Optimal point location in a monotone subdivision
SIAM Journal on Computing
An optimal-time algorithm for slope selection
SIAM Journal on Computing
I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Separation-sensitive collision detection for convex objects
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Collision Detection for Interactive Graphics Applications
IEEE Transactions on Visualization and Computer Graphics
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Dynamically maintaining configurations in the plane (Detailed Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Space-Time Bounds for Collision Detection
Space-Time Bounds for Collision Detection
Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
The Zonotope Abstract Domain Taylor1+
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations
Electronic Notes in Theoretical Computer Science (ENTCS)
Zonotopic guaranteed state estimation for uncertain systems
Automatica (Journal of IFAC)
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Zonotopes are centrally symmetric polytopes with a very special structure: they are Minkowski sums of line segments. In this paper we propose to use zonotopes as bounding volumes for geometry in collision detection and other applications where the spatial relationship between two pieces of geometry is important. We show how to construct optimal, or approximately optimal zonotopes enclosing given set of points or other geometry. We also show how zonotopes can be used for efficient collision testing, based on their representation via their defining line segments --- without ever building their explicit description as polytopes. This implicit representation adds flexibility, power, and economy to the use of zonotopes as bounding volumes.