Single words to differentiate direction relative to point and direction of motion

I am writing a game engine where I have an identifier built up of multiple words, in the format `average-team-attribute`, e.g. `median-red-distance`. There is only really space for a single word in each category.

I have two attributes that I need to disambiguate. The direction that the average position is relative to the observer's direction (relative or egocentric direction) and the average direction in which the team is moving (assuming a stationary observer).

Example sentences:

Their [motion direction] is perpendicular to ours.

The average [positional direction] seems to be to the left.

What single words can I put here?

• You could say that (relative to us) they are at a heading of roughly 90. TheIr bearing is perpendicular to ours.
– Jim
Apr 4, 2018 at 6:14

One possibility is to use acronyms for the corresponding mathematical terms.

What you call 'motion direction' is in differential geometry called tangent unit vector, denoted T (see e.g. here). Another name for it that anyone who knows the relevant math would understand might be normalized velocity (or perhaps unit velocity). To emphasize the vectorial nature, instead of 'velocity' one may say 'velocity vector', although this is, strictly speaking, redundant.

What you call 'positional direction' is normalized displacement or unit displacement (again, for emphasis you may attach 'vector' at the end, though it is redundant). I am not aware of a standard name for it, but the notation for it would definitely be r with a caret on top of it, or possibly d with a caret on top of it. Unfortunately, I don't know how to typeset these symbols here, but, for comparison, here is what u with a caret on top of it looks like: û.

So how about 'TUV' ('tanget unit vector') for 'motion direction', and 'DUV' ('displacement unit vector') for 'positional direction'?

• Maybe... This is almost correct, but falls short in three aspects: a vector has a magnitude (which I'll ignore because it's probably 1 or otherwise irrelevant to the meaning - unit seems to imply this); the value won't be provided in vector format, which could cause confusion; and the order of the words in the name seem to vary across websites I've found (e.g. Unit Tangent Vector) so I suspect that these are not well known or well used acronyms (so I might as well invent my own acronyms). This is the best so far, though, so I might end up using it. Apr 2, 2018 at 19:35
• @wizzwizz4 As far as the magnitude: yes, that is precisely the point. Both 'unit' and 'normalized' imply that the vectors in question have unit magnitude. Unit vectors in general are used as 'pure directions' in geometry. If you are willing to ignore the magnitude completely, though, then the words you want are velocity and displacement. Apr 2, 2018 at 19:56
• @wizzwizz4 As far as unit tangent vector vs. tangent unit vector, yes, I suppose both are used in the literature. However, they always refer to one and the same object. The reason is that it does not matter if you first find a tangent vector, then normalize it (to unit length) , or if you first consider all unit vectors and isolate the one that is tangent to the curve at the point of interest and points in the direction of increasing curve parameter ('time'). Apr 2, 2018 at 19:58
• @wizzwizz4 As far as the value not being provided in the vector format... as long as the unit vector can be reconstructed from the available data, I would think it's fine. Apr 2, 2018 at 20:00
• I think 'vector' , in its more symbolic meaning, would work only from relative positions from the starting place of what is described itself, not the relative direction one entity is taking relative to the position of another. But, see my edits to my other answer (not saying my answer is correct though ) Apr 2, 2018 at 20:20

trajectory and distance are possibilities (however this is a qualified answer, I believe helpful in terms of a English word a users would likely understand was addressing what you ask for but not necessarily precise in any science orientated way)

I think you should use two words for clarity like Opponent Trajectory and Opponent Distance (as distance really is key in a users mind .. or if the player has multiple ships it would be enemy 1 distance from ship one ... (ok -getting away from english there)

Edit: internally, without going into computing, you are almost certainly going to want to track any entities speed in each direction like (dx, dy, and dz(if three dimensional)) as well as the entities absolute position x, y, and z - although, there are choices there too. You might have an array of enemy options each with their hahsed or object x, y, and z locations and x, y, and z speeds)

"Opponent Trajectory" or "Opponent Distance" (or Enemy ) might word better for the user however they would likely be computed values with multiple values needed to be presented or used to give the player a description they could understand to the degree of precision you choose to give.

How you would tell an player in a human readable way what the opponent trajectory is it problematic. Certainly you could subtract your X, Y, and Z speed from each of those for them and present relative speed in each direction but I don't think many players could grok both and x, y, and z position and relative difference in speed in a meaningful way.

With enough computations and array of best fits you might come up with ways of letting them know if the ship is getting closer or outwards to your trajectory and which direction on the horizontal plain from their trajectory the other ship is traveling by a clock point (i.e. 2 o'clock would be from the ne if you were flying at a constant altitude but also 2 o'clock in any 3d environment flying in a straight line .. but that would also require an 'above' or 'below" ... and it would be rough to use simple words to know if they were closing on your path or closing on your present location etc)

Still, I think "trajectory" is a good human description of that relative direction of travel even if it would be far from a single value unless you had a list of approximations ( "Foward and Outbound at 2'Oclock", "Closing From Behind and Below to Intercept") .. I am sure there are some flaws in those but .. again the word might work even though it wouldn't likely be a data store itself.

• A trajectory is a path... which implies direction and speed are known, as well as the force. That doesn't quote work, unfortunately. Offset has the same problem; it's distance and direction so it's still ambiguous. Apr 2, 2018 at 18:51
• @wizzwizz4 yeah, I hastely wrote it up and while out realized that the variable name would be useless or innacurate . You certainly need an X and Y speed as well as an X and Y location. Internally the "trajectory" must really be speed. It could however be array data with the first element being x speed and the second being y speed (and third being z speed) and ... well objects, arrays etc .. we shouldn't get off into computing but yeah, regardless I am correcting or deleting my answer Apr 2, 2018 at 19:41
• @wizzwizz4 also removed "offset" entirely as that would be more of a computational stage that never really got stored itself - and you would have the UI perhaps show a negative value on an horizontal axis as "left" and a postive number "right" etc. Internally only position of each would be stored. Apr 2, 2018 at 20:25
• These aren't variable names; I don't want to go into details because I haven't finished the prototype yet, but this is essentially a transformed view that is plugged into something else by the user, who won't directly use the values. These are the internal names, but I want them to be descriptive because I don't want a `T_PAAMAYIM_NEKUDOTAYIM`. It will internally be stored as x, y, z but that's not too relevant to this ELU question. Apr 2, 2018 at 22:10
• @wizzwizz4 I'm not sure why you say that trajectory implies that speed and force need be known. All that it implies is that the geometry is known, e.g. that it is a line, or a parabola, or what have you; see e.g. here. Apr 2, 2018 at 22:25

"The direction that the average position is relative to the observer's direction (relative or egocentric direction) and the average direction in which the team is moving (assuming a stationary observer)."

Here you're purely talking about direction, not distances, so you are talking about attitude or rotations. Suggestions of "vector" don't match your description, because vectors have a magnitude, and directions don't or at least that's not the point. A direction can be described by a vector (usually normalised to a unit vector, which does have a magnitude), but that's not the point of a direction, it can also be a rotation matrix or quaternion.

Usually when doing this sort of stuff you use "world" or "absolute" compared to "relative" or "local".

If you attach a sword mesh to a knight mesh, and it's transformed to point 90 degrees upward, the sword transformation is its local transformation relative to its parent's transformation, which may be the knight's world transformation. "Absolute" may be used for "world", depending. Also, I noticed you used the term egocentric. Another concept that might be helpful is parent and child. An object's local/relative transformation relative to its parent, for example.

If you look at any game engine SDK/editor, or 3D design program they all use these terms for differentiating the reference point of their transformation. This is from my understanding of your question that it's referring to direction, not position or movement.