Computational geometry: an introduction
Computational geometry: an introduction
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Point location in fat subdivisions
Information Processing Letters
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
Efficient and accurate collision detection for granular flow simulation
CVGIP: Graphical Models and Image Processing
Fast Collision Detection Among Multiple Moving Spheres
IEEE Transactions on Visualization and Computer Graphics
Penetration depth of two convex polytopes in 3D
Nordic Journal of Computing
Interactive Collision Detection for Molecular Graphics
Interactive Collision Detection for Molecular Graphics
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3-D Technology) (The Morgan Kaufmann Series in Interactive 3D Technology)
A multi-sphere scheme for 2D and 3D packing problems
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Nonlinear optimization to generate non-overlapping random dot patterns
Proceedings of the Winter Simulation Conference
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In this paper, we consider a collision detection problem of spheres which asks to detect all pairs of colliding spheres in a set of n spheres located in d-dimensional space. We propose a collision detection algorithm for spheres based on slab partitioning technique and a plane sweep method. We derive a theoretical upper bound on the time complexity of the algorithm. Our bound tells that if both the dimension and the maximum ratio of radii of two spheres are bounded, then our algorithm runs in O(n log n + K) time with O(n + K) space, where K denotes the number of pairs of colliding spheres.