Notice of Retraction: The continuity of Cubic extension Bézier curves and surfaces

2010 ◽  
Author(s):  
Xinqiang Qin ◽  
Fei Liu ◽  
Gang Hu ◽  
Wei Guo ◽  
Faning Dang
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces ◽  
Cubic Extension

Curvature of singular Bézier curves and surfaces

2011 ◽  
Vol 28 (4) ◽  
pp. 233-244 ◽  
Author(s):  
Thomas W. Sederberg ◽  
Hongwei Lin ◽  
Xin Li
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces

Biquadratic TC-Bézier Curves with Shape Parameter

2011 ◽  
Vol 467-469 ◽  
pp. 57-62
Author(s):  
Xu Min Liu ◽  
Xian Peng Yang ◽  
Yan Ling Wu
Keyword(s):  
Shape Parameter ◽  
Free Form ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces ◽  
G1 Continuity ◽  
Shape Controlling

Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

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