Polyhedral Assembly Partitioning with Infinite Translations or The Importance of Being Exact

  • Efi Fogel
  • Dan Halperin
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 57)


Assembly partitioning with an infinite translation is the application of an infinite translation to partition an assembled product into two complementing subsets of parts, referred to as a subassemblies, each treated as a rigid body. We present an exact implementation of an efficient algorithm to obtain such a motion and subassemblies given an assembly of polyhedra in ℝ3. We do not assume general position. Namely, we handle degenerate input, and produce exact results. As often occurs, motions that partition a given assembly or subassembly might be isolated in the infinite space of motions. Any perturbation of the input or of intermediate results, caused by, for example, imprecision, might result with dismissal of valid partitioning-motions. In the extreme case, where there is only a finite number of valid partitioning-motions, no motion may be found, even though such exists. The implementation is based on software components that have been developed and introduced only recently. They paved the way to a complete, efficient, and concise implementation. Additional information is available at



Central Projection Primal Vertex Polyhedral Surface Motion Space Strong Connectivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Efi Fogel
    • 1
  • Dan Halperin
    • 1
  1. 1.Tel-Aviv UniversityTel AvivIsrael

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