Algorithms for computer algebra
Algorithms for computer algebra
Modern computer algebra
Bounding ellipsoids for ray-fractal intersection
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
An algebraic condition for the separation of two ellipsoids
Computer Aided Geometric Design
Obstacle Collision Detection Using Best Ellipsoid Fit
Journal of Intelligent and Robotic Systems
Efficient collision detection for moving ellipsoids using separating planes
Computing - Geometric modelling dagstuhl 2002
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Uniqueness results for minimal enclosing ellipsoids
Computer Aided Geometric Design
Real algebraic numbers and polynomial systems of small degree
Theoretical Computer Science
Continuous Collision Detection for Ellipsoids
IEEE Transactions on Visualization and Computer Graphics
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
Continuous Collision Detection for Two Moving Elliptic Disks
IEEE Transactions on Robotics
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We present algebraic expressions for characterizing three configurations formed by two ellipsoids in R^3 that are relevant to collision detection: separation, external touching and overlapping. These conditions are given in terms of explicit formulae expressed by the subresultant sequence of the characteristic polynomial of the two ellipsoids and its derivative. For any two ellipsoids, the signs of these formulae can easily be evaluated to classify their configuration. Furthermore, based on these algebraic conditions, an efficient method is developed for continuous collision detection of two moving ellipsoids under arbitrary motions.