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Comment by fabien_sanglard | Hacker News Reader

How come you decided for a coordinate system with Z pointing up instead of the traditional right hand/left hands coordinate systems ?

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Actually, Z-up coordinate systems can also be called right or left handed depending on which way Y points. :-)

But really, it was just personal preference. Way back when I was learning 3D graphics, I found it easiest to visualize Z as elevation above the XY plane. I'd also used some software that followed that convention (like trueSpace and later 3D Studio Max).

These days, I mainly work with software that tends to favor a Y-up convention by default.

In non-programming math contexts, it's pretty standard for Z to point up. I have no idea why, as it seems to me like the typical way it works in graphics programming is the more obvious extension of 2D plotting into 3D.

As far as I know, in the CAD world Z is typically up/down. It makes sense if you look at the scene from above, like an architect a floor plan - world-space X and Y map to screen-space X and Y, and Z is then the depth. In a 3D virtual world, on the other hand, the perspective is usually of a person embedded in the world, in which case "Y is up" is more intuitive.

OK, thinking about the architecture angle finally made it click for me.

It makes sense if you think of the X and Y axis as being drawn on paper, which usually lies flat on the desk.

Sort of, kind of, but it's a stretch. "Up and down" on a page are not oriented according to gravity, but according to the top and bottom of the page. If you say "Well, we'll make the z-axis vertical because vertical is perpendicular to the plane of the desk, and that's depth", and then you put the z-axis toward the top of the page, you're using two completely different definitions of "vertical" in the same sentence.

When I took Calculus III, Z was up. When I took Engineering Physics the same semester, Y was up.

According to legend, this is why the Math and Physics departments hate each other.

With the right rotation, any direction can be pointing "up".

So the difference between Math and Physics can be described as a single rotation matrix?

I thought it was coming from the fact Nobel's wife had an affair with a mathematician. Thus explaining why there is no Nobel Price for Mathematics.

There are several reasons to believe that that urban legend isn't true. One of them being that Nobel was never married.

I always use Z for up/down even though I'm a programmer. For some reason I just find it easier to reason about. In fairness, my first forays into 3D were extending a 2D top-down game with an "altitude".

I'm a game programmer, and I have an answer for my preference of Z being up: I want positive values going into the screen (away from the viewer) but I also want a right handed coordinate system (mostly because physics become more intuitive - especially wrt torque).

X is almost always to the right, so this gives me Y and Z to work with. To satisfy both the positive values into the screen and right handedness I need either Z forward and Y down or Y forward and Z up. Since most of the time you draw a graph with an axis going up rather than down, that settles it.

It's entirely arbitrary in the end, a single matrix will fix any dispute you have amongst peers.

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