An algebraic condition for the separation of two ellipsoids
Computer Aided Geometric Design
Classifying the Nonsingular Intersection Curve of Two Quadric Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
Journal of Symbolic Computation
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We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently the type of the real intersection. This classification is at the core of the design of the algorithms, presented in Part III, for computing, in all cases of singular intersection, a near-optimal parameterization with polynomial functions, that is a parameterization in projective space whose coordinate functions are polynomial and such that the number of distinct square roots appearing in the coefficients is at most one away from the minimum.