Orthogonal Dissection into Few Rectangles.
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| Title: | Orthogonal Dissection into Few Rectangles. |
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| Authors: | Eppstein, David1 (AUTHOR) eppstein@uci.edu |
| Source: | Discrete & Computational Geometry. Jan2025, Vol. 73 Issue 1, p129-148. 20p. |
| Subjects: | Polynomial time algorithms, Rectangles, Dissection, Rotational motion |
| Abstract: | We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 01795376 |
| DOI: | 10.1007/s00454-023-00614-w |
