Computational geometry: an introduction
Computational geometry: an introduction
Constraint satisfaction in logic programming
Constraint satisfaction in logic programming
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Communications of the ACM
Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Search Strategies for Rectangle Packing
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A global constraint for nesting problems
Artificial Intelligence Review
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
| Hi-index | 0.00 |
This paper deals with non-overlapping constraints between convex polytopes. Non-overlapping detection between fixed objects is a fundamental geometric primitive that arises in many applications. However from a constraint perspective it is natural to extend the previous problem to a non-overlapping constraint between two objects for which both positions are not yet fixed. A first contribution is to present theorems for convex polytopes which allow coming up with general necessary conditions for non-overlapping. These theorems can be seen as a generalization of the notion of compulsory part which was introduced in 1984 by Lahrichi and Gondran [7] for managing nonoverlapping constraint between rectangles. Finally, a second contribution is to derive from the previous theorems efficient filtering algorithms for two special cases: the non-overlapping constraint between two convex polygons as well as the non-overlapping constraint between d-dimensional boxes.