Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


$C^2$ Hermite interpolation by Pythagorean Hodograph space curves
HTML articles powered by AMS MathViewer

by Zbyněk Šír and Bert Jüttler PDF
Math. Comp. 76 (2007), 1373-1391 Request permission


We solve the problem of $C^2$ Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of $C^2$ space boundary data (two points with associated first and second derivatives) we construct a four–dimensional family of PH interpolants of degree $9$ and introduce a geometrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. First, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Second, it has the best possible approximation order 6. Third, it is symmetric in the sense that the interpolant of the “reversed” set of boundary data is simply the “reversed” original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree $9$ which is globally $C^2$, and for simple rational approximation of pipe surfaces with a piecewise analytical spine curve. The algorithms are presented along with an analysis of their error and approximation order.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 68U07, 53A04, 65D17
  • Retrieve articles in all journals with MSC (2000): 68U07, 53A04, 65D17
Additional Information
  • Zbyněk Šír
  • Affiliation: Johannes Kepler University, Institute of Applied Geometry, Altenberger Str. 69, 4040 Linz, Austria
  • Address at time of publication: Charles University, Sokolovská 83, 18675 Prague, Czech Republic
  • Email:
  • Bert Jüttler
  • Affiliation: Johannes Kepler University, Institute of Applied Geometry, Altenberger Str. 69, 4040 Linz, Austria
  • Email:
  • Received by editor(s): May 24, 2005
  • Received by editor(s) in revised form: October 27, 2005
  • Published electronically: February 1, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1373-1391
  • MSC (2000): Primary 68U07; Secondary 53A04, 65D17
  • DOI:
  • MathSciNet review: 2299779