An algebraic condition for the separation of two ellipsoids
Computer Aided Geometric Design
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
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By using several tools coming from Real Algebraic Geometry, Computer Algebra and Projective Geometry (Sturm-Habicht sequences and the classification of pencils of conics in P2(R)), a new approach for characterizing the ten relative positions of two ellipses is introduced.Each relative position is exclusively characterized by a set of equalities and inequalities depending only on the matrices defining the two considered ellipses and does not require in advance the computation or knowledge of the intersection points between them.Moreover, this characterization is specially well adapted for computionally treating the case where the considered ellipses depend on one or several parameters.