Metric problems for algebraic manifolds: Analytical approach

The problem of distance evaluation from a point to an algebraic manifold in R
ⁿ
is treated in the framework of elimination of variables procedure applied for the algebraic equation system generated by Lagrange's method. The resulting univariate distance equation possesses a zero set coinciding with that of critical values of the squared distance function. We discuss also the problem of nearest point coordinates evaluation. For the case of a quadric manifold, the distance approximation formulas are suggested in the form of analytical expressions with respect to the coefficients of the manifold.