IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v79y2009i12p3556-3566.html
   My bibliography  Save this article

The Frenet frame beyond classical differential geometry: Application to cartographic generalization of roads

Author

Listed:
  • Reinoso, J.F.
  • Moncayo, M.
  • Pasadas, M.
  • Ariza, F.J.
  • García, J.L.

Abstract

The reconstruction of curves from their curvature is a problem not very well-solved in cartographic generalization of roads. Frenet’s formulas theoretically solve this problem. The result shows that there exists a curve (up to rigid motion) with prefixed curvature function and torsion. By the use of the curvature and torsion functions, in closed forms, it is possible to obtain many beautiful examples in connection with this classical construction. In the case of plane curves, the torsion is equal to zero and the curve is characterized by the curvature. Nevertheless, if our starting point is a discrete set of arc length curvature experimental measures, the application of the Frenet frame is not straightforward. This study aims to describe how to adapt the classical Frenet frame to more realistic contexts derived from practical requirements. Our approach is applied to numerical measures derived from roads defined by Spanish Cartography, more precisely, by the Mapa Topográfico Nacional 1:25.000 (MTN25). The method described will be used to obtain generalizations of the original road by performing a standard wavelet decomposition on the curvature before the application of the Frenet frame for plane curves.

Suggested Citation

  • Reinoso, J.F. & Moncayo, M. & Pasadas, M. & Ariza, F.J. & García, J.L., 2009. "The Frenet frame beyond classical differential geometry: Application to cartographic generalization of roads," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3556-3566.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:12:p:3556-3566
    DOI: 10.1016/j.matcom.2009.04.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475409001104
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2009.04.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:matcom:v:79:y:2009:i:12:p:3556-3566. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.