Computational complexity of motion and stability of polygons
Computational complexity of motion and stability of polygons
The complexity of robot motion planning
The complexity of robot motion planning
Analytical methods for dynamic simulation of non-penetrating rigid bodies
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
An O(nlogn) algorithm for 1-D tile compaction
WG '89 Proceedings of the fifteenth international workshop on Graph-theoretic concepts in computer science
Implicitly searching convolutions and computing depth of collision
SIGAL '90 Proceedings of the international symposium on Algorithms
A hierarchy preserving hierarchical compactor
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Two-dimensional compaction by “zone refining”
DAC '86 Proceedings of the 23rd ACM/IEEE Design Automation Conference
A modeling system based on dynamic constraints
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Constraints methods for flexible models
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Collision Detection and Response for Computer Animation
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Minkowski operations for satellite antenna layout
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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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.