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Abstract: An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P 1 ; P 2 ; P 3 ; : : : ; P k in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any perturbation of the polygons increases the overlap. Overlap minimization is modified to create a practical algorithm for compaction: starting with a non-overlapping layout in a rectangular... (Update)
Context of citations to this paper: More
...packing of general shapes is the textile industry, which seeks to optimize the use of fabric for manufacturing clothing. For example, [13] uses a global optimization technique to find a locally optimal oriented packing of complex and possibly concave polygons. Hence, we...
.... compaction of two dimensional part layouts [14] He has also generalized the compaction algorithm to allow rotations in two dimensions [17]. However, the position update algorithm we present here is not simply a three dimensional A B n Figure 3: Separating plane between bodies...
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BibTeX entry: (Update)
V. J. Milenkovic. Rotational polygon overlap minimization and compaction. Computational Geometry: Theory and Applications, 10:305--318, 1998. http://citeseer.ist.psu.edu/article/milenkovic98rotational.html More
@article{ milenkovic98rotational,
author = "Victor J. Milenkovic",
title = "Rotational polygon overlap minimization and compaction",
journal = "Computational Geometry. Theory and Applications",
volume = "10",
number = "4",
pages = "305--318",
year = "1998",
url = "citeseer.ist.psu.edu/article/milenkovic98rotational.html" }
Citations (may not include all citations):84 A Kinetic Framework for Computational Geometry (context) - Guibas, Ramshaw et al. - 1983
38 The Polygon Containment Problem (context) - Chazelle - 1983
34 Translational polygon containment and minimal enclosure usin.. - Milenkovic, Daniels - 1995
34 Translational polygon containment and minimal enclosure usin.. - Milenkovic - 1996
34 Translational Polygon Containment and Minimal Enclosure usin.. - Milenkovic, Daniels - 1997
33 Polygon placement under translation and rotation (context) - Avnaim, Boissonnat - 1988
32 Computing the intersection-depth of polyhedra - Dobkin, Hershberger et al. - 1993
22 Compaction algorithms for nonconvex polygons and their appli.. - Li - 1994
19 Containment algorithms for nonconvex polygons with applicati.. - Daniels - 1995
16 Multiple Translational Containment (context) - Milenkovic - 1997
15 Compaction and separation algorithms for nonconvex polygons .. - Li, Milenkovic - 1995
15 The complexity of compaction problem - Li, Milenkovic - 1993
12 Solution approaches to irregular nesting problems (context) - Dowsland, Dowsland - 1995
9 A polynomial solution for the potato-peeling problem (context) - Chang, Yap - 1986
7 Optimal blank nesting using simulated annealing (context) - Jain, Fenyes et al. - 1992
7 Position-based physics: simulating the motion of many highly.. - Milenkovic - 1996
6 Mathematical model and method of searching for a local extre.. (context) - Stoyan, Novozhilova et al. - 1996
6 A new algorithm for the two-polygon containment problem (context) - Grinde, Cavalier - 1996
6 Largest placement of one convex polygon inside another - Agarwal, Amenta et al. - 1996
5 parts within irregular boundaries (context) - Lamousin, Waggenspack et al. - 1996
5 Computing upper and lower bounds on textile nesting problems (context) - Heckmann, Lengauer - 1996
4 Two-stage approach for nesting in two-dimensional cutting pr.. (context) - Han, Na - 1996
4 A sliding algorithm for optimal nesting of arbitrarily shape.. (context) - Prasad, Somasundaram et al. - 1995
4 Irregular shape nesting and placing with evolutionary approa.. (context) - Bounsaythip, Maouche - 1997
4 A new technique for nesting irregular shapes based on rectan.. (context) - El-Aal - 1996
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