Here is yet another presentation about a VBA function that was recoded in Python.
In structural engineering, we must constantly deal with axes transformations. Mostly we have right handed coordinates (RHC), but sometimes left handed coordinates (LHC). For example, LHCs might occur when South or East map coordinates are used. Certain engineering software packages use LHC.
A few quick questions:
- How many XYZ orientations are there?
- How many RHC XYZ orientations are there?
- How many LHC XYZ orientations are there?
- Imagine the XYZ system in your head
- Label the directions as 1, 2, 3
- Label the directions as 4, 5, 6
- Now imagine transforming to .
- Let’s say (∴ 1) and (∴ 3)
- We could use the two digit notation  for the new system orientation
- There are 4 orientations starting with 1:
- : isn’t legal. and must have different directions
- : isn’t legal. and cannot be in opposite directions
- Consider then two digit orientations 2_, 3_, 4_, 5_, 6_
- For each of these we can have four orientations
- Therefore, there are 24 RHC orientations; 6 choices for times 4 choices for
- Therefore, there are 24 RHC orientations
- Then allow RHC or LHC orientations
- Therefore, there are 24 LHC orientations
- Therefore, there are 48 total orientations
This makes it almost trivial to think through the transformation desired.