3-D Coordinate Systems

Typically 3-D graphics applications use two types of Cartesian coordinate systems: left-handed and right-handed. In both coordinate systems, the positive x-axis points to the right, and the positive y-axis points up. You can remember which direction the positive z-axis points by pointing the fingers of either your left or right hand in the positive x-direction and curling them into the positive y-direction. The direction your thumb points, either toward or away from you, is the direction that the positive z-axis points for that coordinate system. The following illustration shows these two coordinate systems.

If you use a left-handed coordinate system and you are porting an application that is based on a right-handed coordinate system, you must make two changes to the data.

Flip the order of triangle vertices so that the system traverses them clockwise from the front. In other words, if the vertices are v0, v1, v2, pass them as v0, v2, v1.

Although left-handed and right-handed coordinates are the most common systems, there is a variety of other coordinate systems used in 3-D software. For example, it is not unusual for 3-D modeling applications to use a coordinate system in which the y-axis points toward or away from the viewer, and the z-axis points up. In this case, right-handedness is defined as any positive axis (x, y, or z) pointing toward the viewer. Left-handedness is defined as any positive axis (x, y, or z) pointing away from the viewer. If you are porting a left-handed modeling application where the z-axis points up, you must do a rotation on all the vertex data in addition to the previous steps.

Here an example that shows that the backside of the cube is smaller than the front, it uses a left-handed coordinate system.