A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
Quisp: a computer processor for the design and display of quadric-surface bodies
Quisp: a computer processor for the design and display of quadric-surface bodies
Analysis of Quadric-Surface-Based Solid Models
IEEE Computer Graphics and Applications
Natural quadrics: projections and intersections
IBM Journal of Research and Development
Automatic parsing of degenerate quadric-surface intersections
ACM Transactions on Graphics (TOG)
A surface intersection algorithm based on loop detection
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
On the planar intersection of natural quadrics
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)
An Optimal Sensing Strategy for Recognition and Localization of 3D Natural Quadric Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Incremental Boundary Evaluation Using Inference of Edge Classifications
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Architectural Issues in Solid Modelers
IEEE Computer Graphics and Applications
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Efficient collision detection for moving ellipsoids using separating planes
Computing - Geometric modelling dagstuhl 2002
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
A robust algorithm for finding the real intersections of three quadric surfaces
Computer Aided Geometric Design
Class relationships and user extensibility in solid geometric modeling
COOTS'96 Proceedings of the 2nd conference on USENIX Conference on Object-Oriented Technologies (COOTS) - Volume 2
Rendering for an interactive 360° light field display
ACM SIGGRAPH 2007 papers
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
A robust algorithm for finding the real intersections of three quadric surfaces
Computer Aided Geometric Design
A reliable extended octree representation of CSG objects with an adaptive subdivision depth
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Multisensory learning cues using analytical collision detection between a needle and a tube
HAPTICS'04 Proceedings of the 12th international conference on Haptic interfaces for virtual environment and teleoperator systems
Topological classification of non-degenerate intersections of two ring tori
Computer Aided Geometric Design
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Quadric surfaces occur frequently in the design of discrete piece parts in mechanical CAD/CAM. Solid modeling systems based on quadric surfaces must be able to represent intersection curves parametrically and in a fashion that allows the underlying surfaces to be partitioned. An algebraic approach originally developed by Levin meets these needs but is numerically sensitive and based on solutions to fourth-degree polynomial equations. In this paper we develop geometric approaches that are robust and efficient, and do not require solutions to polynomials of degree higher than 2.