IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4615-8157-4_16.html
   My bibliography  Save this book chapter

Oriented Projective Geometry with Clifford Algebra

In: Clifford Algebras with Numeric and Symbolic Computations

Author

Listed:
  • Richard C. Pappas

    (Widener University, Department of Mathematics)

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.

Suggested Citation

  • Richard C. Pappas, 1996. "Oriented Projective Geometry with Clifford Algebra," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 233-250, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_16
    DOI: 10.1007/978-1-4615-8157-4_16
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4615-8157-4_16. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.