An algebraic approach to continuous collision detection for ellipsoids

DOI10.1016/j.cagd.2011.01.004zbMath1233.65020OpenAlexW2025591272MaRDI QIDQ543838

Xiaohong Jia, Yi-King Choi, Wenping Wang, Mourrain, Bernard

Publication date: 17 June 2011

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-00646511/file/CCD.3.0.pdf

zbMATH Keywords

overlappingnumerical examplesseparationbounding volumescontinuous collision detectionexternal touchingfree-from moving objectsminimal bounding ellipsoid moving ellipsoids

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (9)

Comparison of methods computing the distance between two ellipsoids ⋮ Random generation of periodic hard ellipsoids based on molecular dynamics: a computationally-efficient algorithm ⋮ Topological classification of the intersection curves of two quadrics using a set of discriminants ⋮ Computing the intersections of three conics according to their Jacobian curve ⋮ Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space ⋮ Algorithms for determining relative position between spheroids and hyperboloids with one sheet ⋮ Classification of the relative positions between a small ellipsoid and an elliptic paraboloid ⋮ Solving the interference problem for ellipses and ellipsoids: new formulae ⋮ Contact detection between a small ellipsoid and another quadric

Cites Work

• Using signature sequences to classify intersection curves of two quadrics
• Obstacle collision detection using best ellipsoid fit
• Uniqueness results for minimal enclosing ellipsoids
• Minimum-volume enclosing ellipsoids and core sets
• Real algebraic numbers and polynomial systems of small degree
• On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
• Division-free computation of subresultants using Bezout matrices
• Algorithms in real algebraic geometry
• An algebraic condition for the separation of two ellipsoids
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