Largest placement of one convex polygon inside another

P. K. Agarwal; N. Amenta; M. Sharir

doi:10.1007/PL00009337

Largest placement of one convex polygon inside another

P. K. Agarwal^*
, N. Amenta
, M. Sharir

^*Corresponding author for this work

School of Computer Science and AI

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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(mn² log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn²), and that it can also be computed in O(mn² log n) time.

Original language	English
Pages (from-to)	95-104
Number of pages	10
Journal	Discrete and Computational Geometry
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/PL00009337
State	Published - Jan 1998

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Funders	Funder number
National Science Foundation	8920161

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10.1007/PL00009337

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title = "Largest placement of one convex polygon inside another",

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(mn2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn2), and that it can also be computed in O(mn2 log n) time.",

author = "Agarwal, \{P. K.\} and N. Amenta and M. Sharir",

year = "1998",

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AB - 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(mn2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn2), and that it can also be computed in O(mn2 log n) time.

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Largest placement of one convex polygon inside another

Abstract

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