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Largest Placement of One Convex Polygon inside Another (1995)
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| Venue: | Geom |
| Citations: | 12 - 3 self |
BibTeX
@ARTICLE{Agarwal95largestplacement,
author = {Pankaj K. Agarwal and Nina Amenta and Micha Sharir},
title = {Largest Placement of One Convex Polygon inside Another},
journal = {Geom},
year = {1995},
volume = {19},
pages = {95--104}
}
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Abstract
We show that the largest similar copy of a convex polygon P with m edges inside a convex polygon Q with n edges can be computed in O(mn 2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn 2 ), and that it can also be computed in O(mn 2 log n) time. Let P be a convex polygon with m edges and Q a convex polygon with n edges. Our goal is to find the largest similar copy of P inside Q (allowing translation, rotation, and scaling of P ); see Figure 1. A restricted version of this problem, in which we just determine whether P can be placed inside Q without scaling, was solved by Chazelle [4], in O(mn 2 ) time. See also [1, 6, 12] for other approaches to the more general problem, in which Q is an arbitrary polygonal region. (We remark that the complexity of the algorithms for the general case is considerably higher, about O(m 2 n 2 ) in [1], O(m 3 n 2 ) in [12], and O(m 4 n 2 ) in [6].) Problems concernin...
