Properties of G1 continuity conditions between two B-spline surfaces

Nailiang Zhao; Weiyin Ma

doi:10.1007/11784203_73

Properties of G1 continuity conditions between two B-spline surfaces

Nailiang Zhao
, Weiyin Ma

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

2 Citations (Scopus)

Abstract

This paper addresses some properties of G¹ continuity conditions between two B-spline surfaces with arbitrary degrees and generally structured knots. Key issues addressed in the paper include necessary G¹ continuity conditions between two B-spline surfaces, general connecting functions, continuities of the general connecting functions, and intrinsic conditions of the general connecting functions along the common boundary. In general, one may use piecewise polynomial functions, i.e. B-spline functions, as connecting functions for G¹ connection of two B-spline surfaces. Based on the work reported in this paper, some recent results in literature using linear connecting functions are special cases of the general connecting functions reported in this paper. In case that the connecting functions are global linear functions along the common boundary commonly used in literature, the common boundary degenerates as a Bézier curve for proper G¹ connection. Several examples for connecting two uniform biquadratic B-spline surfaces with G¹ continuity are also presented to demonstrate the results. © Springer-Verlag Berlin Heidelberg 2006.

Original language	English
Title of host publication	Advances in Computer Graphics
Subtitle of host publication	24th Computer Graphics International Conference, CGI 2006, Hangzhou, China, June 26-28, 2006, Proceedings
Editors	Tomoyuki Nishita, Qunsheng Peng, Hans-Peter Seidel
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	743-752
ISBN (Electronic)	978-3-540-35639-4
ISBN (Print)	9783540356387
DOIs	https://doi.org/10.1007/11784203_73
Publication status	Published - 2006
Event	24th International Conference on Computer Graphics (CGI 2006) - Hangzhou, China Duration: 26 Jun 2006 → 28 Jun 2006

Publication series

Name	Lecture Notes in Computer Science
Volume	4035
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	24th International Conference on Computer Graphics (CGI 2006)
Place	China
City	Hangzhou
Period	26/06/06 → 28/06/06

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Zhao, N., & Ma, W. (2006). Properties of G1 continuity conditions between two B-spline surfaces. In T. Nishita, Q. Peng, & H.-P. Seidel (Eds.), Advances in Computer Graphics: 24th Computer Graphics International Conference, CGI 2006, Hangzhou, China, June 26-28, 2006, Proceedings (pp. 743-752). (Lecture Notes in Computer Science; Vol. 4035). Springer . https://doi.org/10.1007/11784203_73

Zhao, Nailiang ; Ma, Weiyin. / Properties of G1 continuity conditions between two B-spline surfaces. Advances in Computer Graphics: 24th Computer Graphics International Conference, CGI 2006, Hangzhou, China, June 26-28, 2006, Proceedings. editor / Tomoyuki Nishita ; Qunsheng Peng ; Hans-Peter Seidel. Berlin, Heidelberg : Springer , 2006. pp. 743-752 (Lecture Notes in Computer Science).

@inproceedings{6286fdcc50e846a18c32e3b4d7b87eec,

title = "Properties of G1 continuity conditions between two B-spline surfaces",

abstract = "This paper addresses some properties of G1 continuity conditions between two B-spline surfaces with arbitrary degrees and generally structured knots. Key issues addressed in the paper include necessary G1 continuity conditions between two B-spline surfaces, general connecting functions, continuities of the general connecting functions, and intrinsic conditions of the general connecting functions along the common boundary. In general, one may use piecewise polynomial functions, i.e. B-spline functions, as connecting functions for G1 connection of two B-spline surfaces. Based on the work reported in this paper, some recent results in literature using linear connecting functions are special cases of the general connecting functions reported in this paper. In case that the connecting functions are global linear functions along the common boundary commonly used in literature, the common boundary degenerates as a B{\'e}zier curve for proper G1 connection. Several examples for connecting two uniform biquadratic B-spline surfaces with G1 continuity are also presented to demonstrate the results. {\textcopyright} Springer-Verlag Berlin Heidelberg 2006.",

