ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Matrix Polynomials, Matrix Functions and Applications

Wed 11:30–12:00, Room AV 03.12
Using the roots of a characteristic polynomial to characterize the relative positions between a sphere and a hyperboloid.
María José Pereira-Sáez (Universidade da Coruña)
Joint work with Miguel Brozos-Vázquez (Universidade da Coruña); María-José Souto-Salorio (Universidade da Coruña); Ana D. Tarrío-Tobar (Universidade da Coruña)

Contact detection is a broad problem of great interest nowadays. A simple formulation is: determining whether two or more bodies make contact at one or more points or not. We study a characteristic polynomial defined for any pair of quadrics that was used before to analyze the contact of two ellipsoids (see [1]). Analyzing its roots we can characterize the relative position between a convex body (sphere) and a non-convex body (hyperboloid) by a simple calculation and see if the two quadrics intersect, if they are tangent or if they do not touch each other.

  1. Wang, W., Wang, J., Kim, M.-S.; An algebraic condition for the separation of two ellipsoids, Computer Aided Geometric Design 18 (6) (2001), pp. 531–539.