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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Efficient Algorithms for Factorization and Join of Blades
verfasst von : Daniel Fontijne, Leo Dorst
Erschienen in: Geometric Algebra Computing
Verlag: Springer London
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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.