Geometric ambiguities in boundary representations
Computer-Aided Design
Automatic parameterization of rational curves and surfaces 1: conics and conicoids
Computer-Aided Design
Geometric approaches to nonplanar quadric surface intersection curves
ACM Transactions on Graphics (TOG)
Automatic parametrization of rational curves and surfaces II: cubics and cubicoids
Computer-Aided Design
Analysis of Quadric-Surface-Based Solid Models
IEEE Computer Graphics and Applications
Parametric cubics as algebraic curves
Computer Aided Geometric Design
Geometric method of intersecting natural quadrics represented in trimmed surface form
Computer-Aided Design
Parametrizing and graphing nonsingular cubic curves
Computer-Aided Design
On computing the intersection of a pair of algebraic surfaces
Computer Aided Geometric Design
Automatic parsing of degenerate quadric-surface intersections
ACM Transactions on Graphics (TOG)
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Singular points of algebraic curves
Journal of Symbolic Computation
Projective splitting of quadric faces
Computer-Aided Design
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Using multivariate resultants to find the intersection of three quadric surfaces
ACM Transactions on Graphics (TOG)
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Graphical Models and Image Processing
Identification of inflection points and cusps on rational curves
Computer Aided Geometric Design
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
Computing real inflection points of cubic algebraic curves
Computer Aided Geometric Design
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
Efficient collision detection for moving ellipsoids using separating planes
Computing - Geometric modelling dagstuhl 2002
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
A robust algorithm for finding the real intersections of three quadric surfaces
Computer Aided Geometric Design
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Tangency of conics and quadrics
ISCGAV'06 Proceedings of the 6th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
Implicitization and parametrization of quadratic surfaces with one simple base point
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
A robust algorithm for finding the real intersections of three quadric surfaces
Computer Aided Geometric Design
Journal of Symbolic Computation
Robustly computing intersection curves of two canal surfaces with quadric decomposition
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Centroidal Voronoi Tessellation of Line Segments and Graphs
Computer Graphics Forum
Topological classification of non-degenerate intersections of two ring tori
Computer Aided Geometric Design
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Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve is computed first and the intersection curve of the two quadrics is then found by transforming the cubic curve by a rational quadratic mapping. Topological classification and parameterization of the intersection curve are achieved by invoking results from algebraic geometry on plane cubic curves.