280
Views
12
CrossRef citations to date
0
Altmetric
SECTION B

Shape preserving C2 rational quartic interpolation spline with two parameters

&
Pages 2160-2177 | Received 27 Jul 2013, Accepted 26 Aug 2014, Published online: 31 Oct 2014
 

Abstract

Constructing shape-preserving interpolation spline has been a hot topic in industrial design and scientific data visualization during the past 30 years. In the existing shape preserving C2 interpolation spline methods, however, some methods can be only used to preserve the monotonic data set, while others can be only used to preserve the convex data set, and often for C2 continuity, it is requested to solve a linear system of consistency equations for the derivative values at the knots. In this paper, a new explicit representation of a C2 rational quartic interpolation spline with two local tension parameters is developed. A convergence analysis establishes an error bound and shows that the order of approximation is O(h2) accuracy. Sufficient conditions for the proposed interpolation spline to preserve the shape of positive, monotonic, and convex set of data are derived.

2000 AMS Subject Classifications::

Acknowledgments

We thank the anonymous reviewers for their valuable remarks for improvements. The research is supported by the National Natural Science Foundation of China (No. 10871208, No. 11271376) and Graduate Students Scientific Research Innovation Project of Hunan Province (No. CX2012B111).

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,129.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.