author = "Nailiang Zhao and Weiyin Ma",

year = "2006",

doi = "10.1007/11784203\_73",

language = "English",

isbn = "9783540356387",

series = "Lecture Notes in Computer Science",

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pages = "743--752",

editor = "Nishita, \{Tomoyuki \} and Peng, \{Qunsheng \} and Seidel, \{Hans-Peter \}",

booktitle = "Advances in Computer Graphics",

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Zhao, N & Ma, W 2006, Properties of G1 continuity conditions between two B-spline surfaces. in T Nishita, Q Peng & H-P Seidel (eds), Advances in Computer Graphics: 24th Computer Graphics International Conference, CGI 2006, Hangzhou, China, June 26-28, 2006, Proceedings. Lecture Notes in Computer Science, vol. 4035, Springer , Berlin, Heidelberg, pp. 743-752, 24th International Conference on Computer Graphics (CGI 2006), Hangzhou, China, 26/06/06. https://doi.org/10.1007/11784203_73

Properties of G1 continuity conditions between two B-spline surfaces. / Zhao, Nailiang; Ma, Weiyin.
Advances in Computer Graphics: 24th Computer Graphics International Conference, CGI 2006, Hangzhou, China, June 26-28, 2006, Proceedings. ed. / Tomoyuki Nishita; Qunsheng Peng; Hans-Peter Seidel. Berlin, Heidelberg: Springer , 2006. p. 743-752 (Lecture Notes in Computer Science; Vol. 4035).

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

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AU - Ma, Weiyin

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N2 - This paper addresses some properties of G1 continuity conditions between two B-spline surfaces with arbitrary degrees and generally structured knots. Key issues addressed in the paper include necessary G1 continuity conditions between two B-spline surfaces, general connecting functions, continuities of the general connecting functions, and intrinsic conditions of the general connecting functions along the common boundary. In general, one may use piecewise polynomial functions, i.e. B-spline functions, as connecting functions for G1 connection of two B-spline surfaces. Based on the work reported in this paper, some recent results in literature using linear connecting functions are special cases of the general connecting functions reported in this paper. In case that the connecting functions are global linear functions along the common boundary commonly used in literature, the common boundary degenerates as a Bézier curve for proper G1 connection. Several examples for connecting two uniform biquadratic B-spline surfaces with G1 continuity are also presented to demonstrate the results. © Springer-Verlag Berlin Heidelberg 2006.

AB - This paper addresses some properties of G1 continuity conditions between two B-spline surfaces with arbitrary degrees and generally structured knots. Key issues addressed in the paper include necessary G1 continuity conditions between two B-spline surfaces, general connecting functions, continuities of the general connecting functions, and intrinsic conditions of the general connecting functions along the common boundary. In general, one may use piecewise polynomial functions, i.e. B-spline functions, as connecting functions for G1 connection of two B-spline surfaces. Based on the work reported in this paper, some recent results in literature using linear connecting functions are special cases of the general connecting functions reported in this paper. In case that the connecting functions are global linear functions along the common boundary commonly used in literature, the common boundary degenerates as a Bézier curve for proper G1 connection. Several examples for connecting two uniform biquadratic B-spline surfaces with G1 continuity are also presented to demonstrate the results. © Springer-Verlag Berlin Heidelberg 2006.

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

SN - 9783540356387

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Zhao N, Ma W. Properties of G1 continuity conditions between two B-spline surfaces. In Nishita T, Peng Q, Seidel HP, editors, Advances in Computer Graphics: 24th Computer Graphics International Conference, CGI 2006, Hangzhou, China, June 26-28, 2006, Proceedings. Berlin, Heidelberg: Springer . 2006. p. 743-752. (Lecture Notes in Computer Science). Epub 2006 Sept 29. doi: 10.1007/11784203_73

Properties of G1 continuity conditions between two B-spline surfaces

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