Theoretical Computer Science
Orthogonal polyhedra as geometric bounds in constructive solid geometry
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Hybrid Systems II
Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Proceedings of the International Workshop on Hybrid and Real-Time Systems
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Verifying Safety Properties of Differential Equations
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Approximation Techniques for Non-linear Problems with Continuum of Solutions
Proceedings of the 5th International Symposium on Abstraction, Reformulation and Approximation
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Hybrid Control of a Truck and Trailer Vehicle
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Approximating Continuous Systems by Timed Automata
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Generating and Analyzing Symbolic Traces of Simulink/Stateflow Models
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
A geometric approach to the problem of unique decomposition of processes
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Reconstructing orthogonal polyhedra from putative vertex sets
Computational Geometry: Theory and Applications
The two variable per inequality abstract domain
Higher-Order and Symbolic Computation
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Choice of directions for the approximation of reachable sets for hybrid systems
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Automata-Based symbolic representations of polyhedra
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Data Structures for Higher-Dimensional Rectilinear Packing
INFORMS Journal on Computing
Specification-guided controller synthesis for linear systems and safe linear-time temporal logic
Proceedings of the 16th international conference on Hybrid systems: computation and control
Skeletal representations of orthogonal shapes
Graphical Models
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In this paper we investigate orthogonal polyhedra, i.e. polyhedra which are finite unions of full-dimensional hyper-rectangles. We define representation schemes for these polyhedra based on their vertices, and show that these compact representation schemes are canonical for all (convex and non-convex) polyhedra in any dimension. We then develop efficient algorithms for membership, face-detection and Boolean operations for these representations.