Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 17

Left-hand rule Right-hand rule

Figure 1.14. The left-hand rule and right-hand rule define which direction is considered
“positive” rotation.

axis,” how do I know which way to rotate? We need to agree between us
that one direction of rotation is the positive direction, and the other di-
rection is the negative direction. The standard way to tell which is which
in a left-handed coordinate system is called the left-hand rule. First, we
must define which way our axis “points.” Of course, the axis of rotation is
theoretically infinite in length, but we still consider it having a positive and
negative end, just like the normal cardinal axes that define our coordinate
space. The left-hand rule works like this: put your left hand in the “thumbs
up” position, with your thumb pointing towards the positive end of the axis
of rotation. Positive rotation about the axis of rotation is in the direction
that your fingers are curled. There's a corresponding rule for right-handed
coordinate spaces; both of these rules are illustrated in Figure 1.14.
As you can see, in a left-handed coordinate system, positive rotation
rotates clockwise when viewed from the positive end of the axis, and in a
right-handed coordinate system, positive rotation is counterclockwise. Ta-
ble 1.1 shows what happens when we apply this general rule to the specific
case of the cardinal axes.
Any left-handed coordinate system can be transformed into a right-
handed coordinate system, or vice versa. The simplest way to do this is
by swapping the positive and negative ends of one axis. Notice that if we