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User's Guide ‐ Rotation Pivot
Source Level Editor 2.104
The regular way a selection rotates is around the center of its bounding box; in some cases, particularly when trying to precisely align model props, it is desirable to use the pivot - such as when aligning doors, furniture, levers, vehicles, etc.

It can be turned on and off by using the toolbar button with a red "P" and a yellow arrow (seen above), using the hotkey Alt + R, or through Map->Use Rotation Pivot.

When the Pivot is enabled, it will render in 2D Views as a crossed circle.
When using the transform selection mode in 3D Views (toggled by pressing X), the Pivot renders as a red sphere.
It starts at 0, 0, 0 XYZ coordinates and can be moved with the left mouse button, or quickly moved to the center of the selection by using the right mouse button context menu and selecting Center Rotation Pivot or through Tools->Center Rotation Pivot, and then adjusted with the mouse.

Note that the Pivot does not stay with the selection if you move it! It is defined universally for all selected objects, and needs to be moved each time you want to update it.
The result of rotating the model while using the Pivot.
Without it, it would rotate around the bounds center.