Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation

Zhihao Wang; Yajuan Li; Weiyin Ma; Chongyang Deng

doi:10.2312/pg.20181284

Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation

Zhihao Wang, Yajuan Li, Weiyin Ma, Chongyang Deng^*

^*Corresponding author for this work

Department of Mechanical Engineering

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

2 Citations (Scopus)

Abstract

We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. Numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm.

Original language	English
Title of host publication	Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings
Publisher	IEEE Computer Society
Pages	73-76
Volume	2018-October
ISBN (Print)	9783038680734
DOIs	https://doi.org/10.2312/pg.20181284
Publication status	Published - 2018
Event	26th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2018) - City University of Hong Kong, Hong Kong, China Duration: 8 Oct 2018 → 11 Oct 2018 http://sweb.cityu.edu.hk/pg2018/ https://dl.acm.org/doi/proceedings/10.5555/3308497

Publication series

Name	Proceedings - Pacific Conference on Computer Graphics and Applications
Volume	2018-October
ISSN (Print)	1550-4085

Conference

Conference	26th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2018)
Abbreviated title	PG 2018
Place	China
City	Hong Kong
Period	8/10/18 → 11/10/18
Internet address	http://sweb.cityu.edu.hk/pg2018/ https://dl.acm.org/doi/proceedings/10.5555/3308497

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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Wang, Z., Li, Y., Ma, W., & Deng, C. (2018). Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation. In Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings (Vol. 2018-October, pp. 73-76). (Proceedings - Pacific Conference on Computer Graphics and Applications; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.2312/pg.20181284

Wang, Zhihao ; Li, Yajuan ; Ma, Weiyin et al. / Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation. Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings. Vol. 2018-October IEEE Computer Society, 2018. pp. 73-76 (Proceedings - Pacific Conference on Computer Graphics and Applications).

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title = "Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation",

abstract = "We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. Numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm.",

author = "Zhihao Wang and Yajuan Li and Weiyin Ma and Chongyang Deng",

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language = "English",

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booktitle = "Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings",

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Wang, Z, Li, Y, Ma, W & Deng, C 2018, Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation. in Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings. vol. 2018-October, Proceedings - Pacific Conference on Computer Graphics and Applications, vol. 2018-October, IEEE Computer Society, pp. 73-76, 26th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2018), Hong Kong, China, 8/10/18. https://doi.org/10.2312/pg.20181284

Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation. / Wang, Zhihao; Li, Yajuan; Ma, Weiyin et al.
Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings. Vol. 2018-October IEEE Computer Society, 2018. p. 73-76 (Proceedings - Pacific Conference on Computer Graphics and Applications; Vol. 2018-October).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

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AU - Wang, Zhihao

AU - Li, Yajuan

AU - Ma, Weiyin

AU - Deng, Chongyang

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2018

Y1 - 2018

N2 - We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. Numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm.

AB - We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. Numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm.

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DO - 10.2312/pg.20181284

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9783038680734

VL - 2018-October

T3 - Proceedings - Pacific Conference on Computer Graphics and Applications

SP - 73

EP - 76

BT - Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings

PB - IEEE Computer Society

T2 - 26th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2018)

Y2 - 8 October 2018 through 11 October 2018

ER -

Wang Z, Li Y, Ma W, Deng C. Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation. In Pacific Graphics 2018 - 26th Pacific Conference on Computer Graphics and Applications, Short Papers and Posters Proceedings. Vol. 2018-October. IEEE Computer Society. 2018. p. 73-76. (Proceedings - Pacific Conference on Computer Graphics and Applications). doi: 10.2312/pg.20181284

Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation

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