Computational geometry: an introduction
Computational geometry: an introduction
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Efficient generation of k-directional assembly sequences
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The Complexity and Decidability of Separation
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Separating a Polyhedron by One Translation from a Set of Obstacles (Extended Abstract)
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
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We consider the problem of separating a collection of isothetic polygons in the plane by translating one polygon at a time to infinity. The directions of translation are the four isothetic (parallel to the axes) directions, but a particular polygon can be translated only in one of these four directions. Our algorithm detects whether a scene is separable in this sense and computes a translational ordering of the polygons. The time and space complexities of our algorithm are O(n log n) and O(n) respectively, where n is the total number of vertices of the polygons in the scene. The best previous algorithm in the plane for this problem has complexities of O(n log2 n) time and O(n log n) space.