While I'm not a true mathimatician, I can tell you something about floating point math from a programming standpoint.

1) Most ll CMM software uses double precision floating point numbers to do their calcs. This means that the stored data values have a 15 digit mantissa (ie - 1.23456789012345 E 01). If my memory serves me, this is a 8-byte number (or 6?). The only other option is single precision which has a 7 digit mantissa (ie - 1.234567 E 01 :4 bytes). If you used single precision numbers you would have stack-up errors during complex multi-point calculations.

2) Most all CMM software uses a "Transformation Matrix" to establish a given Defined Coordinate System. The TM for Machine Coordinates is:
1 0 0
0 1 0
0 0 1
Any alignment changes to the MCS alter the TM. This is how a CMM can store several Defined Coordinate Systems, by storing multiple TM's.

A clever person can edit, store or save these TM's because they are usually written to the Hard Disk as part of the setup file.

3) If you are selecting an IBM PC to run CMM software, look for a machine with a FAST Math-Coprocessor system, because floating point math is done by the coprocessor. The Coprocessor is built into all 80486DX, Pentium, PII,and PIII chips. The PII and PIII have the best coprocessors built in them. The new AMD chip (K7-600?), has the FASTEST coprocessor ever and would be a good choice for CMM software.
If you ask a more specific question I will try to focus in on the specific issue.

Hope I didn't overexplain...

Pat McSwain
Quality Inspection