Efficient Algorithms for Factorization and Join of Blades

  • Daniel FontijneEmail author
  • Leo Dorst


Subspaces are powerful tools for modeling geometry. In geometric algebra, they are represented using blades and constructed using the outer product. Producing the actual geometrical intersection (meet) and union (join) of subspaces, rather than the simplified linearizations often used in Grassmann–Cayley algebra, requires efficient algorithms when blades are represented as a sum of basis blades. We present an efficient blade factorization algorithm and use it to produce implementations of the join that are approximately 10 times faster than earlier algorithms.


Geometric Algebra Code Size Outer Product Factorization Algorithm Geometric Product 
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Copyright information

© Springer-Verlag London 2010

Authors and Affiliations

  1. 1.University of AmsterdamAmsterdamThe Netherlands
  2. 2.Intelligent Systems LaboratoryUniversity of AmsterdamAmsterdamThe Netherlands

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