Cutting a Country for Smallest Square Fit

Kreveld, Marc van; Speckmann, Bettina

doi:10.1007/3-540-36136-7_9

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…Chazelle [31] gave an algorithm to decide whether one convex polygon fits into another. Other papers dealing with polygon containment include [16,20,21,58]; applications in manufacturing, cartography and image processing are described in [41,61,62], respectively.…”

Section: Related Workmentioning

confidence: 99%

Scandinavian Thins on Top of Cake: New and Improved Algorithms for Stacking and Packing

et al. 2013

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We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure. We also give efficient algorithms to find the smallest rectangle simultaneously enclosing a given pair of convex polygons.

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Section: Related Workmentioning

confidence: 99%

Scandinavian Thins on Top of Cake: New and Improved Algorithms for Stacking and Packing

et al. 2013

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“…Kreveld and Speckmann [14] discuss the problem of cutting a simple polygon with n vertices into two pieces such that-if they reposition one piece disjoint of the other, without rotation (e.g. a map spread over two adjacent pages)-they have the minimum possible bounding square.…”

Section: Introductionmentioning

confidence: 99%

A simple method for fitting of bounding rectangle to closed regions

Chaudhuri

Samal

2007

Pattern Recognition

134

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“…This problem shows up in efficient use of fabric in cloth manufacturing [4,13,17]. Other applications are in cartography [24]. One of the basic questions that arises is: Given two simple polygons with n vertices in total, compute their Minkowski sum.…”

Section: Introductionmentioning

confidence: 99%

Approximate Unions of Lines and Minkowski Sums

Kreveld

Stappen

2004

Algorithms – ESA 2004

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We study the complexity of and algorithms to construct approximations of the union of lines and of the Minkowski sum of two simple polygons. We also study thick unions of lines and Minkowski sums, which are inflated with a small disc. Let b = D/ε be the ratio of the diameter of the region of interest and the maximum distance (or error) of the approximation. An approximate union of lines or Minkowski sum has complexity Θ(b 2 ) in the worst case. The thick union of n lines has complexity Ω(n + b 2 ) and O(n + b √ bn), and thick Minkowski sums have complexity Ω(n

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Cutting a Country for Smallest Square Fit

Cited by 7 publications

References 6 publications

Scandinavian Thins on Top of Cake: New and Improved Algorithms for Stacking and Packing

Scandinavian Thins on Top of Cake: New and Improved Algorithms for Stacking and Packing

A simple method for fitting of bounding rectangle to closed regions

Approximate Unions of Lines and Minkowski Sums

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