Rotating Surfaces: Simplifying Sketching with Normalized Equations

[SprucerMoose]

Hi all,

I wasn't sure what section to put this under, but I was wondering if there is a simple, or at least algorithmic, process to sketching surfaces like ellipsoids, hyperboloids, saddles, etc. when they have been rotated. I seem to be able to manage (...just), with surfaces oriented to the standard x,y,z basis, but if cross terms are involved in the original expression and I construct a new expression for the surface in terms of a new orthonormal basis (where no cross terms appear), my drawings get extremely messy and all sense is lost. I find drawing a surface on a set of axis rotated in 3 dimensions quite difficult.

Any advice would be appreciated.

 

[fresh_42]

You should normalize the equations first and draw the result. You then can still re-enter the old coordinates and rotate then.