
Cell Attribute Matrix (Image Geometry Only)	AttributeMatrixSelection		The path to the Cell level data that should be interpolated. Only applies when selecting an Image Geometry.

Optional Output Transform Matrix

Parameter Name	Parameter Type	Parameter Notes	Description
Save Transformation Matrix	Bool		Save the generated transform matrix as a Data Array
Transform Matrix Output Path	ArrayCreation		The output array that contains the transformation Matrix.

Example Pipelines

• Pipelines/SimplnxCore/Examples/apply_transformation_basic.d3dpipeline

• Pipelines/SimplnxCore/Examples/apply_transformation_image.d3dpipeline

• Pipelines/SimplnxCore/Examples/apply_transformation_node.d3dpipeline

License & Copyright

Please see the description file distributed with this plugin.

DREAM3D-NX Help

If you need help, need to file a bug report or want to request a new feature, please head over to the DREAM3DNX-Issues GitHub site where the community of DREAM3D-NX users can help answer your questions.