[b]Proposition:[/b] [i]Transform an ellipse in the form[/i] [math]\;{\small {\bf x}(t) = \cos(t) {\bf a} + \sin(t) {\bf b}}\;[/math] [i]to[/i]
[math]\;\;\;\;{\small {\bf x}_T(t) = \cos(t) {\bf u_1} + \sin(t) {\bf u_2},\;\;\;{\bf u_1}⊥ {\bf u_2}} [/math]
I have defined u1 to the major axis, and filled in the missing limit conditions from last worksheet. The transformation is now always defined. It is also continuous under manipulation except in the special case where the reference axis must pass from major to minor.
I have also bundled it up in a tool.
This oddly specific problem has a purpose...
