TY - JOUR
T1 - Rotational polygon overlap minimization and compaction
AU - Milenkovic, Victor J.
N1 - Funding Information:
Variations of the layout problem have a variety of names: nesting, packing, and so forth. In the computational geometry literature, containment refers to the task of placing k input polygons This research was funded by the Textile/Clothing Technology Corporation from funds awarded by the Alfred E Sloan Foundation, by NSF grant CCR-91-157993 and 97-12401, and by a subcontract of a National Textile Center grant to Auburn University, Department of Consumer Affairs. * http://www.cs.miami.edu.
PY - 1998/7
Y1 - 1998/7
N2 - An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1, P2, P3, . . . , Pk 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 container, plan a non-overlapping motion that diminishes the length or area of the container to a local minimum. Experiments show that both overlap minimization and compaction work well in practice and are likely to be useful in industrial applications.
AB - An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1, P2, P3, . . . , Pk 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 container, plan a non-overlapping motion that diminishes the length or area of the container to a local minimum. Experiments show that both overlap minimization and compaction work well in practice and are likely to be useful in industrial applications.
KW - Compaction
KW - Containment
KW - Layout
KW - Linear programming
KW - Minimum enclosure
KW - Packing or nesting of irregular polygons
UR - http://www.scopus.com/inward/record.url?scp=0006479544&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0006479544&partnerID=8YFLogxK
U2 - 10.1016/S0925-7721(98)00012-1
DO - 10.1016/S0925-7721(98)00012-1
M3 - Article
AN - SCOPUS:0006479544
VL - 10
SP - 305
EP - 318
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
SN - 0925-7721
IS - 4
ER -