Find the projection of point P in R^n on the ellipsoid
E = { x = x0 + U*(z.*radii) : |z| = 1 }, where U is orthogonal matrix of the orientation of E, radii are the axis lengths, and x0 is the center.
Or on generalized conic E = { x : x'*A*x + b'*x + c = 0 }.
The projection is the minimization problem:
min | x - P | (or max | x - P|) for x in E.
Method: solve the Euler Lagrange equation with respect to the Lagrange multiplier, which can be written as polynomial equation (from an idea by Roger Stafford) |