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Given two ellipsoids, we show that their characteristic equation has at least two negative roots and that the ellipsoids are separated by a plane if and only if their characteristic equation has two distinct positive roots. Furthermore, the ellipsoids touch each other externally if and only if the characteristic equation has a positive double root. An… (More)

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discrim-inant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number… (More)

Advances in medical and surgical care of the high-risk neonate have led to increased survival. A significant number of these neonates suffer from neurodevelopmental delays and failure in school. The focus of clinical research has shifted to understanding events contributing to neurological morbidity in these patients. Assessing changes in cerebral… (More)

We present a simple, accurate and efficient algorithm for collision detection among moving ellipsoids. Its efficiency is attributed to two results: (i) a simple algebraic test for the separation of two ellipsoids, and (ii) an efficient method for constructing a separating plane between two disjoint ellipsoids. Inter-frame coherence is exploited by using the… (More)

Computing the intersection curve of two quadric surfaces is an important problem in geometric computation, ranging from shape modeling in computer graphics and CAD/CAM, collision detection in robotics and computational physics, to arrangement computation in computational geometry. We present the solution to the fundamental problem of complete classification… (More)

a r t i c l e i n f o a b s t r a c t We present a method that uses signature sequences to classify the intersection curve of two quadrics (QSIC) or, equivalently, quadric pencils in PR 3 (3D real projective space), in terms of the shape, topological properties, and algebraic properties of the QSIC. Specifically, for a QSIC we consider its singularity,… (More)

Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effective filtering… (More)