A shape preserving corner cutting algorithm with an enhanced accuracy

Hyoseon Yang, Jinyoung Kim, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The class of order-3 exponential B-spline subdivision schemes is a natural extension of Chaikin's corner cutting algorithm. However, order-3 exponential B-spline subdivision schemes can provide at most the approximation order ‘two’ (when a suitable normalization parameter is applied) and generally do not guarantee the monotonicity or convexity preserving properties. To overcome these limitations, this study aims to present an improved shape preserving non-uniform corner cutting (SPNC) subdivision algorithm by generalizing the subdivision of an order-3 exponential B-spline reproducing two exponential polynomials. Each refinement rule of the SPNC scheme has an internal shape parameter. We propose a method for selecting a locally-optimized parameter and then formulate it on the construction of refinement rules. Accordingly, the proposed SPNC scheme achieves an improved approximation order three, while retaining the convexity as well as monotonicity preservation properties under some mild conditions. The proposed algorithm generates C1 limit functions like Chaikin's corner cutting method. To validate the effectiveness of the SPNC algorithm, several numerical examples are presented.

Original languageEnglish
Article number108487
JournalApplied Mathematics Letters
Volume137
DOIs
StatePublished - Mar 2023

Bibliographical note

Funding Information:
This research was supported by the grants NRF- 2022R1F1A1066389 (H. Yang) and NRF- 2020R1A2C1A01005894 (J. Yoon) of the National Research Foundation of Korea .

Publisher Copyright:
© 2022 Elsevier Ltd

Keywords

  • Corner cutting
  • Monotonicity and convexity preservation
  • Order of accuracy
  • Smoothness
  • Subdivision

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