Akima and Renner Subsplines

  • Gisela Engeln-Müllges
  • Frank Uhlig


As in the case of interpolating cubic splines, the interpolating Akima subsplines and Renner subsplines are composed of cubic polynomials on subintervals. The main difference, however, consists in the fact that these subsplines need only be once continuously differentiable in contrast to the cubic splines of chapter 10, which were constructed to be twice continuously differentiable everywhere. Deviating slightly from the original papers of Akima [AKIM70] and Renner [RENN81], [RENN82], we present useful modifications that follow the suggestions of R. Wodicka [WODI91]. One of them is to represent corners as corners, i.e., a continuous derivative is not required everywhere. If corners are not desired for the curve, they can be avoided by inserting additional nodes. An essential advantage of the Akima and Renner subsplines lies in the fact that no linear system of equations must be solved to form them.


Straight Line Segment Curve Segment Unit Tangent Vector Euclidean Vector Norm Monotonic Order 
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  1. [AKIM70]; [RENN81]; [RENN82]; [WODI91].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Gisela Engeln-Müllges
    • 1
  • Frank Uhlig
    • 2
  1. 1.Fachhochschule AachenAachenGermany
  2. 2.Department of MathematicsAuburn UniversityAuburnUSA

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