3D coordinate systems

There are many slightly different 3D coordinate systems. These coordinate systems will affect the way that things are calculated and represented. When a model is created, it could be done in one system and then when it is used by an application like a game, it could be in a completely different system. This is why it is important to know the system you are working in.

Left hand vs right hand

Let's begin our talk on coordinate systems by looking at left vs right handed, Y-Up systems. Direct-X uses a left handed system. openGL uses a right handed system.

So, why are they called what they are called....

Take your left hand, extend your fore finger and thumb so that your fore finger points up, and your thumb points to the right. Your thumb now points to positive X while your fore finger to positive Y. Now, extend your third finger, and the only way it can point is away from you (or into the screen). This is the direction of positive Z. You won't be able to make your third finger point out without doing some serious damage to yourself.

Similarly if you make your thumb on the right hand point to positive X, fore finger on right hand point to positive Y, your third finger would have to point at you (or out from screen). In a right-handed system, your third finger is now pointing in the direction of positive Z.

As you can see, between left-handed and right-handed systems, positive Y and positive X match directions, while positive Z is mirrored depending on the choice of system. This is why left-handed vs right-handed is an important choice when designing a 3D system.

Z-UP vs Y-UP

In a 3D coordinate system, the idea of "up" is purely semantic. That's to say, it does not affect objects within the coordinate system (unlike left-handed vs right-handed), it simply affects how we interpret the coordinate system.

There are two popular choices for the "up" axis. Those are Z-up and Y-up. Z-up means that the Z axis goes up and down where as Y-up means the that the Y axis goes up and down.

3DS Max is Z-up.