The degree reduction of tensor product rational Bézier surfaces

2008 ◽  
Author(s):  
Mao Shi ◽  
Zhenglin Ye ◽  
Baosheng Kang
Keyword(s):  
Tensor Product ◽  
Degree Reduction ◽  
Bézier Surfaces ◽  
Bezier Surfaces

L-2 DEGREE REDUCTION OF TRIANGULAR BÉZIER SURFACES WITH COMMON TANGENT PLANES AT VERTICES

2005 ◽  
Vol 15 (05) ◽  
pp. 477-490 ◽  
Author(s):  
ABEDALLAH RABABAH
Keyword(s):  
Closed Form ◽  
Error Term ◽  
Least Squares Method ◽  
Computational Cost ◽  
Degree Reduction ◽  
Common Tangent ◽  
Matrix Representations ◽  
Bézier Surfaces ◽  
The Matrix ◽  
Bezier Surfaces

In this paper, we present a method of degree reduction for triangular Bézier surfaces. The approximate and the original triangular Bézier surfaces have common tangent planes at the vertices. We use the least squares method with the L 2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the Bézier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.

Optimal multi-degree reduction of C-Bézier surfaces with constraints

2017 ◽  
Vol 18 (12) ◽  
pp. 2009-2016 ◽  
Author(s):  
Lian Zhou ◽  
Xin-hui Lin ◽  
Hong-yan Zhao ◽  
Jun Chen
Keyword(s):  
Degree Reduction ◽  
Bézier Surfaces ◽  
Bezier Surfaces
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