# What is an adjective for the side of a mathematically-defined thing that usually points upwards?

First, some background: A software product that I'm documenting allows the user to position things in three-dimensional space however they choose. The three-dimensional space has x, y, and z axes (or up/down, east/west, and north/sound directions, if you prefer). The things in this space have no defined size, but do have positions defined by their co-ordinates in Euclidean space, and orientations defined by two vectors: One "forward vector" that indicates the direction towards which the thing is facing, and another vector that is perpendicular to the first vector that defines the direction to the top of the thing from its center. (The direction to the top of the thing may potentially differ from the direction that is up, as a thing may occasionally be upside-down or otherwise rotated.) By knowing both vectors, the facing, pitch, and yaw of the thing can be calculated.

I need a name for the vector that points toward the top of the thing, so that I can write sentences like "The orientation of an emitter in three-dimensional space is defined by its forward and ____ vectors."

Calling it the "up vector" would be misleading, as it ceases to be up if the thing is rotated (for example) upside-down. I also thought of "anterior," but that usually means toward the front rather than toward the top. "Dorsal" could mean towards the top or towards the back, but I'd prefer to avoid that ambiguity.

Is there are word or short phrase that unambiguously means towards the top of something that has a defined top, and which would work in this context?

• Comments are not for extended discussion; this conversation has been moved to chat.
– NVZ
Commented Jul 14, 2022 at 2:56

Upward

upward (adjective) 1 : directed toward or situated in a higher place or level :

And it has a symmetry with forward. Of course, it is only upward with respect to a point of reference, and in open space upward is meaningless, but no less so than forward.

If the points as you say have no size then they are like true classical points meaning that direction and orientation would have little meaning. But since you refer to Yaw then clearly the use of the point is to track its motion in space.

Vectors for such a point would be two; one for the direction of motion, whether powered travel or drift, and another for the up-down orientation relative to either an upward lift or downward acceleration due to gravity.

If you only wish to describe the vector that points to the top of the cabin, whether it tips to one side or another, then I think calling it the normal vector, or the Normal, would be suitable. It is perpendicular both to the forward vector as well as the attitude described by your yaw.

Edit: Thank you for clarifying your meaning. Even so the forward "direction" vector is the one you indicated, where it is headed or pointing to, even if it is not in motion. The Normal, up pointing vector would still serve the purpose you describe as it points to the top of the object whether it is leaning or yawing.

• My apologies, but this is not the case. As was pointed out by another user, I was using "point" incorrectly, as points do not have orientations; I have since edited the question to no longer use that word. The two vectors in this system describe the orientation of the thing with these vectors. The thing's velocity might be in a direction unrelated to either vector, or even completely nonexistent; in any case, it is not relevant to this question. Commented Jul 13, 2022 at 4:58

I don't know the details of the space you're working in, but in 3D modeling terms what you're describing might be a normal (wikipedia), that is, a vector that is the 'up' direction from a surface. Not sure how that works as an adjective, but if I have the concept correct, maybe you could adapt your sentence.

• There's no surface, alas, so normal doesn't fit. Thanks for the answer, though. Commented Jul 12, 2022 at 23:12

It sounds to me like you are essentially using a spherical coordinate system to describe the orientation of the object, in which case the "forward" vector is essentially the azimuth, and the yet-to-be-named vector is the inclination. (You don't need a distance, since you can treat the object as always being at the origin point.)

• We are not using the kind of spherical coordinate system that you describe. If we were, it would make no sense for the second vector to be perpendicular to the first as described in the question, as in such a system the inclination is the angle between vectors rather than a vector itself, and this angle would have to vary for the system to work. Or to put it another way, a vector is a quality with both a direction and a magnitude, but inclination is an angle, which only has a magnitude and no direction. Commented Jul 15, 2022 at 4:02

The yaw axis describes a vector that points up/down relative to an object. The direction an object is pointing is defined by its pitch and yaw axes.

(from Wikipedia)

You could borrow terminology from aircraft, and use "Longitudinal" for what you were calling forward, "Lateral" for sideways, and "Vertical" for upwards. Note that for aircraft, just as in your situation, vertical doesn't necessarily mean upward in the gravitational sense; aircraft can be in any orientation with respect to the ground.