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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 dimesions quite difficult.

Any advice would be appreciated.