ByCoordinateSystems (i.e. the Tekla API method)? AlignCoordinateSystem (the AutoCAD .net API method)? What are they? What do they mean?

What problem does it solve?

Suppose I say to someone:

• The treasure is located at (0,0,0).

That is very good. Except (0,0,0) is using my coordinate system. And that only makes sense to me. How do I tell someone else where the treasure is using THEIR coordinate system.

That is where a change of basis operation comes in - or if you are using Tekla a ByCoordinateSystems matrix transformation or a AlignCoordinateSystem if you are using AutoCAD.

How would this be done?

By aligning coordinate systems.

But it can be confusing. Here’s how I think about it.

• We transform a point in that makes sense in the first coordinate system, into another point that makes sense in another coordinate system. But BOTH POINTS ARE THE SAME. They just have different ways of being referenced!

Consider both examples: