Oriented Projective Geometry with Clifford Algebra

Richard C. Pappas ()
Additional contact information
Richard C. Pappas: Widener University, Department of Mathematics

A chapter in Clifford Algebras with Numeric and Symbolic Computations, 1996, pp 233-250 from Springer

Abstract: Abstract Classical projective geometry can be efficiently formulated using the Clifford-algebra based “geometric algebra” developed by Hestenes and Sobczyk. In this formulation, points, lines, planes, etc. in a projective space P n−1 are represented by equivalence classes of vectors, bivectors, trivectors, etc. in the Clifford algebra Cℓn. Two k-blades A and B are in the same equivalence class iff AB = A · B ; that is, iff A and B differ by a scalar factor. We show that if the notion of equivalence is restricted, so that two blades of the same grade are equivalent iff they differ by a positive scalar factor, then the geometric objects represented inherit an orientation and provide the building blocks for oriented projective spaces. Projective concepts such as meet, join, duality, and collineation can be extended to such spaces, while new features, such as relative orientation, give these spaces a much richer structure with many important applications. Examples of computations using CLICAL are provided.

Keywords: Projective geometry; orientation (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-8157-4_16

Ordering information: This item can be ordered from
http://www.springer.com/9781461581574

DOI: 10.1007/978-1-4615-8157-4_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().