X,Y,Z -> up, down, left, right, forward, backward - conventions?[Edited to fix typo]

What are some conventions for relating X,Y,Z coordinates to human descriptive terms like up, down, left, right, forward, and backward?

I looked around a little and found conventions relating to drawing 2D and 3D graphs, and to MRI image discussion and other medical imaging, and to CAD systems, and to computer graphics. I also found discussions of righthanded and lefthanded systems, which relate more specifically to which direction along each axis is the larger-valued direction. It seems to me that in most fields people expect a Z axis to be vertical with larger values upward, but don’t know whether X goes left to right and Y goes forward - backward or the other way round, with the exception that 3D graphs generally make X rightward, Y upward, and Z “into the screen”, the screen itself being vertical.

I have a project to do involving the description of a space in which somebody will build a machine. The space is part of a building, and I’d think architectural or construction conventions (if there are any) would apply. The machine would be designed with a solid modeling package and that package’s conventions would apply (and I know about these).

Of course, one can do the internal computations in any arbitrary coordinate system, even nonorthagonal and nonlinear and noncartesian ones. But the interesting question keeps coming up of what conventions there might be out there, and whever I learn lots about conventions late in a project I find I have started with an unconventional system that becomes unwelcome extra baggage, so I thought I’d ask.

Thanks to anybody who feels like chipping in!

I’d say positive values for X to the right, Y forward, and Z up.

In civil engineering drafting, at least with use of AutoCAD, in 2 dimensions X is left-right (positive rightward, negative leftward) and Y is up-down (positive up, negative down). When you go to 3 dimensions, this is flopped down (like a table top in front of you) so that X is still right-left, Y is into and out of the screen and Z is up and down.

The 2 dimension labeling is the same as I have always seen it with graphs in math. The flop down effect for the 3-D effect confused me at first with Z direction now, at least on the screen, appearing to be up-down where that was previously the direction represented by the Y axis.

Right-hand vs. left-hand is the most important issue. I’d say right-hand is much more common.

Right is usually positive for one of the axes. If Z is up and X is right, and if it’s a right-hand system, then Y is into the paper (away from the observer).

For something that’s roughly rotationally symmetric (e.g. cylindrical), Z is usually the axis of symmetry (length direction of the cylinder). This carries over to optics as well, the light (at least initially) travels in the +Z direction. X and Y are therefore parallel to the surface of the lens/mirror.

Note: I edited the thread title to fix a typo.

Colibri
General Questions Moderator

On measuring devices that do geometrical computations, I’ve found the usual default arrangement is this.

Going up is a positive movement of the device for the Z axis.
Going to the right is a positive movement for the X axis.
Going away from you is a positive movement for the Y axis.

You can usually change the device to do it differently in a few steps.

Once you start defining planes and lines for alignment, the order in which datum points occur will affect the positive directions of the individual axises.

I work in CGI all the time, and it seems like the XYZ conventions in 3D package applications like Maya, Cinema 4D and such are:

X = positive, Right; negative, Left. (red axis)
Y = positive, Up; negative, Down (green axis)
Z = positive backward, negative forward. (blue axis)

All this from an absolute zero point.

More or less everyone can agree that if you draw a pair of axes on a sheet of paper (x axis horizontal, y axis vertical) then the positive z direction ought to be coming straight out of the page. This is sometimes referred to as the right handed orientation for the coordinate axes. If you hold your right hand flat with your fingers pointing in the positive x direction and your palm in the positive y direction your thumb will point in the positive z direction.

This orientation has been suggested by all of the previous posters.

If you change any one direction (or all three directions simultaneously) you will have the opposite oientation. This is equivalent to looking at your original setup in the mirror. It will line up with your left hand (fingers, palm and thumb pointing in the positive x, y, and z directions, respectively).

When I was in high school my AP Physics prof was a bit of an odd man. He had this thing where he would describe right/left hand rules in terms of ninjas. That is, if a ninja were to attack you his probable course of action would be to poke you in the throat with his extended fingers, slap you in the face with his palm dagger and then gouge out your eyes with his thumb. I was more or less on board with all of this except for the palm dagger bit.

You know, a palm dagger. It’s a big spike that extends perpendicularly from your palm so that when you get into a ninja-girl-fight with your archnemesis you’ll really be throwing around some firepower.

Here are some coordinate frames used outside of buildings. East-North-Up is common for surface navigation, and North-East-Down is common for air navigation. Unless you’re doing large scale CAD architecture, I doubt either of these would be in widespread use.