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Is there a concise, accepted term for a piece of information that describes location (translation from origin) plus orientation (angular position / attitude), but ignoring magnitude?

In a little more detail

My formal mathematical training ended with differential equations in engineering school some 10 years ago, so forgive me if I use the wrong terms here. From what I know, and the limited fruits of my Googling:

Given three fundamental geometrical aspects in n-dimensional space:

  • Location
  • Orientation
  • Magnitude

I can find terms that describe:

  • Location only: location, point, position, location vector, position vector
  • Orientation only: orientation, attitude, angular position
  • Magnitude only: magnitude, length
  • Orientation + magnitude: vector, spatial vector, geometric vector

I cannot find terms that describe:

  • Location + orientation (this is specifically what I'm looking for)
  • Location + magnitude
  • Location + magnitude + direction

The context

I'm writing a code library that's focused on describing and manipulating shapes in a two dimensional plane. Both in the code itself and in my natural language discussions of it, it would be very expedient to be able to name the location-plus-orientation of the entities. Just as in engineering it is so frequent that we need to discuss the orientation-and-magnitude of things (such as forces) that we use a single word for it: commonly just 'vector'. I'm on the verge of coming up with my own hacky portmanteau, but if there is an existing accepted term I would prefer to use that.

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  • $\begingroup$ So you mean you have an object which is sitting somewhere in space and pointing in a specific direction? This can be described using two vectors, one is the position vector which can take values in the whole of the ambient space you're working in (probably $\mathbb{R}^2$ or $\mathbb{R}^3$), and the other is the orientation vector which will be a unit vector (magnitude identical to $1$) which will take values in the sphere of the appropriate dimension. $\endgroup$
    – Dan Rust
    Aug 10, 2014 at 14:05
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    $\begingroup$ @DanielRust Yes, exactly. I'm looking for a single term--ideally a single word--that describes the two together. I've added a brief paragraph to my question explaining why this matters. $\endgroup$ Aug 10, 2014 at 14:17
  • $\begingroup$ Perhaps the word 'configuration' is suitable? It at least seems to me that you are describing points in a 'configuration space'. relevant $\endgroup$
    – Dan Rust
    Aug 10, 2014 at 14:21
  • $\begingroup$ @DanielRust That looks spot on. Post it as an answer and I'll mark it as such. $\endgroup$ Aug 10, 2014 at 14:30

2 Answers 2

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Although this term can be used in a more general setting (it's very commonly used in robotics for instance to describe the space of all possible states or, for example, a robotic arm with articulated joints) I think the word configuration would be suitable for your purposes. The wiki page on configuration spaces specifically mentions the case of the term being used when describing spaces of possible positions and orientations of rigid bodies in space. This can of course be generalised to higher/lower dimensions and also take into account other parameters if needed.

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  • $\begingroup$ That's it. The discussion of rigid bodies in $\mathbb{R}^3$ is perfectly analogous to what I'm doing in $\mathbb{R}^2$. $\endgroup$ Aug 10, 2014 at 14:37
  • $\begingroup$ Glad I could help. $\endgroup$
    – Dan Rust
    Aug 10, 2014 at 14:41
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In robotics or computer vision the term pose is generally used to describe the position and orientation of a rigid object.

Wikipedia says:

The combination of position and orientation is referred to as the pose of an object. [...] The pose can be described by means of a rotation and translation transformation which brings the object from a reference pose to the observed pose.

You could also use the term rigid transformation, to describe a transformation that contains a translation component and a rotation component, but no scale component. Although this usually refers more to the change in location than the location itself.

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