TY - GEN

T1 - Compaction algorithm for non-convex polygons and its application

AU - Li, Zhenyu

AU - Milenkovic, Victor

PY - 1993/12/1

Y1 - 1993/12/1

N2 - Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

AB - Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

UR - http://www.scopus.com/inward/record.url?scp=0027830221&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:0027830221

SN - 0897915828

T3 - Proceedings of the 9th Annual Symposium on Computational Geometry

SP - 153

EP - 162

BT - Proceedings of the 9th Annual Symposium on Computational Geometry

A2 - Anon, null

PB - Publ by ACM

T2 - Proceedings of the 9th Annual Symposium on Computational Geometry

Y2 - 19 May 1993 through 21 May 1993

ER -