Details:
Title  Metric problems for quadrics in multidimensional space  Author(s)  A. Yu. Uteshev, Marina V. Yashina  Type  Article in Journal  Abstract  Abstract Given the equations of the first and the second order manifolds in R n , we construct the distance equation, i.e. a univariate algebraic equation one of the zeros of which (generically minimal positive) coincides with the square of the distance between these manifolds. To achieve this goal we employ Elimination Theory methods. In the frame of this approach we also deduce the necessary and sufficient algebraic conditions under which the manifolds intersect and propose an algorithm for finding the coordinates of their nearest points. The case of parameter dependent manifolds is also considered.  Keywords  Ellipsoid, Quadric, Distance, Intersection of algebraic manifolds  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717114000893 
Language  English  Journal  Journal of Symbolic Computation  Volume  68, Part 1  Number  0  Pages  287  315  Year  2015  Edition  0  Translation 
No  Refereed 
No 
