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my units have a function that returns a position (vec3) and a facing (quaternion) for any point in time.

A position and direction is perhaps called a ray or, in some contexts, a line segment; however, neither of these sounds appropriate in this context and neither normally has a quaternion...

What better name should a compound position and facing be called?

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A distinction to make against the ray/line case is that while a ray has direction, it doesn't have an unique orientation. – Lars Viklund Sep 24 '12 at 17:08
@Tetrad yes I have the accepted answer on that linked question; I'd call it transform if I'd flattened it into a matrix. I guess I can call 'pose' transform too... – Will Sep 25 '12 at 10:00

Well, the Robotics people call it pose (position+orientation).

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It's usually called a Transform (sometimes shortened to xForm). It also usually includes scale.

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