Geometry Principal Components Node

The Geometry Principal Components node performs a Principal Component Analysis (PCA) on a field of positions.

PCA analyzes how the positions are distributed, finding the center of the data along with the orthogonal axes that best describe its orientation and shape. The resulting axes are ordered by how much the data varies along each direction, from greatest to least.

This is useful for determining the dominant orientation of geometry, aligning objects to point clouds, generating local coordinate systems, or measuring the extent of a distribution.

Inputs

Geometry

Geometry containing the points to analyze.

All geometry component types except volumes are supported.

Position

Position values used in the analysis.

Outputs

Group Center

Center of the analyzed group.

Rotation

Rotation whose local axes correspond to the principal axes of the data.

Principal Components

Variance of the data along each principal axis.

Larger values indicate greater spread along the corresponding axis.

Principal Axes

Longest Axis

Unit vector corresponding to the direction of greatest variance.

Intermediate Axis

Unit vector corresponding to the direction of intermediate variance.

Together with the other axes, it forms a right-handed orthogonal basis.

Shortest Axis

Unit vector corresponding to the direction of least variance.