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ACM Transactions on Graphics (TOG)
Automatic parsing of degenerate quadric-surface intersections
ACM Transactions on Graphics (TOG)
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Graphical Models and Image Processing
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
An algebraic condition for the separation of two ellipsoids
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Journal of Intelligent and Robotic Systems
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
Classifying the Nonsingular Intersection Curve of Two Quadric Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
Intersecting quadrics: an efficient and exact implementation
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils
Journal of Symbolic Computation
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Journal of Symbolic Computation
Real algebraic numbers and polynomial systems of small degree
Theoretical Computer Science
An algebraic approach to continuous collision detection for ellipsoids
Computer Aided Geometric Design
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Topological classification of non-degenerate intersections of two ring tori
Computer Aided Geometric Design
Journal of Symbolic Computation
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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, reducibility, the number of its components, and the degree of each irreducible component, etc. There are in total 35 different types of non-degenerate quadric pencils. For each of the 35 types of QSICs given by these non-degenerate pencils, through a detailed study of the eigenvalue curve and the index function jump we establish a characterizing algebraic condition expressed in terms of the Segre characteristics and the signature sequence of the quadric pencil. We show how to compute a signature sequence with rational arithmetic and use it to determine the type of the intersection curve of any two quadrics which form a non-degenerate pencil. As an example of application, we discuss how to apply our results to collision detection of cones in 3D affine space.