Matrix representation for multi-degree reduction of Bézier curves

2005 ◽  
Vol 22 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Hasik Sunwoo
Keyword(s):  
Matrix Representation ◽  
Degree Reduction ◽  
Bezier Curves ◽  
Bézier Curves

scholarly journals Approximate Multidegree Reduction ofλ-Bézier Curves

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Gang Hu ◽  
Huanxin Cao ◽  
Suxia Zhang
Keyword(s):  
Shape Control ◽  
Control Parameter ◽  
Linear Equations ◽  
Least Square ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Degree Reduction ◽  
Bezier Curves ◽  
Bézier Curves

Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction ofλ-Bézier curves in theL2-norm. By analysing the properties ofλ-Bézier curves of degreen, a method which can deal with approximatingλ-Bézier curve of degreen+1byλ-Bézier curve of degreem  (m≤n)is presented. Then, in unrestricted andC0,C1constraint conditions, the new control points of approximatingλ-Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement.

Multi-degree reduction of Bézier curves using reparameterization

2011 ◽  
Vol 43 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Xiao-Diao Chen ◽  
Weiyin Ma ◽  
Jean-Claude Paul
Keyword(s):  
Degree Reduction ◽  
Bezier Curves ◽  
Bézier Curves

scholarly journals Degree reduction of composite Bézier curves

2017 ◽  
Vol 293 ◽  
pp. 40-48
Author(s):  
Przemysław Gospodarczyk ◽  
Stanisław Lewanowicz ◽  
Paweł Woźny
Keyword(s):  
Degree Reduction ◽  
Bezier Curves ◽  
Bézier Curves
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