Ellipse from arbitrary pair of vectors
- Ryan Hirst
The axes are continuous under transformation: Drag points A, B. The vector u1 will not flip from side to side, but changes smoothly. When is this condition violated? The axes moves briskly when the figure approaches a circle. And in fact this transformation is undefined for |a| = |b|. For example, try typing SetValue[A, O + prp (B-O)]. (I use a matrix to rotate vectors 90° counterclockwise. ) Slumberland will address this shortly. To preserve continuity, there is a correct answer: preserve the last good directions of u1, u2, whenever the transformation is undefined. If continuity does not matter, the choice may be arbitrary. Is that all? No. I say, we can still bring about an instantaneous rotation of the axes by 90°. How? In context, this may or may not be descriptive of the problem. Time to define the limit cases.