Machining centers that have fixture offsets (also called coordinate system shifting) allow the user to specify the position of the program zero point within offsets, keeping the assignment of program zero separate from the program.

Zero Points allow parts to be programmed without regard for their position on the machine or to machine more than one part on the machine without re-coding all the points.

It is common for six zero points to be available, but this varies from control to control. The commands to activate them are usually G54, G55, G56, G57, G58 and G59. The X, Y and Z values in the Zero Point become the new zero position when the command G5x is used and all axis movement is now relevant to this new position until either another zero point is activated or the zero point is cancelled with a G53 command.
The G53 command makes all axis moves relative to Machine Zero. This is used for tool changing and work piece changing.