DocumentCode
526530
Title
Notice of Retraction
The continuity of Cubic extension Bézier curves and surfaces
Author
Xinqiang Qin ; Fei Liu ; Gang Hu ; Wei Guo ; Faning Dang
Author_Institution
Sch. of Sci., Xi´an Univ. of Technol., Xi´an, China
Volume
3
fYear
2010
fDate
9-11 July 2010
Firstpage
489
Lastpage
493
Abstract
Notice of Retraction
After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.
We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.
The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.
Cubic extension Bézier curves (CE-Bézier curves) are constructed by a natural extension of the traditional cubic Bézier curves. While retaining noticeable properties of cubic Bézier curves, CE-Bézier curves have the advantages such as adjustable shape parameters and better approximation property. In this paper, terminal behaviors of CE-Bézier curves, which are closely related to shape parameters, are carefully examinated and geometric interpretations of shape parameters are explicitly presented. Subsequently, the necessary and sufficient condition ensuring G1 and G2 continuity requirements is respectively established for the first category CE-Bézier curves. Parallel to CE-Bézier curves, Geometric condition ensuring G1 continuity requirement between CE-Bézier surfaces are rigorously investigated, and relevant examples of geometric modeling are provided. Theoretical results and concrete examples have validated that, with appropriately selected control parameters, mosaic technique of CE-Bézier curves and surfaces can be widely applied to the representation and modeling of engineering curves and surfaces.
After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.
We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.
The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.
Cubic extension Bézier curves (CE-Bézier curves) are constructed by a natural extension of the traditional cubic Bézier curves. While retaining noticeable properties of cubic Bézier curves, CE-Bézier curves have the advantages such as adjustable shape parameters and better approximation property. In this paper, terminal behaviors of CE-Bézier curves, which are closely related to shape parameters, are carefully examinated and geometric interpretations of shape parameters are explicitly presented. Subsequently, the necessary and sufficient condition ensuring G1 and G2 continuity requirements is respectively established for the first category CE-Bézier curves. Parallel to CE-Bézier curves, Geometric condition ensuring G1 continuity requirement between CE-Bézier surfaces are rigorously investigated, and relevant examples of geometric modeling are provided. Theoretical results and concrete examples have validated that, with appropriately selected control parameters, mosaic technique of CE-Bézier curves and surfaces can be widely applied to the representation and modeling of engineering curves and surfaces.
Keywords
curve fitting; engineering graphics; shape control; solid modelling; continuity condition; cubic extension Bezier curves; engineering curves modeling; geometric interpretations; geometric modeling; shape parameters; CE-Bézier curve; CE-Bézier surface; Continuity condition; Shape parameter;
fLanguage
English
Publisher
ieee
Conference_Titel
Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on
Conference_Location
Chengdu
Print_ISBN
978-1-4244-5537-9
Type
conf
DOI
10.1109/ICCSIT.2010.5564499
Filename
5564499
Link To Document