# Is there are term for location plus orientation, without magnitude?

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.

• 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. Aug 10, 2014 at 14:05
• @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. Aug 10, 2014 at 14:17
• Perhaps the word 'configuration' is suitable? It at least seems to me that you are describing points in a 'configuration space'. relevant Aug 10, 2014 at 14:21
• @DanielRust That looks spot on. Post it as an answer and I'll mark it as such. Aug 10, 2014 at 14:30

• That's it. The discussion of rigid bodies in $\mathbb{R}^3$ is perfectly analogous to what I'm doing in $\mathbb{R}^2$. Aug 10, 2014 at 14:37