Curve interpolation based on Catmull-Clark subdivision scheme

2003 ◽  
Vol 13 (2) ◽  
pp. 142
Author(s):  
Jingqiao ZHANG
Keyword(s):  
Subdivision Scheme ◽  
Curve Interpolation

An Improved Four Point Interpolatory Subdivision Scheme

2013 ◽  
Vol 380-384 ◽  
pp. 1555-1557
Author(s):  
Xin Fen Zhang ◽  
Yu Zhen Liu
Keyword(s):  
Chord Length ◽  
Subdivision Scheme ◽  
Shape Preserving ◽  
Curve Interpolation ◽  
Interpolatory Polynomial ◽  
Interpolatory Subdivision

In this paper we propose a new kind of geometry driven subdivision scheme for curve interpolation. We use cubic Lagrange interpolatory polynomial to construct a new point, selecting parameters by accumulated chord length method. The new scheme is shape preserving. It can overcome the shortcoming of the initial four point subdivision scheme proposed.

A Generalized Four Point Interpolatory Subdivision Scheme for Curve Design

2012 ◽  
Vol 586 ◽  
pp. 378-383
Author(s):  
Xin Fen Zhang
Keyword(s):  
Subdivision Scheme ◽  
Curve Design ◽  
Curve Interpolation ◽  
Interpolatory Subdivision

ßIn this paper we propose a new kind of nonlinear and geometry driven subdivision scheme for curve interpolation. We introduce serval parameters in the new scheme.When the parameter ß is taken as 0, the new scheme presented in this paper regresses to the initial four point subdivision scheme, and when ß→∞ , the new scheme is convexity preserving. With proper choices of the subdßivision parameters,it can overcome the shortcoming of the initial four point subdivision scheme proposed.

Incenter subdivision scheme for curve interpolation

2010 ◽  
Vol 27 (1) ◽  
pp. 48-59 ◽  
Author(s):  
Chongyang Deng ◽  
Guozhao Wang
Keyword(s):  
Subdivision Scheme ◽  
Curve Interpolation

scholarly journals A non-stationary subdivision scheme for curve interpolation

2008 ◽  
Vol 44 ◽  
pp. 216 ◽  
Author(s):  
M. K. Jena ◽  
P. Shunmugaraj ◽  
P. C. Das
Keyword(s):  
Subdivision Scheme ◽  
Curve Interpolation ◽  
Stationary Subdivision

A biarc based subdivision scheme for space curve interpolation

2014 ◽  
Vol 31 (9) ◽  
pp. 656-673 ◽  
Author(s):  
Chongyang Deng ◽  
Weiyin Ma
Keyword(s):  
Space Curve ◽  
Subdivision Scheme ◽  
Curve Interpolation

scholarly journals Improved binary four point subdivision scheme and new corner cutting scheme

2010 ◽  
Vol 59 (8) ◽  
pp. 2647-2657 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Kashif Rehan
Keyword(s):  
Subdivision Scheme ◽  
Corner Cutting

scholarly journals A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc–Deslauriers subdivision scheme

2014 ◽  
Vol 17 (1) ◽  
pp. 226-232
Author(s):  
H. E. Bez ◽  
N. Bez
Keyword(s):  
Recent Result ◽  
Operator Norm ◽  
Subdivision Scheme ◽  
Sharp Bounds

AbstractWe analyse the mask associated with the $2n$-point interpolatory Dubuc–Deslauriers subdivision scheme $S_{a^{[n]}}$. Sharp bounds are presented for the magnitude of the coefficients $a^{[n]}_{2i-1}$ of the mask. For scales $i \in [1,\sqrt{n}]$ it is shown that $|a^{[n]}_{2i-1}|$ is comparable to $i^{-1}$, and for larger power scales, exponentially decaying bounds are obtained. Using our bounds, we may precisely analyse the summability of the mask as a function of $n$ by identifying which coefficients of the mask contribute to the essential behaviour in $n$, recovering and refining the recent result of Deng–Hormann–Zhang that the operator norm of $S_{a^{[n]}}$ on $\ell ^\infty $ grows logarithmically in $n$.

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