> For the complete documentation index, see [llms.txt](https://docs.openbrim.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.openbrim.org/templates/openbrimfea/coordinate-systems-fea/coor-sys-fea.md).

# Coor. Sys. \[FEA]

Coordinate systems define local reference frames that can be assigned to nodes and elements. They allow you to define positions and orientations relative to a custom origin and rotation, rather than the global coordinate system. This is useful for skewed supports, inclined members, and structures with complex geometry.

## Properties

**Origin X:** The X coordinate of the coordinate system's origin in the global reference frame.

**Origin Y:** The Y coordinate of the coordinate system's origin in the global reference frame.

**Origin Z:** The Z coordinate of the coordinate system's origin in the global reference frame.

## Euler

Euler angles define the rotation of the local coordinate system relative to the global system using a ZYX rotation sequence (first rotate about Z, then Y, then X).

**Rotation Z (ZYX order):** The first rotation angle about the Z axis (in radians). This is applied first in the ZYX rotation sequence.

**Rotation Y (ZYX order):** The second rotation angle about the (rotated) Y axis (in radians). This is applied after the Z rotation.

**Rotation X (ZYX order):** The third rotation angle about the (rotated) X axis (in radians). This is applied last in the ZYX rotation sequence.

## Quaternion

Quaternions provide an alternative way to define the rotation of the local coordinate system. They avoid gimbal lock issues that can occur with Euler angles and are useful for arbitrary 3D orientations.

**Quaternion x:** The x component of the rotation quaternion.

**Quaternion y:** The y component of the rotation quaternion.

**Quaternion z:** The z component of the rotation quaternion.

**Quaternion w:** The w (scalar) component of the rotation quaternion. For a unit quaternion representing a valid rotation, x² + y² + z² + w² = 1.


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