Volume 38, Issue 5
Corner-Cutting Subdivision Surfaces of General Degrees with Parameters

Yufeng Tian & Maodong Pan

J. Comp. Math., 38 (2020), pp. 732-747.

Published online: 2020-04

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  • Abstract

As a corner-cutting subdivision scheme, Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves: vertex splitting plus repeated midpoint averaging. In this paper, we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting, and generalize the strategy to arbitrary topological surfaces of general degree. By adjusting the free parameter, the proposed method can generate subdivision surfaces with flexible shapes. Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.

  • Keywords

Lane-Riesenfeld algorithm, Spline curves, Subdivision curves/surfaces, Corner-cutting subdivision surfaces.

  • AMS Subject Headings

65D17, 68U07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

tyf2015@mail.ustc.edu.cn (Yufeng Tian)

mdpan@mail.ustc.edu.cn (Maodong Pan)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-732, author = {Tian , Yufeng and Pan , Maodong }, title = {Corner-Cutting Subdivision Surfaces of General Degrees with Parameters}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {5}, pages = {732--747}, abstract = {

As a corner-cutting subdivision scheme, Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves: vertex splitting plus repeated midpoint averaging. In this paper, we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting, and generalize the strategy to arbitrary topological surfaces of general degree. By adjusting the free parameter, the proposed method can generate subdivision surfaces with flexible shapes. Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1905-m2018-0274}, url = {http://global-sci.org/intro/article_detail/jcm/16667.html} }
TY - JOUR T1 - Corner-Cutting Subdivision Surfaces of General Degrees with Parameters AU - Tian , Yufeng AU - Pan , Maodong JO - Journal of Computational Mathematics VL - 5 SP - 732 EP - 747 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1905-m2018-0274 UR - https://global-sci.org/intro/article_detail/jcm/16667.html KW - Lane-Riesenfeld algorithm, Spline curves, Subdivision curves/surfaces, Corner-cutting subdivision surfaces. AB -

As a corner-cutting subdivision scheme, Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves: vertex splitting plus repeated midpoint averaging. In this paper, we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting, and generalize the strategy to arbitrary topological surfaces of general degree. By adjusting the free parameter, the proposed method can generate subdivision surfaces with flexible shapes. Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.

Yufeng Tian & Maodong Pan. (2020). Corner-Cutting Subdivision Surfaces of General Degrees with Parameters. Journal of Computational Mathematics. 38 (5). 732-747. doi:10.4208/jcm.1905-m2018-0274
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