A family of non-uniform subdivision schemes with variable parameters for curve design

Mei e. Fang, Byeongseon Jeong, Jungho Yoon

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12 Scopus citations


In this paper, we present non-uniform subdivision schemes with variable parameter sequences. A locally different tension parameter is set at each edge of the initial control polygon to control locally the shape of the resulting curve such that the scheme becomes non-uniform. Due to the variable parameters, the scheme can reproduce locally different analytic curves such as conics, Lissajous, trigonometric and catenary curves. Hence blending curves including such analytic components can be successfully generated. We discuss the convergence and smoothness of the proposed non-uniform schemes and present some numerical results to demonstrate their advantages in geometric modeling. Furthermore, as an application, we propose a chamfering algorithm which can be used in designing automobile and mechanical products.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalApplied Mathematics and Computation
StatePublished - 15 Nov 2017

Bibliographical note

Funding Information:
Jungho Yoon was supported by the grant NRF-2015-R1A5A1009350 and NRF-2015-R1D1A1A09057553 through the National Research Foundation of Korea. M. Fang was supported by National Science Foundation of China (Grant no. 61272032, 60904070). B. Jeong was supported by the grant NRF- 2017R1C1B2008566 funded by the Korea government (MSIP).

Publisher Copyright:
© 2017 Elsevier Inc.


  • Blending curves
  • Chamfering algorithm
  • Non-uniform subdivision
  • Smoothness
  • Variable parameter sequence


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