Hi Brian,

> So the x-axis and y-axis direction vectors used to create the
> new frame would be (or could be) in world coordinate frame.

Yup, normally those direction vectors are in world coordinates. The origin is also in world coordinates - the whole package of data gives the position and orientation of the frame's coordinate system.


> A new y-axis, parallel to the world coordinate y-axis would
> have the same vector direction, (0,1,0).

Yup that's correct.


> The new x-axis vector direction can be calculated from
> the two points, mathematically, or with vectorMath...

Yup, but the x-axis vector should be one that is at a 90 degree angle to the y axis vector. But it can be pivoted around the x-axis, like for example here in red are different possible x-axis lines that would work with the given green y axis:



- Michael

Thank you Michael.
Should have enough now to finish a catenary curve script hanging from two points in 3D, even with different z values, with
gravity in the -y direction. There is plenty of code on the internet.
Yes, the new x-axis "rotates" about the new y-axis, to "zero out" the z values.

Just figured out that a minus sign "-" is not the same as a dash "–".

So cut and paste of formulas with dashes for minus signs, from Microsoft Word to Notepad++, creates parse errors in javascript.