Geometric approaches to nonplanar quadric surface intersection curves
ACM Transactions on Graphics (TOG)
Blending quadric surfaces with quadric and cubic surfaces
SCG '87 Proceedings of the third annual symposium on Computational geometry
Loop detection in surface patch intersections
Computer Aided Geometric Design
Geometric method of intersecting natural quadrics represented in trimmed surface form
Computer-Aided Design
On computing the intersection of a pair of algebraic surfaces
Computer Aided Geometric Design
Natural quadrics: projections and intersections
IBM Journal of Research and Development
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Automatic parsing of degenerate quadric-surface intersections
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Cyclides in computer aided geometric design
Computer Aided Geometric Design
On cyclides in geometric modeling
Computer Aided Geometric Design
Intersection of two lines in three-space
Graphics gems
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
The virtues of cyclides in CAGD
Mathematical methods in computer aided geometric design II
Planar intersection, common inscribed sphere and Dupin blending cyclides
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Planar intersection and blending of natural quadrics
Planar intersection and blending of natural quadrics
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
Using Tangent Balls to Find Plane Sections of Natural Quadrics
IEEE Computer Graphics and Applications
Dupin Cyclides as Blending Surfaces Cones
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
A novel algorithm for computing intersections of two surfaces of revolution
Geometric modeling
Intersecting quadrics: an efficient and exact implementation
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
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
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
Circles in torus-torus intersections
Journal of Computational and Applied Mathematics
Rational fixed radius rolling ball blends between natural quadrics
Computer Aided Geometric Design
Communication: On families of quadratic surfaces having fixed intersections with two hyperplanes
Discrete Applied Mathematics
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In general, two quadric surface intersect in a space quartic curve. However, the intersection frequently degenerates to a collection of plane curves. Degenerate cases are frequent in geometric/solid modeling because degeneracies are often required by design. Their detection is important because degenerate intersections can be computed more easily and allow simpler treatment of important problems. In this paper, we investigate this problem for natural quadrics. Algorithms are presented to detect and compute conic intersections and linear intersections. These methods reveal the relationship between the planes of the degenerate intersections and the quadrics. Using the theory developed in the paper, we present a new and simplified proof of a necessary and sufficient condition for conic intersection. Finally, we present a simple method for determining the types of conic in a degenerate intersection without actually computing the intersection, and an enumeration of all possible conic types. Since only elementary geometric routines such as line intersection are used, all of the above algorithms are intuitive and easily implementable.