Generating uniform incremental grids on SO(3) using the hopf fibration

Anna Yershova, Swati Jain, Steven M. Lavalle, Julie C. Mitchell

Research output: Contribution to journalArticlepeer-review


The problem of generating uniform deterministic samples over the rotation group, SO(3), is fundamental to computational biology, chemistry, physics, and numerous branches of computer science. We present the best-known method to date for constructing incremental, deterministic grids on SO(3); it provides: (1) the lowest metric distortion for grid neighbor edges, (2) optimal dispersion-reduction with each additional sample, (3) explicit neighborhood structure, and (4) equivolumetric partition of SO(3) by the grid cells. We also demonstrate the use of the sequence on motion planning problems.

Original languageEnglish (US)
Pages (from-to)801-812
Number of pages12
JournalInternational Journal of Robotics Research
Issue number7
StatePublished - Jun 2010


  • Grids
  • Haar measure
  • Motion planning
  • Orthogonal group
  • Uniform sampling

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Mechanical Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering
  • Applied Mathematics

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